intermediate macro

Intermediate Macroeconomics - 73240

Laurence Ales

This version: April 30, 2014

73-240 – Spring 2014

This version: April 30, 2014 2 Prof. Laurence Ales

Contents

I Syllabus 6

II Class Notes 13

1 Introduction and Methodology 14

2 Measurament 242.1 GDP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.2 Forecasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392.3 Trend and Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482.4 Nominal and Real GDP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

3 The Household 62

4 The Firm 77

5 The Government 88

6 Equilibrium 93

7 Optimality 1047.1 Optimal Taxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

8 Growth 1198.1 Malthus and Solow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1298.2 Endogenous Growth Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

9 Dynamic Model 1529.1 Forecasting: Part 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1529.2 The Household . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1609.3 The Government . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

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9.4 Elastic Labor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1779.5 The Firm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1809.6 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

10 Credit Imperfections 203

11 Money 21611.1 Monetary model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22111.2 The Fed and Monetary Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . 22611.3 What Economists Do . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236

12 The End: 7 lessons from this course 241

III Problem Sets 244


Acknowledgements

This document has evolved over the years with contributions from:Laurence Ales, Nicolas Petrosky-Nadeau, Chris Sleet, Sevin Yeltekin.

Invaluable feedback was also provided by students of 73-240 at Carnegie Mellon’s Tep-per School of Business. And by the numerous teaching assistants of those classes.

These materials are subject to copyright and are being provided for the personal educa-tional use by students enrolled in this course. Any other use, including further repro-duction and distribution of the materials (whether in hard copy or electronic form) isstrictly prohibited. As an example, you may not copy any of these materials and uploadthem to any other web sites without the prior permission of the applicable copyrightholder.

Some graphs and diagrams are taken from:

1. Williamson, Macroeconomics, 5th edition.

2. Hoover, Applied Intermediate Macroeconomics

3. Abel, Bernanke, Croushore, Macroeconomics.

4. Jones, Macroeconomics, 2nd edition.

5. Acemoglu, Introduction to modern economic growth.

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Part I

Syllabus

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73-240 – Spring 2014

73-240 – Intermediate Macroeconomics

Prof. Laurence Ales

Instructor : Laurence Alese-mail: [email protected] Web: BlackboardOffice: GSIA 328Office Hours: Th 3:30-5:30

TA 1 : Antonio Andres Bellofattoe-mail: [email protected] A: F 1:30-2:20 POS MN AUDOffice Hours: GSIA 301 T 1:30-3:30

TA 2 : Minyoung Rhoe-mail: [email protected] B: F 1:30-2:20 WEH 5421Office Hours: GSIA 310 Th 1:30-3:30

Class times: MW 01:30PM 02:50PM in POS MN AUD

Textbook:

Stephen D. Williamson: Macroeconomics, 5/E

ISBN-10: 0132991330

ISBN-13: 978-0132991339

Publisher: Addison-Wesley

Copyright: 2013

Learning objectives:

By the end of this course the student will be able to...

1. ...Understand and be able to use the various measures of an aggregate economy’sperformance and well-being;

2. ...Be able to perform simple forecast of macroeconomic variables;

This version: January 11, 2014 1 Prof. Laurence Ales

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3. ...Understand how aggregate macroeconomic behavior is affected by microeconomicbehavior and equilibrium restrictions;

4. ...Be able to answer simple macroeconomic policy questions by formulating a model,finding the data and deriving an analytical and quantitative answer;

5. ...Understand the factors that cause economic growth and be able to describe thepatterns of economic development across countries and over time;

6. ...Understand how credit and labor frictions operate and how they might impact macroeconomic behavior.

Course Description:

The goal of this course is to provide a rigorous framework for understanding modern macroe-conomics. The study of the macroeconomy will be divided in two fronts: theory and data.The theory part will focus in constructing and analyzing the benchmark “workhorse” modernmacroeconomic model. This model will be casted both in a short run and long run version.The short run version will allow us to study policies that are often discussed in the mediaand the political arena; the long run version will allows us to understand what is behindthe phenomenon of growth observed in the last three centuries. The data part of the coursewill focus on studying actual macroeconomic U.S. data. The study will be both of empiricalin nature: studying past data and forecasting future behavior; and quantitative in naturebuilding a tight link between the macroeconomic model and the data.

Prerequisites:

Formal: (73100) and (73230) and (21120) and (21259 or 21256 or 21268 or 21269).

Informal: In the homework I will ask for extensive data work. I advice you to learn aspreadsheet software (i.e. Excel, Google docs) as soon as possible. Also, I will require thehomework to be typed, now is a good time to brush up your typing skills! Finally I expectyou to be able to apply basic tools of mathematics, statistics and economics.

Course material:

Textbook: The textbook will be used as a guide and a reference book. I adopt the organi-zation of the book, but do not follow it verbatim. The fourth edition of the book is also an


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acceptable version.

An additional textbook that I will occasionally cite in the slides (this book is not required)is: Applied Intermediate Macroeconomics by Kevin Hoover.

Twitter and other News: This year I will experiment with Twitter. The class officialtwitter feed is @cmu73240. In this feed I will post class announcements (that will be mir-rored in the Blackboard website) and interesting macroeconomic news. Every week, as aform of “digest”, I will summarize the most relevant macroeconomics news at the beginningof class.

Slides: I will make slides available on the class Blackboard website. However, I will notmake the slides available before class. This is done to encourage discussion during class. Inparticular, not posting slides before classes allows me to ask questions that might otherwisebe answered by looking at the next slide. During the semester I will also prepare the slidesin book format. The idea is for you to have a document that you might keep for years tocome.

Blackboard: I will make some additional material available on the class website: unless Ispecify otherwise these are not a required reading (but most of the times are very interest-ing!). Check Blackboard regularly: the TAs and I will use the site to communicate additionalinformation to you, to post slides and update the syllabus.

Feedback and Email:

Together with the usual evaluation forms, I set up an on-line, live, anonymous feedbacksystem, you can access it here: http://tinyurl.com/evaluations-ales

This is a large class, in order to communicate more efficiently I will follow the following emailpolicy:

• During the week, I will answer student emails usually within 24 hours.

• Usually I will not be able to answer homework emails the night before they are due!

• Any regrading request must be submitted to your TA first. If an issue persists I willbe happy to help after that.


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Requirements and Grades:

Final Grade: The final grade will be computed according to the following components:

• 6 assignments (30% of total grade)

• 2 midterms (35% of total grade). Note that no midterm will be dropped.

• 1 comprehensive final exam (25% of total grade).

• 10% for attendance and class participation. I will have random roll calls during thesemester.

Final grades will be determined on a relative basis: students with the highest total pointswill receive A’s, those next in line will receive B’s, etc. I will not disclose cutoff values.

The class will feature instant quizzes during classes. These non-graded quizzes will be anony-mous and will be used to sample your knowledge of the material we will cover in class. Insteadof using a clicker system I decided to administer quizzes via a web version that you can accessfrom your phone (this will save you the cost of buying a clicker). The form can be accessedhere: http://tinyurl.com/73240-ales so make sure to bookmark it!

Additional Policies:

1. Students with Disabilities: If you have a disability, let me know ass soon as possibleand contact the Office of Disability Resource to request appropriate accommodation.

2. Class room behavior: Private conversations, browsing the web and checking email willbe considered inappropriate. If you do it, you will be cold called.

3. Final score regrading: any regrading request must be submitted to the economicsprogram at the beginning of the fall semester.

4. Class Material: I will provide lectures slides, notes etc. These materials are subject tocopyright and are being provided for the personal educational use by students enrolledin this course. Any other use, including further reproduction and distribution of thematerials (whether in hard copy or electronic form) is strictly prohibited. For example,you may not copy any of these materials and upload them to any other web sites withoutthe prior permission of the applicable copyright holder.

Homeworks Policies:


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1. Turning in Homework: Homework must be turned in on the day it is due (usually ona Friday) your TA will collect the homework in class. Late homework will NOT beaccepted unless you are sick and have a doctor’s note.

2. Homework regrading:If you believe a question has been incorrectly graded, please takeyour homework to your TA within 2 weeks of it being returned.

3. Working in groups: You may work in groups of up to 4. BUT: You MUST put namesof other group members on your homework. You MUST write up your own set ofanswers. Do NOT simply copy some other person’s work. Copied homework willresult in receiving zero points for that homework as a minimum sanction.

4. TYPE your work. Equations may be hand written. Write your first and last name onthe title of each graph. Graphs that do not contain data may be hand drawn.

5. Buy a stapler!

Schedule

Important dates:

• Midterms on Feb 24th and Apr 9th.

• Final exam date: TBA(for updates check: http://www.cmu.edu/hub/).

• Grades posted by May 15th.

The following is a tentative schedule, refer to Blackboard for updates on dates and topics.


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Week Monday Wednesday Friday1 (Jan 13)

Introduction(Jan 15)Measurement: levels and GDP

(Jan 17)

2 (Jan 20)No class - MLK day

(Jan 22)Nominal and real Quantities;Measurement: fluctuations

(Jan 24)

3 (Jan 27)Introduction to Forecasting

(Jan 29)The Consumer

(Jan 31)

4 (Feb 3)The Consumer

(Feb 5)The Firm

(Feb 7)

5 (Feb 10)The Firm

(Feb 12)The Government

(Feb 14)

6 (Feb 17)Equilibrium andPareto optimality

(Feb 19)Taxation and spending

(Feb 21)

7 (Feb 24)MIDTERM 1

(Feb 26)Growth facts

(Feb 28)

8 (Mar 3)Growth: Malthus

(Mar 5)Growth: Solow

(Mar 7)No class

9 (Mar 10)Spring Break

(Mar 12)Spring Break

(Mar 14)No class

10 (Mar 17)Growth: endogenous growth

(Mar 19)Saving and Investment

(Mar 21)

11 (Mar 24)Inter-temporal model

(Mar 26)Inter-temporal model: Policy

(Mar 28)

12 (Mar 31)Finance and macro

(Apr 2)Finance and macro

(Apr 4)

13 (Apr 7)Review

(Apr 9)MIDTERM 2

(Apr 11)No class

14 (Apr 14)Money

(Apr 16)Monetary model

(Apr 18)No class

15 (Apr 21Monetary model: Policy

(Apr 23)Labor market facts

(Apr 25)

16 (Apr 28)Unemployment, wages

(Apr 30)Final Review

(May 2)


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Part II

Class Notes

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Chapter 1

Introduction and Methodology

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About Myself

My name is: Laurence Ales

• Born in Italy

• B.S. in Physics

• Ph.d. in Economics

• Joined CMU in 2008, as an Assistant Professor of Economics

My research:

• How much inequality in consumption and health should there be?

• How much insurance do workers have?

• How should we tax people?

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The Syllabus

• Make sure to get and read the syllabus!

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Details About the Course

• The class: MW 1:30-2:50

• TA and Recitation:• Antonio Andres Bellofatto

• Minyoung Rho

• Office Hours:• Ales: Th 3:30-5:30

• Bellofatto : T 1.30-3.30

• Rho: Th 1:30-3:30

• The textbook:• Macroeconomics - S. Williamson 5/E

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Hw, Grading and Exams

• 6 Homework- 30% of grade

• 2 Midterms (tentative: Feb 24th; Apr 9th) - 35% of grade

• 1 Final - 25% of grade (check CMU website for dates)

• 10% for attendance and participation

• No midterm dropped

• No mercy for cheating!

• Grade me:• Online, live, anonymous feedback system:

http://tinyurl.com/evaluations-ales

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Recommendations I/II

• Email: for regrading email your TAs first!

• Microeconomics!!

• Math

Ü Find x: log(x + 1)− log(x + 2) = log(1x

).

Ü Find x: maxx f(x) s.t. g(x) = 0.

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Recommendations II/II

• Data Analysis:

Ü We will extensively work with data, review your stats class.

Ü Excel was released in 1985! You should be able (soon) to:

1 Manipulate data;

2 Perform simple manipulations on data;

3 Plot a (nice looking) graph!

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A Bad Graph

• How many bad graphical habits can you spot in this graph?

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Twitter and News

• The class official twitter feed is @cmu73240.

• In this feed I will post:

1 Class announcements(that will be mirrored in the Blackboard website).

2 Macroeconomic news.

• Every week, as a form of “digest”, I will summarize the mostrelevant macroeconomics news at the beginning of class.

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Let’s Start!

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Upcoming...

1 What is this course about?

2 Notes on Methodology.

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Your Questions

Every Slide From The Course

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What Are We Going To Study?

• What does Macroeconomics study?

• From Semantics: large economics systems.

• (Hoover) Is the study of the economy taken as a whole; whereasMicroeconomics is the study of a part of the economy, taking theremainder as given.

• What type of questions does it try to answer?

• What will GDP be one year from now?

• How do economic fluctuations come about?What can we (Government, Fed) do about it?

• Why is the US richer than most countries?How does policy affect growth?

• How should taxes and government debt be used?

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What Do You Want From This Course?

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What Will You Get From This Course?

1 ...Understand and perform simple forecasts of various measures ofan aggregate economy’s performance;

2 ...Understand how aggregate macroeconomic behavior is affected bymicroeconomic behavior and equilibrium restrictions;

3 ...Be able to answer simple macroeconomic policy questions byformulating a model, finding the data and deriving an analyticaland quantitative answer;

4 ...Understand the factors that cause economic growth and be ableto describe the patterns of economic development over time;

5 ...Understand how credit and labor frictions operate and how theymight impact macro economic behavior.

Slide 17 of 27

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Methodology

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Normative vs. Positive Questions

• Economics is interested in two types of fundamental questions.These questions can be either positive or normative.

• Positive questions: questions independent of any ethical or moralconsideration. Focused on “what was/is/will be”. These questionrely on an objective investigation of data.

• Normative questions: questions that deal with the notion of“what should be”. These questions rely on completely specified setof ethical and social goals.

• The “hard” sciences only deal with positive questions.(just for fun try and ask a “normative” physics question!)

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How Do We Get The Answers?

• Economists similarly to “hard” scientists like to build theories.

Why? google: pitch drop experiment

...experiments can take a long time!

...but that is not the only reasons we build theories...

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Friedman on the Role of Theory

• Milton Friedman:2

The ultimate goal of a positive science is the development of a“theory” or, “hypothesis” that yields valid and meaningful (i.e., nottruistic) predictions about phenomena not yet observed. Such atheory is, in general, a complex intermixture of two elements. Inpart, it is a “language” designed to promote “systematic andorganized methods of reasoning.” In part, it is a body of substantivehypotheses designed to abstract essential features of complex reality.

• A theory should:

+ be a language to help us communicate.

+ provide simplifying assumptions that help understand reality.

2Milton Friedman ”The Methodology of Positive Economics” In Essays In PositiveEconomics (Chicago: Univ. of Chicago Press, 1966), pp. 3-16, 30-43.

How Do We Get The Answers?

• A fundamental difference between an economist and a hardscientist is what to do when a theory has been formulated.

• Can economists follow closely the Scientific Method?

Karl Popper on the Scientific Method:

A theory which is not refutable by any conceivable event isnon-scientific. Irrefutability is not a virtue of a theory (as peopleoften think) but a vice. [...] Every genuine test of a theory is anattempt to falsify it, or to refute it. Testability is falsifiability.3

3(Karl Popper, Conjectures and Refutations, London: Routledge and KeaganPaul, 1963, pp. 33-39; from Theodore Schick, ed., Readings in the Philosophy ofScience, Mountain View, CA: Mayfield Publishing Company, 2000, pp. 9-13. )

The Problem With the Scientific Method

• Falsifiability might be impossible: people and firms are smart,a controlled “experiment” might be impossible to achieve.

• Socially, falsifiability may not be very desirable!

Source: The Onion

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Building a Model

• A theory written by an economist is simply a “model”.

• What is a model? A simple virtual representation of a realenvironment.

• Some examples:

• Google maps ⇐⇒ The world

• F = g(m1 ·m2)/d2 ⇐⇒ An apple falling from a tree

• A macroeconomic model ⇐⇒ The U.S. economy

• What makes a good model?It must be simple enough so that we can learn from it!

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The Issue of Realism

• Models, by definition, are simplified representations of reality.

• It is common for economic models to be criticized on the basisof being “unrealistic”.

• Should we be concerned about these type of critiques? If the“unrealistic” assumptions made in the model drastically changesthe results: YES.

• If not, the model should not be evaluated on the basis of realismbut on their predictive power.

• This approach is also common in the sciences: think for examplethe model that Newton considered when thinking of an applefalling from the tree.

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Model Ingredients

• Actors:

• Households

• Firms

• Markets

• Government

• Quantities:

• Households: Consumption, Savings, Hours worked

• Firm: Output, Vacancies

• Markets: Prices, Inflation

• Government: Taxes, Debt, Expenditures

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Roadmap

This week ⇒ Study quantities: GDP, Consumption...

Next week ⇒ Study fluctuations in the data

After that... ⇒ Modeling: household, firm and government

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Chapter 2

Measurament

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2.1 GDP

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A key quantity: GDP

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Gross Domestic Product

Important definition!

Gross domestic product (GDP):

The market value of final goods and services produced within a countryin a given period (usually a year).

Next we look at:

• GDP across countries;

• GDP over time for the U.S.

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GDP Across Countries

What are potential issues in comparing GDP across countries:

1 We need a unit of measure: U.S. dollar;

2 If we care about relative richness,we need to scale per capita;

3 Need to adjust for relative cost of living:power purchasing parity (PPP).

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The Big Mac Index

Comparing the price of a Big Mac around the world:

Country Price in USD

U.S. $ 4.56

Switzerland $ 6.72

China $ 2.61

Euro Area $ 4.66

India $ 1.50

Norway $ 7.51

Data: July 2013. Source:http://www.economist.com/content/big-mac-index

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Appendix: Data

Where To Find Data:

• National:

1 St. Louis Fed: http://research.stlouisfed.org/fred2/(check out their mobile apps!)

2 Bureau of Economic Analysis (BEA): http://www.bea.gov

• International:

1 Penn World Tables: http://pwt.sas.upenn.edu

2 International Monetary Found (IMF):http://www.imf.org/external/research/index.aspx

GDP Per Capita Across Countries

Data taken from the IMF (2013):http://www.imf.org/external/pubs/ft/weo/2013/01/

Country Amount (USD)

U.S. $ 49,922

Canada $ 52,231

Italy $ 33,115

Mexico $ 10,247

Nigeria $ 1,630

Ethiopia $ 482

China $ 6,075

India $ 1,491

HUGE cross country differences: Rich/Poor > 40 !!

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GDP Across Countries

World per Capita Real GDP (in 2000 dollars) 2008

Source: IMF

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Per Capita Real GDP by State

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How about countries over time?

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U.S. GDP Over Time

• In looking at GDP over time we must take care of one thing...

• Prices grow, we need to rescale at a common value:for example choose $ 1 in 2000.

• Check here for “what is a dollar worth calculator”:http://www.minneapolisfed.org/

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U.S. GDP Over Time

A curiosity:

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U.S. GDP Over Time

U.S. real GDP (in 2000 dollars) 1900 - 2013

Source: Officer, Williamson (2012).Data Link: http://www.measuringworth.com/datasets/usgdp12/

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U.S. GDP Over Time: Observations

Some observations:

1 It grows;

2 It fluctuates;

3 There are some big fluctuations, some are “exogenous”.

A question to think about...is it growing faster?

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U.K. GDP Over Time

U.K. Real GDP (in 2006 GBP) 1830 - 2009:

0"

2000"

4000"

6000"

8000"

10000"

12000"

14000"

1830" 1850" 1870" 1890" 1910" 1930" 1950" 1970" 1990"

Real%GDP

%

Year%

Real GDP of England!(Billions of 2006 Pounds)!

Source: Bank of England + Data LinkSlide 18 of 43

History of GDP

• Developed by Simon Kuznets and his team in 1934(once released, data was already 2 years old!)

• First estimate using IRS data and 1929 Census(he measured the national income)

• In 1940 government interested in measuring national production(estimated with: final sales, consumption spending, shipments...)

• In 1960s first value added estimates(estimated with the aid of input-output tables)

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Who Computes GDP Today?

• The Bureau of economic analysis (BEA) periodically publishes theNational Income and Product Accounts (NIPA). They contain:

1 GDP and its components (more on these later)

2 GDP by state, metropolitan area

3 GDP by industry (I-O tables)

4 International accounts (balance of payments)

• You can get all the data here: http://www.bea.gov

• BEA uses data from: Census, Bureau of labor statistics (surveys),Tax returns, Industry estimates...

• BEA releases three versions of its estimates:Advance, Preliminary, Final.

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3 “Definitions” of GDP

BEA uses 3 alternative definitions/approaches to GDP:

• Expenditure Approach: Total spending on newly produced finalgoods and services produced within a nation during a year.

• Income Approach (national income): Total Income generated bynewly produced final production goods and services, profits andtaxes paid by firms and depreciation of capital within a nationduring a year.

• Product Approach (value added): Market value of final goods andservices newly produced within a nation during a year.

We will use the symbol Y to denote either total expenditure,income or value added!

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3 Definitions of GDP (2005 Data)

the national accounts—the Bureau of Economic Analysis sums up C ! I ! G ! (X –M) to arrive at nominal GDP. These nominal estimates are then deflated using priceindexes to arrive at an estimate of real, or inflation-adjusted, GDP. These benchmarkestimates provide a detailed and rich picture of the economy, reflecting the mostrecent methodologies used to organize the underlying data to fit with the economictheory embodied in the national accounts.

Between these benchmark estimates, GDP is estimated on an annual and on aquarterly basis. Most of the data for the annual estimates are from the CensusBureau’s annual surveys, which cover approximately 150,000 reporting units. Mostof the data for quarterly estimates are from the Census Bureau’s monthly surveys,which cover approximately 35,500 reporting units.

The first estimate of GDP for a quarter, the “advance” estimate, appears aboutone month after the end of the most recent quarter. Components of GDP based oninformation for which the Bureau of Economic Analysis has survey-based monthlydata for all three months of the quarter account for about 45 percent of theadvance estimate, as shown in Table 2. For other components, the bureau uses amix of survey data and extrapolations. For example, the estimates of inventories aregenerally based on two months of Census Bureau survey data, and the estimates of

Table 1Three Ways to Measure GDP

I. Value-added (or production) approach2005 share

(percent)

Gross Output (gross sales less change in inventories) 183.5Less: Intermediate inputs 83.5

Equals: Value added for each industry 100.0

II. Income (by type) approach

Sum of: Compensation 56.6Rental income 0.3Profits and proprietors’ income 17.6Taxes on production & imports 7.4

Less: Subsidies 0.5Interest, miscellaneous payments 5.5Depreciation 12.9

Equals: Total domestic incomes earned 100.0

III. Final demand (or expenditures) approach

Sum of: Consumption of final goods and services by households 70.0Investment in plant, equipment, and software 16.7Government expenditures on goods and services 19.0Net exports of goods and services (exports " imports) "5.7

Equals: Final sales of domestic product to purchasers 100.0

Taking the Pulse of the Economy: Measuring GDP 197

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The Components of GDP: Expenditure Approach

GDP s comprised by:

• Consumption expenditures (C): consumer goods and services

• Investment (I): goods produced but not consumed

• Government expenditures (G)

• Net exports (NX):goods and services exported minus goods and services imported

GDP = Y = C + I + G + NX

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The Components of Nominal GDP in 2012/2013

• Table 1.1.5 from NIPA (values are Billions of $)

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The Components of Nominal GDP in 2012/2013

• Some observations:

1 Consumption is the largest component 2/3 of GDP

2 Government is around 15/20% of GDP

3 Net export is negative

4 Services is the largest component of consumption

5 Nonresidential investment is the largest component of investment

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An Example: The Island Economy


Restaurant

Coconut Producer

Consumer

Government

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The Expenditure Approach

• Determine all expenditure by each agent and add governmentexpenditures:

Total expenditures = C + I + G + NX

• Note: in this example by definition G = NX = 0

• Note: in our example some coconuts are sold to the restaurantsome are sold directly.

• Note: government expenditures in our example are onlyfor labor services, so consider wages as expenditure.

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Restaurant

Coconut Producer

Consumer

Government

Expenditure approach:

GDP = $ 8︸︷︷︸Buy coconut

+ $ 30︸︷︷︸Buy Meal

+ $ 5.5︸︷︷︸Government

= $ 43.5

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The Income Approach

Determine all income for each agent:

• For HH: wages + profits from firms + interests;

• For Government: taxes payed by firms.

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Restaurant

Coconut Producer

Consumer

Government

Income approach:

GDP = $ 14.5︸︷︷︸Wages

+ $ 0.5︸︷︷︸Interests

+ $ 24︸︷︷︸Profits

+ $ 4.5︸︷︷︸Taxes from firms

= $ 43.5

Slide 31 of 43

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The Product Approach

Determine the final product by determining the valued added of eachfirm and add government expenditures:

• Note 1: the sum of value added equals the value of final products

• Note 2: what is the valued added of the government?(use value of inputs)

Slide 32 of 43

An example: The Island Economy

Restaurant

Coconut Producer

Consumer

Government

Product approach:

GDP = $ 20︸︷︷︸Coconut Producer

+ $ (30 − 12)︸︷︷︸Restaurant

+ $ 5.5︸︷︷︸Government

= $ 43.5

Slide 33 of 43

National Accounting Identities

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National Accounting Identities

• The 3 definitions of GDP are useful to relate production and income(there is always income related to any value added or production!)

• Another important relation is the disposable income identity:(The idea is to relate income to its disposition by households)

Y − T︸︷︷︸Taxes

+ TR︸︷︷︸Transfers

= C︸︷︷︸Consumption

+ S︸︷︷︸Saving

Slide 35 of 43

The Sectoral Deficit Identity

• Using the definition of GDP and the disposable income identity wecan identify which sector is running a surplus or deficit

Y − T + TR = C + S︸︷︷︸Disposable Income id.

; Y = C + I + G + NX︸︷︷︸GDP Definition

• Substitute out Y and re-arrange:

G− T + TR︸︷︷︸Government Deficit

+ I − S︸︷︷︸Private Sector Deficit

+ NX︸︷︷︸Foreign Sector Deficit

= 0

Not every sector can run a surplus, or deficit!

Slide 36 of 43

The Limits of GDP

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Problems With GDP

What is GDP not counting in measuring the size of the economy?

1 Non-market production:• Home production (think about housework, childcare, DIY)

• In developing countries: subsistence farmers(living with 1$ a day means that most of the cropsare for own consumption, few sold for cash)

2 Underground economy

What does GDP mean?

1 What about environmental costs?

2 What about welfare?

Slide 38 of 43

Underground Economy Across Countries

Data: World Bank (1998).

Country Fraction of GDP

Nigeria 77%

Thailand 70%

Bolivia 67%

Italy 27%

U.S. 10%

Switzerland 9%

Slide 39 of 43

Measuring the Underground Economy

• Direct Approaches:

Ü Surveys;

Ü Tax audits.

• Indirect Approaches:

Ü National accounting statistics;

Ü Labor force statistics;

Ü Transactions;

Ü Currency demand;

Ü Electricity consumption and other inputs.

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Interpreting GDP: Bads and Regrettables

• A “bad” is a good that the more you have of it, the less happy youare about it.

• GDP measures “goods”, by definition bads are not included. Incomparing the state of two economies across time and space weshould also consider:

• Pollution;

• Depletion of natural resources.

Slide 41 of 43

Interpreting GDP: Hours

Is GDP measuring welfare ?

• Leisure, health care, education...

Source: OECD.

Slide 42 of 43

Interpreting GDP: Inequality

• How about inequality?

+ GDP is a sum, contains no information on distributionof consumption/income.

• Interdecile (P90/P10) ratio across countries:

Country in 2010 P90/P10

Denmark 2.72

France 3.39

U.K. 4.21

Italy 4.31

U.S. 5.91

Mexico 8.53

Source OECD: http://dx.doi.org/10.1787/826773162617Slide 43 of 43

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2.2 Forecasting

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From The Previous Class:

U.S. real GDP (in 2000 dollars) 1900 - 2013

Source: Officer, Williamson (2012).

• A natural question: is the U.S growing faster?

Slide 5 of 48

Logs and Growth Rates

Let yt be real GDP at time t; ∆yt we denote growth of yt

∆yt+1 =yt+1 − yt

yt

∆yt+1 =yt+1

yt− 1

log (1 + ∆yt+1) = log(yt+1)− log(yt)

Note log(1 + x) ≈ x if x is small ... so

∆yt+1 ≈ log(yt+1)− log(yt)

• Plotting log of GDP is much easier to identify growth rates.

• In a log GDP plot, the slope determines the growth rate.

Slide 6 of 48

U.S. GDP Over Time

Log of U.S. real GDP (in 2000 dollars) 1900 - 2013

Source: Officer, Williamson (2012).

It’s a line!!...almostThe graph above implies a constant growth rate (approx. 2%)Slide 7 of 48

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U.S. GDP Over Time

• The result holds going back to 1790.

• The result holds looking in per-capita terms.

+ Check for yourself here:http://www.measuringworth.com/datasets/usgdp12/

• Can we use this robust “trend” of U.S GDPto predict future values?

Slide 8 of 48

Forecasting: Introduction

Slide 9 of 48

Forecasting

• This Lecture:

1 Trend forecasting;

2 Single time series forecasting.

• Later In the Course:

1 Multiple time series forecasting.

Slide 10 of 48

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Forecasting

• A good source:

Forecasting in Business and Economics by C.W.J. Granger.

Slide 11 of 48

Forecasting: Basic Definitions

Definition (Time Series)

A time series is a sequence of values recorded at (usually) equidistanttime intervals. We denote with {xn}tn=1 a time series containing t values.

• Loosely: a forecast of a time series xt is a guess about future valuesof it: for example what will GDP be on Apr 30, 2014.

• To formally build a forecast we need to specify:

1 What information we have available for the forecast;

2 What are the cost involved in a wrong forecast!

Slide 12 of 48

Forecasting: Information Sets

Definition (Information Sets)

Let It be the set of information available at time t for a forecast.

• The information set It we will use can be of two types:

1 It = {xn}t−1n=1: for the forecast we have available only past values of

the time series we want to forecast. This will be the case in thislecture.

2 It = {xn}t−1n=1 ∪ {cn}t−1

n=1: for the forecast we have available pastvalues of the time series we want to forecast and of another timeseries ct. We will talk about this later in the course.

Slide 13 of 48

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Forecasting: Errors

Definition (Forecast Errors)

Suppose that at time t we have forecasted the future value: xt+1. Attime t+ 1 we observe the real value: xt+1. Our error is:

et+1 = xt+1 − xt+1.

• Not all type of errors are the same....

• For example, suppose you are forecasting future demand of aproduct. Over-estimating demand will imply a cost due to unsolditems. Under-estimating demand will imply an opportunity costfor lost business.

Slide 14 of 48

Forecasting: Penalty Functions

• Let C(e) be the penalty function associated with error e.

• A good forecast is one that minimizes the overall penalty function.

• A common approach is to use the square of the error Ü C(e) = e2.

• In this class we will do a hands on approach. For a formaltreatment refer to your econometrics and statistics classes.

Slide 15 of 48

Fitting a Linear Trend

• An idea motivated by the above: if log GDP has grownlinearly, is it natural to think it will continue to do so?

Slide 16 of 48

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Back to the 1960s

• An experiment: suppose I was teaching this class on Jan 22, 1960.Suppose I wanted to figure out what GDP would be on Jan 22,2014, how would I proceed?

• In this experiment we only use past real GDP information from1947 to 1960:

I1960 = {xn}1959n=1947.

where yt is GDP in year t.

• We will minimize the square of the error so that:

C(e2014) = (x2014 − x2014)2.

where x2014 is our forecast of GDP for 2014.

Slide 17 of 48

Fitting a Trend

• Excel provides several function to add a linear trend-line.

• SLOPE(known y’s,known x’s)Returns the slope of the linear regression line through data pointsin known y’s (values) and known x’s (dates).

• INTERCEPT(known y’s,known x’s)The intercept point is based on a best-fit regression line plottedthrough the known y’s (values) and known x’s (dates).

+ Refer to your econometrics and regression analysis class forprecise formulas.

Slide 18 of 48

Back to the 1960s: Part 1

Algorithm used to find the linear trend forecast:

1 I use Nominal GDP from NIPA Table 1.1.5

2 I use quarterly data from 1947 to 1960.

3 I take logs (natural logarithm) of the series.

4 Use SLOPE and INTERCEPT to find a linear trend.

5 Extend the linear trend to Jan 22, 2014.

Slide 19 of 48

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25#

26#

27#

28#

29#

30#

31#

1947# 1957# 1967# 1977# 1987# 1997# 2007#

Log$of$Real$GDP$and$Trend$

Log#Real#GDP# Trend#Forecast#

• The forecast is remarkably close to actual data!

• The forecast is under-estimating actual GDP by 15%

• Trend seems to increase in the 70s and decrease in the 90s.Slide 20 of 48

Deviations from trend

Definition (Deviation From Trend)

Let xt the actual values of a time series. Let xt be the values of thefitted trend line. Define the deviation from trend as dt = xt − xt.

From our previous experiment:

!0.1%

0%

0.1%

0.2%

0.3%

0.4%

0.5%

0.6%

1947% 1957% 1967% 1977% 1987% 1997% 2007%

Devia&ons*From*Trend*

• The deviations from trend don’t appear completely random,there seems to be a degree of “correlation” over time.

Slide 21 of 48

Forecasting: Time Series

• A question. How confident are we about our forecast?

• A model for dt can help provide an answer.

• What model should we have for dt? From the previous picture itseems there is a persistence component and a “shock” component.

dt = αdt−1︸︷︷︸Effect of past shocks

+ εt︸︷︷︸Effect of current shock

• dt is an auto-regressive process:

1 α ∈ [0, 1] denotes the persistence of the process.

2 εt is a shock process with variance σ2.

Slide 22 of 48

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Appendix: Autoregressive Processes

• Given an autoregressive process:

dt = αdt−1 + εt

• We have that:

α =cov(dt, dt−1)

var(dt).

• The variance of εt can be computed directly.

σ2 = var(dt − αdt−1).

Q: Why do we care? Knowing σ2 provides confidence intervalsaround our original estimate.

Slide 23 of 48

Appendix: Autoregressive Processes

• Suppose we are performing a forecast k period ahead.

• Given an estimate of α and σ2 let

δ2k =

{kσ2 if α = 11−α2k

1−α2 σ2 if α < 1

• The 95% confidence intervals are given by:

xt+k ± 2√δ2k

where xt+k is our trend forecast k periods ahead.

• The idea is that the more variable a time series is,the least certain we can be about a forecast.

Slide 24 of 48


Algorithm used to find the confidence intervals:

1 Calculated the deviations from trend: dt.

2 Compute α using the function CORREL in Excel.

3 Compute εt = dt − αdt−1.

4 Compute the variance of εt using function VAR in Excel.

5 Compute δ2k.

6 Compute the upper bound: xt+k + 2√δ2k and

lower bound: xt+k − 2√δ2k.

Slide 25 of 48

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25#

26#

27#

28#

29#

30#

31#

1947# 1957# 1967# 1977# 1987# 1997# 2007#

Ln#Real#GDP#and#Trend#

Log#Real#GDP# Trend#Forecast# Lower#Bound# Upper#Bound#

• Actual data is within the 95% confidence bands.

Slide 26 of 48

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2.3 Trend and Cycles

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Recession and Depression

Definitions:

Recession• Two consecutive quarters of decline in real GDP.

• NBER: A significant decline in economic activity spread across theeconomy, lasting more than a few months, normally visible in realGDP, real income, employment, industrial production, andwholesale-retail sales.

Depression• Large output drop > 10% lasting several years

For more information visit here: http://www.nber.org/cycles.html

Slide 28 of 48

Trend and Cycle

• In the previous experiment the fitted trend line was used toperform forecast about the future.

• The fitted trend line is also useful to study separately aspectsconcerning long term growth and short term fluctuations.

• Economist usually study (so will we in class) separately.

Slide 29 of 48

Trend and Cycle

• Trend: captures the long term growth rate of the economy.

• Cycle: captures short lived deviation from the trend.

Slide 30 of 48

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Deviations from trend

Definition (Deviation From Trend)

Let xt the actual values of a time series. Let xt be the values of thefitted trend line. Define the deviation from trend as dt = xt − xt.

From our previous experiment:

!0.1%

0%

0.1%

0.2%

0.3%

0.4%

0.5%

0.6%

1947% 1957% 1967% 1977% 1987% 1997% 2007%

Devia&ons*From*Trend*

• We observe both Large secular fluctuations: “productivityslowdowns”. and Smaller fluctuations: “business cycles”.

Slide 31 of 48

Non-Linear Trend

• The previous plot shows that a linear trend misses the fast growthof the 70s and the slowdown in the 90s.

• This is an artifice of the simple nature of the trend used: a line.

• We now use a more flexible trend (also called a non-linear filter).

• The once considered is the Hodrick-Prescott (HP) filter.

Slide 32 of 48

The Hodrick-Prescott filter

Let yt be GDP in year t. Suppose you have data for T years.Suppose that:

yt = εt︸︷︷︸Cyclical component

+ xt︸︷︷︸Trend component

The HP filter finds the trend solving the following problem

min{gt}Tt=1

{T∑

t=1

(yt − xt)2 + λT−1∑

t=2

[(xt+1 − xt)− (xt − xt−1)]2}

λ is called the smoothing parameter

• Set λ = 100 if GDP is in yearly data

• Set λ = 1600 if GDP is in quarterly data

Slide 33 of 48

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HP Filter and U.S. GDP

• Observe the slow moving trend line.

Slide 34 of 48

HP Filter and U.S. GDP

• Given the trend line is straightforward to computedeviations from trend.

Slide 35 of 48

The Cyclical Component

What to do when we derive the cyclical component?

• We can study the frequency of the fluctuations.

• We can study the amplitude of the fluctuations.

• More important, the cyclical component of GDP can serve as abenchmark for other macroeconomic quantities.

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Business Cycles: Relationship To GDP

Slide 37 of 48

Two Time Variables: How to study them?

Let xt and yt be two time variables (for example: GDP, Inflation).

Natural questions you might ask:

• Are the two variable “related”?

• Is one variable “predicting ” the other?

• Does one variable “move” more than the other?

Slide 38 of 48

Two Time Variables: Correlation

Remember correlation does not imply causation!!!

When the trend is removed from the two variables economist usuallytalk about co-movement rather than correlation

Q: If I have two variables that grow at the same rate anddo not remove the trend what will be the correlation?Slide 39 of 48

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Two Time Variables: Correlation

Definition

A macroeconomic variable is:

• Pro-cyclical: if deviations from trend are positively correlated withdeviations from trend of real GDP.

• Counter-cyclical: if deviations from trend are negatively correlatedwith deviation from trend of real GDP.

• A-cyclical: if deviations from trend are not correlated.

Slide 40 of 48

Two Time Variables: Lead and Lag

If xt and yt are positively correlated,additional information on comovement

Slide 41 of 48

Two Time Variables: Amplitude

• Is also important also to look at the amplitude of deviation fromtrend of the two variables (who fluctuates more?)

To summarize, with two economic variables you should remember:

1 How they are correlated? pro-cyclical, countercyclical

2 How they are synchronized? lead-lag

3 How do the fluctuations compare? amplitude

Slide 42 of 48

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Multiple Time Series: Examples

Slide 43 of 48

Deviation From Trend Consumption vs. GDP

• Consumption is:pro-cyclical, coincident and slightly less variable

Slide 44 of 48

Deviation From Trend Investment vs. GDP

• Investment is: pro-cyclical, coincident and more variable

Slide 45 of 48

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Deviation From Trend Employment Level vs. GDP

• Employment level is pro-cyclical, lagging and less variable

Slide 46 of 48

Relation Between Variables: Summary

Slide 47 of 48

Relation Between Variables: Summary

• Goal for the semester: construct a theory to explain these facts!

• Also, can the theory guide us to “better forecasts”?

Slide 48 of 48

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2.4 Nominal and Real GDP

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Plan For This Lecture

1 Nominal and Real GDP.

+ http://www.youtube.com/watch?v=jTmXHvGZiSY

2 Study Price levels: CPI and GDP deflator.

Slide 2 of 16

Real and Nominal Quantities

Some definitions:

• A nominal quantity: is a dollar denominated quantity, denotingthe market value of a quantity with prices defined at the time ofproduction.

• A real quantity: is a dollar denominated quantity, denoting themarket value of a quantity with prices defined in a given year.

• A price level: is a weighted average of prices at a given time.

• A price index: is the ratio of two price levels.

Slide 3 of 16

A 2 x 2 Economy

Example economy lasts for 2 periods: 2013 - 2014; 2 goods areproduced: Apples and Oranges. The data:

Product/Time 2013 2014

Apples 5 10Oranges 200 250

Prices

Apples 1.2 $ 0.6 $Oranges 0.2 $ 0.24 $

Values

Apples 6 $ 6 $Oranges 40 $ 60 $

Nominal GDP 46 $ 66 $

Quantities and prices are changing, is nominal GDP informative?No. Real GDP will provide a measure about real changes!Slide 4 of 16

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From Nominal to Real GDP

• Once we define a price index we can move between the twoquantities:

Real GDP =Nominal GDP

Price Index

• To define a price index we need to determine a base year.A year for which the price index is normalize to 1.

Price Index(t) =Price level(t)

Price level(base year)

Slide 5 of 16

Keeping Prices Fixed

• Steps to convert Nominal GDP to Real GDP:

1 Determine a base year.

2 Construct a price level; we have two options:

• Fix weights for prices using quantities in the base yearThis is called the Base-weighted or Laspeyres approach.

• Every period change weights for prices using current quantitiesThis is called the Current-weighted or Paasche approach.

3 Construct the price index.

4 Divide the time series of Nominal GDP by theconstructed price index.

Slide 6 of 16

Laspeyres vs Paasche

Let P ti =prices, Xt

i=quantities of good i at time t. Nominal GDP is:

GDP (t) =

N∑

i=1

P tiX

ti

• Let t0 be the base year. The Laspeyres index for year time t is:

PLaspeyres(t) =

∑Ni=1 P

tiX

t0i∑N

i=1 Pt0i Xt0

i

• Let t0 be the base year. The Paasche index for year t is:

PPaasche(t) =

∑Ni=1 P

tiX

ti∑N

i=1 Pt0i Xt

i

Slide 7 of 16

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The Laspeyres Index

Product/Time 2013 Base year 2014

Apples 5 //10 5Oranges 200 ///250 200

Prices

Apples 1.2 $ 0.6 $Oranges 0.2 $ 0.24 $

Values


Laspeyres Index 1 3$+48$6$+40$ = 51$

46$ = 1.11

• To calculate price index in 2014 use quantities of 2013.

• Price Index increases by 11% between 2013 and 2014.

Slide 8 of 16

The Paasche Index

Product/Time 2013 Base year 2014

Apples //5 10 10Oranges ///200 250 250

Prices

Apples 1.2 $ 0.6 $Oranges 0.2 $ 0.24 $

Values


Paasche Index 1 6$+60$12$+50$ = 66$

62$ = 1.064

• To calculate price index in 2014 use quantities of 2014.

• Price Index increases by 6.4% between 2013 and 2014.

Slide 9 of 16

Nominal and Real GDP Growth

Recall:

Real GDP =Nominal GDP

Price Index

Variable ($) 2013 2014 Growth ∆

Nominal GDP 46 66 43.5%

Real GDP - Laspeyres 46/1=46 66/1.11 29.26 %

Real GDP - Paasche 46/1=46 66/1.064 34.86 %

• Two measures of Real GDP growth differ!

• In the US we use two different price indexes:

1 GDP deflator

2 CPI (consumption price index)

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Nominal and Real GDP using GDP Deflator

Question: what happens in 2009?

Slide 11 of 16

GDP Deflator Vs. CPI: Comparing 2014 vs 2009

• Deflator

Key feature 1: keep quantities fixed at the current year

Key feature 2: every good and service enters in the price index

• CPI

Key feature 1: keep quantities fixed at base year (2009)

Key feature 2: only quantities purchased by consumers (C)

CPI(2014) =

∑i∈C P 2014

i X2009i∑

i∈C P 2009i X2009

i

Slide 12 of 16

GDP Deflator vs. CPI

The two quantities differ over time!

Slide 13 of 16

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Inflation

Definition (Inflation)

Inflation (i): the % change in the GDP deflator between two consecutiveyears. For example:

i2014 =Deflator2014 −Deflator2013

Deflator2013∗ 100

• Inflation-CPI determines changes in the cost of living(constructed using CPI rather than GDP deflator)

• Question: If you were a worker in 1970, you would likeyour contract to be indexed to which value of inflation?

Slide 14 of 16

Inflation in the US

• Inflation is rarely negative.

• Period of high inflation in the 70s.

Slide 15 of 16

Putting Things in Perspective

Zimbabwe 2008: How about 231,000,000% Inflation?

Slide 16 of 16

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Chapter 3

The Household

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News of the week

How many new jobs/hires are there each month?

http://www.bls.gov/news.release/pdf/jolts.pdf

Slide 3 of 42

Plan for This Lecture

1 The Household

• Data

• The utility function

• Indifference Curves

2 Household constraints

3 Househols optimization

+ Income and Substitution effects

4 Aggregation

Slide 4 of 42

The Household

Who are the “households” in the US economy?

• In our model a households will be a unit working and consuming.To whom should we model after?

• From US Census: population clock as of Jan 28 2014: 317,441,572

(http://www.census.gov/main/www/popclock.html)

• From BLS: Number of consumer units (2012): 124,416,000

(http://www.bls.gov/news.release/cesan.nr0.htm)

Slide 5 of 42

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The Average Household: Working

• From BLS: Civilian labor force: 154,408,000

Unemployed (Dec 2013): 9,984,000

(http://www.bls.gov/news.release/empsit.t01.htm)

• Average hours worked per week (2013): 34.4

Average hourly earnings: $ 24.17 (2013)

(http://www.bls.gov/news.release/empsit.b.htm)

Slide 6 of 42

The Average Household: Not Working

What about unemployment rate (U)?

U =labor force− employment

labor force· 100 =

unemployed

labor force· 100

Using previous data

U =9, 984, 000

154, 408, 000· 100 ≈ 6.46%

• Note in this part of the course we will not model unemployment.Instead we will focus in changes of average hours worked.

Slide 7 of 42

The Average Household: Consuming

1 Excellent source: consumer expenditure survey

http://www.bls.gov/cex/

2 Average annual expenditures (2012): $ 50, 631

Some spending categories:

Category Expenses

Food $ 6,532Housing $ 16,940

Transportation $ 8,505Healthcare $ 3,466

Slide 8 of 42

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The Household

• The Household (a.k.a the representative consumer), cares about:

1 Consumption: c

2 Leisure: l

(Note, in GDP consumption is C here is c...it is not a typo, check the end of the lecture!)

• The household (HH) has a goal: be happy.

Slide 9 of 42

The Household: Assumptions

We assume that:

1 All the households have the same tastes

2 Households are very smart!(understand how the world works and can solve max)

3 Households are not jealous, do not have regrets...

4 For the next month: households live one period(we do not have to worry about savings just yet)

Slide 10 of 42

About Assumptions

• Are these good or bad assumptions?

• To answer this question we follow the paper by Friedman

“The Methodology of Positive Economics” (On blackboard)

• Do not evaluate assumption by realistic appeal(Think about Newton modeling apple falling in a vacuum)

• Evaluate assumption by ability to replicate data(Think about Newton prediction of flight-time of the apple falling)

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The Decision of The Household

The household (HH) has a goal: be happy

• The utility function U represents the happiness of the HH:

• For every bundle (c, l), U(c, l) associates a level of utility

• We say that (c1, l1) is preferred to (c2, l2) if and only if

U(c1, l1) > U(c2, l2)

• The objective of the HH is to maximize U(c, l) on every pair(c, l) that it has available (feasible and affordable)

Slide 12 of 42

Some Math Notes

• A function f(x) is a relation that uniquely associates members ofone set with members of another set.

• A derivative of function f(x), denoted f ′(x) is a function that atevery point x associates the slope of f .

df(x)

dx≡ f ′(x) = lim

∆x→0

f(x+ ∆x)− f(x)

∆x

Note: d2f(x)dx2 ≡ df ′(x)

dx

Slide 13 of 42

Properties of the Utility Function

Properties of the utility function:

1 Utility is increasing (more is preferred to less)

dU(c, l)

dc> 0;

dU(c, l)

dl> 0

2 Concavity: each additional unit of consumption and leisure addsless utility(eating twice as much does not make you twice as happy)

d2U(c, l)

dc2< 0;

d2U(c, l)

dl2< 0

Important Implication: Households do not like risk.

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From U to Indifference Curves

• We look at 2 dimensional utility functions(HH cares about c AND l)

• How can we summarize preference? using indifference curves

Definition (indifference curve)

An Indifference curve is a curve connecting all values of consumptionand leisure among which the consumer is indifferent.

Slide 15 of 42

Indifference Curves

• Utility is increasing ⇒ Indifference curves are downward sloping

• HH like diversity ⇒ Indifference curves are convex

Question: can indifference curves cross each other?Slide 16 of 42

Household Constraints

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HH Constraints

In our economic model, HH have

• Limited amount of time available: let Ns be time working

l +Ns = 24 hours = h

Slide 18 of 42

HH Constraints

In the data what else we know about usage of time?

• Usage of time for American residents:http://tinyurl.com/usage-time

Slide 19 of 42

The Budget Constraint

• Limited disposable income: a budget constraint

Let:

• c = consumption

• h = time endowment

• l = leisure time

• w = hourly wage

• π = dividend income

• T = lump sum taxes (rebates)

c = w(h− l) + π − T

Question: How would you write an income tax?

Slide 20 of 42

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Transfer Income in the US

If T < 0 we call it a Transfer to the household. In the US the followingare the biggest source of transfers to the Households:

• Food Stamps:http://www.fns.usda.gov/pd/snapmain.htm

• Unemployment Insurance:http://www.ows.doleta.gov/unemploy/index.asp

• Disability Insurance:http://www.ssa.gov/disability/

• Temporary assistance for needy families (TANF):http://www.acf.hhs.gov/programs/ofa/

Slide 21 of 42

Unemployment Insurance

• Claims for unemployment insurance is a leading indicator:

Slide 22 of 42


• Wages determines the slope of the budget constraint.

• π and T determine the intercept.

Slide 23 of 42

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• Suppose now T < π: positive consumption even with no work

Slide 24 of 42

Consumer Maximization

Slide 25 of 42

Consumer Maximization

A consumption-leisure bundle is:

• Affordable if it lies on or within the budget set.

• Optimal if it is affordable and is on the highest indifference curve.

Slide 26 of 42

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Optimal and Sub-optimal Bundles

Only H is optimal!!

Slide 27 of 42

Consumer Maximization: Math!

The household problem:

maxc,l

U(c, l)

s.t. w(h− l) + π − T = c

Write the lagrangian:

L(c, l, λ) = U(c, l) + λ[w(h− l) + π − T − c]

where λ is our lagrange multiplier. First order conditions

(C) : Uc(c, l)− λ = 0

(l) : Ul(c, l)− wλ = 0

(λ) : w(h− l) + π − T − c = 0

Slide 28 of 42

Consumer Maximization: More Math!

Let’s substitute out λ from the two first order conditions:

Ul(c, l)− w · Uc(c, l) = 0

Ul(c, l)

Uc(c, l)= w

And what is Ul(c,l)Uc(c,l)?

⇒ Ul(c,l)Uc(c,l) = MRSl,c = w

Slide 29 of 42

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The Marginal Rate of Substitution

Definition (Marginal Rate of Substitution)

The marginal rate of substitution is the rate at which a consumer iswilling to give up one good in exchange for another good whilemaintaining the same level of utility.

• A consumption-leisure bundle is optimal when:

• Is on the budget line (Walras law)

• Slope of indifference curve = Slope of budge line

Which implies⇒ MRSl,c︸︷︷︸Marginal rate of substitution

= w

Slide 30 of 42

Choosing Unemployment

• Be careful with corner solutions!!Slide 31 of 42

Income and Substitution Effects

Slide 32 of 42

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Effect of changing parameters of the model (comparative static)can be decomposed in:

Definition

• Income Effect:The effect on quantities as a result of havingdifferent income holding prices constant.

• Substitution Effect:The effect on quantities given a price changeholding utility constant.

Slide 33 of 42

Income and Substitution Effects: Example

• Pure Income Effect: winning the lottery Ü

• Pure Substitution Effect: high wage only for 1 day Ü

• Income + Substitution Effect: permanent high wage Ü

Slide 34 of 42

Income and Substitution Effects: Example

• Pure Income Effect: winning the lottery Ü more leisure.

• Pure Substitution Effect: high wage only for 1 day Ü less leisure.

• Income + Substitution Effect: permanent high wage Ü leisure ?

Slide 35 of 42

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• Income Effect: more income Ü more leisure.

• Substitution Effect: higher wage Ü less leisure.

Note:

1 A higher wage (lower income tax) induces bothan income and substitution effect.

2 The overall effect is undetermined, we must proceed quantitatively.

Slide 36 of 42

Comparative Static: Changing π − T• Suppose π increases or T decreases.

• Since c and l are normal goodsÜ the richer you are the more you want

• So what happens when you give tax rebates??Slide 37 of 42

Comparative Static: Changing Wages

• Suppose your wage goes up.

• Remember: leisure is more expensive• In general this case features both income and

substitution effects Ü leisure changes are undetermined.Slide 38 of 42

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From One to Many Housholds

• So far we have studied problem of a single household.

• We need to compare aggregate quantities (GDP, C,...)and household decision (called ci and li in this slide)

• In Macro Economics the problem of going from one to manyhousehold is referred to as an: aggregation problem.

The Issue:

1 In the data we have household with disparate income levels.

2 In the data we have household with different tastes.

Slide 39 of 42

The Solution: Assumptions

Definition (Homogeneous of Degree One)

Homogeneous function of degree 1: if for all n ∈ R:

n · f(x) = f(n · x)

• Key assumptions:

1 Utility function is homogeneous of degree one.

2 Households have similar preferences.

Slide 40 of 42

Aggregation

We have:

N∑

i=1

maxci,li

ui(ci, li)⇒ N maxc,l

u(c, l)⇒ maxc,l

u(N · c︸︷︷︸C

, N · l︸︷︷︸L

)

• C = N · c: aggregate consumption;

• L = N · l: aggregate leisure.

Slide 41 of 42

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The High Income Household: Consuming

Q: How good is the assumption that ci is the same for everybody?(I.e how good is assumption about homogeneity?)

12% 1%

32%

3% 16%

5%

6%

15%

10%

High income households

Food Alcoholic beverages Housing

Apparel and services Transporta7on Healthcare

Entertainment Personal insurance and pensions Misc.

16%

1%

41% 5%

14%

8%

4%

2% 9%

Low income households

Food Alcoholic beverages Housing Apparel and services Transporta7on Healthcare Entertainment Personal insurance and pensions Misc.

A: Not too bad..Check your micro lectures for the notion of homotheticity/homogeneity

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Chapter 4

The Firm

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Suppose 10% of U.S. capital stock gets destroyed.How much will GDP decrease by?

Your answer here: http://tinyurl.com/73240-ales

Slide 2 of 31

Plan for this Lecture

1 The Firm

• Data: firms in the US

• The representative firm

• The production function

2 Firm maximization

Ü Calibrating the capital share: α

Note: with this lecture we finish Ch.4 - Review it!!

Slide 3 of 31

U.S. Firms: Data

How many businesses?

• Non-employers (firms with no payroll): 21,708,021(census data 2008)

• Employers (firms with payroll): (census data 2008)

Firms 6,022,127

Establishments 7,601,160

Employment 119,917,165

Source: http://www.census.gov/epcd/www/smallbus.html

Slide 4 of 31

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U.S. Firms: Size Distribution

What is the distribution of firm size?

Firm Sizes: Facts to Fantasies Axtell

3

II The Facts

In previous work (Axtell 2001) I have reported that the distribution

of U.S. firm sizes closely follows the Pareto distribution with exponent

near unity, i.e., the Zipf distribution.1 Noting the size of a firm by S, with

s referring to some specific size, the tail CDF of this distribution is

!

Pr S " s[ ] =s0

s

#

$ %

&

' (

)

, (1)

where s0 is the minimum size and ! is a parameter. This distribution is a

classical example of a power or scaling law. The empirical data for 1997

are shown binned as a PDF in figure 1 below, with size measured by

employees, along with a line having ! = 1.059.2

Figure 1: PDF of U.S. firm sizes, 1997 Economic Census data

Thee Zipfian character of this distribution is robust to alternative

definitions of firm size (e.g., firm receipts).

Data of such vast regularity are highly unusual in the social

sciences. Only at the extremes of the support do the data depart in any

systematic way from the distribution. Indeed, there are relatively too few

very small and very large firms in the data. Such deviations are often

1 The Zipf distribution is usually considered a discrete distribution; more on this below.2 The origin of these data are tax filings and, for reasons of confidentiality, only binneddata are available. The kinds of statistical procedures used on these data are thereforenot generally commensurate with other papers in this volume that analyze raw data.

(source: Robert Axtell)

• Look on the web for Zipf law!

• A firm over time: LINKSlide 5 of 31

U.S. Firms: Data

• Source: http://www.bea.gov/industry/• Look at behavior of Professional vs Manufacturing.

The Representative FirmAnd

The Production Function

Slide 7 of 31

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The Firm

• A firm converts inputs (factors of productions)into output (consumption goods)

• Goal of the firm: maximize profits

Assumptions:

1 Firms are very smart

2 They all have similar technology Ü exists a representative firm

3 They use only two factors of productions: capital and labor

4 Live 1 period (relaxed later in the course)

5 No financing issues (relaxed later in the course)

Slide 8 of 31


Let:

• Capital: K

• Labor employed: Nd

• Total Factor Productivity (TFP): z

• Output: Y

Ability of a firm to transform factors of production into output issummarized by the production function F

Y = zF (K,Nd)

Slide 9 of 31

Properties of the Production Function

1 F is increasing

dF (K,N)

dK> 0

dF (K,N)

dN> 0

2 F exhibits constant return to scale“Double the size double the output”

zF (xK, xNd) = xzF (K,Nd)

Note: This –as for the consumer– is key to study a representative firm

Note: decreasing (increasing) returns to scale

zF (xK, xNd) < (>) xzF (K,Nd)

Slide 10 of 31

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Marginal Products

• Marginal product of capital (labor) MPK (MPN ) is the additionaloutput produced by increasing capital (labor) by one unit,keeping fixed the other input.

Slide 11 of 31

Properties of the Production Function

Note: MPK = z dFdK and MPN = z dFdN

3 F is concave:• MPN decreases as N increases (alternatively d2F

dN2 < 0)

• MPK decreases as K increases (alternatively d2FdL2 < 0)

(Example: double the size of a study group)

4 MPN increases as capital increases:

(Example: buy a laptop for a student)

Slide 12 of 31

Example: TFP Shock

• Consider two economies 1 and 2 with z2 > z1

Why do we care? Think how wages change with technologySlide 13 of 31

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Very popular production function is the Cobb-Douglas

Y = zKα(Nd)(1−α)

With 0 < α < 1 (α =capital share). Examples:

• Kenya vs. U.S.zkenya < zU.S.

• U.S. (1776) vs. U.S. (2014)

z1776 < z2014

K1776 < K2014

α??

Question: what are α and z for the U.S. today?Slide 14 of 31

Firm Maximization

Slide 15 of 31

The Problem of the Firm

Some additional assumption:

1 The objective of a firm is to maximize profits.

2 A firm owns the capital(later we will introduce the investment decision.)

3 Firms takes the wage as given from the market.

4 No taxes in the baseline environment.

5 The firm sets the demand for labor: Nd.

Slide 16 of 31

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Profits

Let:

Revenue: zF (K,Nd)

Variable cost: wNd

Profits = π = zF (K,Nd) − wNd

The firm solves:

maxNd

zF (K,Nd) − wNd

Question: Why doesn’t the firm choose Nd VERY large?

Slide 17 of 31

Optimal Labor Choice

Choose Nd so that: MPN = w

Slide 18 of 31

Solution: Intuition

Suppose MPN > w

Ü Then raise Nd very little: revenue raise faster than the costs

Suppose MPN < w

Ü Then lower Nd very little: revenue decrease slower than the costs

In both cases we reach a contradiction so that the only alternative is:

MPN = w

Slide 19 of 31

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What is α?

Slide 20 of 31

Solution: Example

Useful property of a Cobb-Douglas production function:

MPN = z(1 − α)KαN1−αN−1

= (1 − α)zKαN1−αN−1

MPN = (1 − α)Y

N

+ We can relate MPN to output per worker N/Y .

Slide 21 of 31

The Labor Share of Income

We now calculate α from the data . Start from previous equation:

MPN = w = (1 − α)Y

N

Solve for 1 − α:

1 − α =wN

Y

Where:

1 wN is the compensation of employees

2 Y is GDP

+ Both can be obtained from the data!

Slide 22 of 31

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Calculating The Labor Share From Data

Remember the three ways to calculate Y ?

CONCEPTS AND METHODS OF THE U.S. NATIONAL INCOME AND PRODUCT ACCOUNTS

GDP and Other Major NIPA Measures

Three ways to measure GDP

In the NIPAs, GDP is defined as the market value of the final goods and services

produced by labor and property located in the United States. Conceptually, this measure

can be arrived at by three separate means: as the sum of goods and services sold to final

users, as the sum of income payments and other costs incurred in the production of goods

and services, and as the sum of the value added at each stage of production (chart 2.1).

Although these three ways of measuring GDP are conceptually the same, their calculation

may not result in identical estimates of GDP because of differences in data sources,

timing, and estimation techniques.

Chart 2.1—Three Ways to Measure GDP

Gross output

Less: Intermediate purchases

Personal consumption

expenditures

Equals: Gross value added

Compensation of employees

Gross private domestic fixed

investment

Taxes on production and

imports less subsidies

Change in private inventories

Net operating surplus

Government consumption

expenditures and gross investment

Consumption of fixed capital

Net exports

GDI The sum of income payments

and costs incurred in

production

Gross Value Added The sum of gross value

added—gross output less

intermediate purchases—

across all private industries

and government

= = GDP The sum of final

expenditures

1. As the sum of goods and services sold to final users. This measure, known as the

expenditures approach is used to identify the final goods and services purchased by

persons, businesses, governments, and foreigners. It is arrived at by summing the

following final expenditures components.

2-7

Let’s compute α from the BEA data: Table 2.1

Slide 23 of 31

Changes in Capital Stock and α

• At the beginning of class I asked you about the effect of a 10%decrease in the U.S. capital stock. The number provided isconnected with α.

• From Lecture 3 we have that:

Growth Rate of Yt = log(Yt+1) − log(Yt)

• In our example:

log(Yt) = zt + α log(Kt) + (1 − α) logNt

So that (if Nt and zt do not change)

Growth Rate of Yt = log(Yt+1) − log(Yt) = α · Growth Rate of Kt︸︷︷︸10%

Labor Demand

Slide 25 of 31

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U.S. Firm Data: Employment

• Source: http://www.bls.gov/web/cewbd/

Slide 26 of 31

Who Affects Un-Employment?

• Source: http://www.bls.gov/web/cewbd/

• Note how the recession unemployment due tocontractions rather than failures.

Slide 27 of 31

Solution of the Firm Problem

Consider F (K,N) = KαN1−α (notice: I removed the superscript D)

The firm solves:

maxN

π(N) = maxN

zKαN1−α − wN

To solve, take first order condition:

dπ

dN= z(1 − α)KαN−α − w = 0

Our optimality condition:

z(1 − α)

(K

N

)α

︸︷︷︸MPN

= w

Slide 28 of 31

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Labor Demand

• The firm problem provides the key equation that determines thedemand for labor:

N =

[z(1 − α)Kα

w

] 1α

• Comparative statics:

1 z increases Ü N increases

2 K increases Ü N increases

3 w increases Ü N decreases

Slide 29 of 31

Labor Demand: Exercise

• Labor Demand:

N =

[z(1 − α)Kα

w

] 1α

• Suppose K changes by 1%.

1 By how much should we expect N to change?

2 What key assumption are we making?

• Proceeding as before:

logNt =1

α

[log zt − logwt + log(1 − α) + α logKt

]

• Assume wt does not change.

• The growth rate of N depends 1:1 with growth rate of K.

Slide 30 of 31

Firm Problem: Other Examples

We can now study what happens if:

1 Government taxes revenues.

2 Government subsidizes employment.

3 Firm have a minimum firm size N .

Note these are partial equilibrium examples. What are we missing?

Slide 31 of 31

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Chapter 5

The Government

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The Government

Slide 3 of 41

The Government: Size

• Employed (2012) ⇒ Federal + State and Local : 21,973,000http://research.stlouisfed.org/fred2/series/USGOVT

• Government expenditures:

Slide 4 of 41

Governments Size Across Countries

Source: OECDSlide 5 of 41

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The Government

In our model the government is benevolent:

Ü maximizes welfare of its citizen

Question: why do we need a government?

It provides public goods:

• Schools, Police, Fire, Military

• Infrastructures

It corrects market failures:

• SEC, FTC, Retirement (?), CO2

Slide 6 of 41

The Government: Budget Constraint

Let G be the dollar value of the public goods. In a static world thebudget constraint is:

G = T

When we will look at dynamics we will have

G = T + ∆debt

Slide 7 of 41

Governments in Europe: Debt size

In 2012:

Slide 8 of 41

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The Government: Data

TH

E B

UD

GE

T F

OR

FISC

AL

YE

AR

2011153

Policy Outlays by Category

Other Mandatory Programs and Disaster Costs

Net InterestSecurity Discretionary

Non-Security Discretionary

Social SecurityMedicare

Medicaid

Policy Revenues by Source

Borrowing and Other Net Financing

Social Security

Payroll Taxes

Excise Taxes

Corporation Income Taxes

Unemployment InsuranceMedicare Payroll Taxes

Individual Income Taxes

Other Receipts

2011 2011

2015 2015


Social Security

Payroll Taxes

Excise Taxes



Medicare Payroll Taxes


Other ReceiptsSecurity DiscretionaryNon-Security Discretionary

Social Security

Medicare Medicaid

Net Interest


Source: U.S budget 2011

• Current Budget: LINK

• Historical data: LINK

Slide 9 of 41


• Static government budget constraint is:

G = T

• Taxes T also appear in the household budget constraint:

C = wN + π − T

• In the data from where does the government draws revenue?

Slide 10 of 41

The Government: Data

TH

E B

UD

GE

T F

OR

FISC

AL

YE

AR

2011153

Policy Outlays by Category


Net InterestSecurity Discretionary

Non-Security Discretionary

Social SecurityMedicare

Medicaid

Policy Revenues by Source


Social Security

Payroll Taxes

Excise Taxes


Unemployment InsuranceMedicare Payroll Taxes


Other Receipts

2011 2011

2015 2015


Social Security

Payroll Taxes

Excise Taxes



Medicare Payroll Taxes


Other ReceiptsSecurity DiscretionaryNon-Security Discretionary

Social Security

Medicare Medicaid

Net Interest


Source: U.S budget 2011

Slide 11 of 41

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The impact of Government policy on HH and Firm:

• τy: income tax (appears in HH budget constraint)

C = (1− τy)wN s + π − T

• τc: tax on consumption (appears in HH budget constraint)

(1 + τc)C = wN s + π − T

• τr: tax on revenues (appears in firm profits)

Y = (1− τr)zF (k,Nd)− wNd

Slide 12 of 41

Who Pays Income Tax?

Source:http://www.cbo.gov/publications/collections/tax/2010/graphics.cfm

Slide 13 of 41

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Chapter 6

Equilibrium

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Competitive Equilibrium

Slide 14 of 41

Why do we Need an Equilibrium Concept

Example of equilibrium fallacy:

Here is a great way to warm up the house: On Dec 1st turn the heatingup to 70. Once the house gets to 70. Turn them off for the rest of thewinter, that’s it the house will remain at 70. We might need to turn ACON on May 1st...

Slide 15 of 41

Why do we Need an Equilibrium Concept

Some potential fallacies:

• Suppose government consumption (G) Increases by 20%

Ü what happens to C and I?

• Suppose government subsidizes employment?

Ü what happens to wages?

Slide 16 of 41

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A Note on Aggregation

Remember:

• Our consumer is a representative consumer: it represents ALLof the consumers in the US

• Our firm is a representative firm: it represents ALLof the firms in the US

Slide 17 of 41

Equilibrium

The idea:

1 Set some external conditions(exogenous variables)

2 Determine what happens to all of the other variables of interests(endogenous variables)

In our static model:

1 Exogenous variables: (K,G, z)

2 Endogenous variables: (C,N s, Nd, T, Y, w)

Notation: Nd = labor demanded; N s = labor supplied

Slide 18 of 41

Equilibrium

How do we know what is going to happen?

1 Must be optimal:

Ü everybody (household and firm) must like the decisionit has taken.

2 Must be feasible:

Ü cannot have more consumption than goods produced.

Slide 19 of 41

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Competitive Equilibrium: Static

Definition (Competitie Equilibrium)

For a set of exogenous variables (K,G, z) A competitive equilibrium is aset of endogenous variables (C,N s, Nd, T, Y, w), so that:

1 The consumer chooses C (consumption) and NS (labor supply)optimally, taking as given w (wage), T (taxes), π (dividends)

2 The firm chooses Nd (labor demand) to maximize profits, taking asgiven w (wage), K (capital stock), z (productivity)

+ Turn to next page...

Slide 20 of 41

Competitive Equilibrium: Static

Definition (Competitie Equilibrium (continued))

[...] continued:

3 Government balances the budget: G = T

4 Labor market clears: Nd = N s

5 Goods market clears: Y = C +G

Question: nice definition, but does it exist?

Answer: YES! (take my word, or better take theirs nobelprize.org)

Slide 21 of 41

Working With the Model

Next step is to characterize the equilibrium:

• Our first approach: find a graphical summary representation

Ü The production possibility frontier (PPF)

• Then: characterize equilibrium by solving system of nonlinearequations.

Slide 22 of 41

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Working With the Model

Derive a relation (production possibility frontier - PPF) so that given(K,G, z) we can determine all the feasible (C, l) pairs

Y = zF (K,Nd)

since market clear Nd = N s:

Y = zF (K,N s)

substitute feasibility of hours of household: N s = h− l

Y = zF (K,h− l)substitute the goods market clearing: Y = C +G

C = zF (K,h− l)−G

Slide 23 of 41

The Production Possibilities Frontier

Some properties of the PPF:

C(l) = zF (K,h− l)−G

1 Equilibrium consumption decreasing in leisure: dC(l)dl = −z dF ()

dN < 0

2 Decreasing returns - PPF is concave: d2C(l)dl2

< 0

Slide 24 of 41

The Production Possibilities Frontier

Slide 25 of 41

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The Marginal Rate of Transformation

Minus the slope of the PPF is the marginal rate of transformation

C(l) = zF (K,h− l)−Gthis implies

MRTl,C = −dC(l)

dl= z

dF (k, h− l)dN

= MPN

or in words:

Marginal rate of transformation = marginal product of labor

Ü for any (C, l) on the PPF we can find the wage!

Slide 26 of 41

Moving Towards the Competitive Equilibrium

To the production possibilities frontier we need to add:

1 Add the household’s budget constraint C = w(h− l) + π − T

Ü Find the slope: done

Ü Find the intercept: in appendix

2 Add indifference curves.

Slide 27 of 41

The Competitive Equilibrium

D'

Slide 28 of 41

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The Competitive Equilibrium

Algorithm to find a Competitive Equilibrium:

1 Find the values of capital (K), government expenditures (G) andproductivity (z): these are the exogenous variables.

2 Given exogenous variables determine PPF,

3 Find point of tangency between PPF and preferences,

4 Recover endogenous variables (C,N s, Nd, T, Y, w).

5 Use the constructed equilibrium to determine relationship betweenexogenous and endogenous variables: Ü comparative statics.

Slide 29 of 41

APPENDIX: Adding The Consumer

We show that the segments ADB constitute the budget constraint

Step 1: segment AD has slope −wStep 2: Need to show that segment DB is of length π − T

To see this note that

• Segment D′D has length h− l∗ = N∗

• So that segment JD′ has length wN∗

• Since J is at hight equal to C∗ it follows that

DB = J − JD′

DB = C∗ − wN∗ = π − T

Slide 30 of 41

Online Survey!

Q: Suppose the government increases expenditures by ∆G.What happens to GDP

A: Your answer here: http://tinyurl.com/73240-ales

1 Increases by more than ∆G

2 Increases by ∆G

3 Increases by less than ∆G

Slide 31 of 41

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Examples

Slide 32 of 41

Examples

We are going to consider the following two exogenous changes:

1 Changes in government expenditures: G.

2 Changes in productivity: z.

Slide 33 of 41

Government Spending

Suppose the government increases its expenditure : ∆G > 0

Slide 34 of 41

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Government Spending

Suppose the government increases its expenditure : ∆G = G2 −G1 > 0

1 Balanced budget Ü if G2 > G1 then T2 > T1;

2 Reduces household’s disposable income Ü C2 < C1 and l2 < l1;

3 Increase in equilibrium hours worked: N2 > N1 implies Y2 > Y1.

Question 1: ∆C vs. ∆G?

Question 2: what has happened to the real wage?

Question 3: does GDP increase?

Question 4: does the household prefer the increase in G?

Slide 35 of 41

The effects of government spending: DATA

Suppose the government increases its expenditure : ∆G > 0

Slide 36 of 41

Testing the prediction of the model: ∆G

• Look at the relation between ∆G and ∆C(we expect a negative correlation)

• Look at the relation between ∆G and ∆N(we expect a positive correlation)

For G and C we use NIPA table 1.1.6:http://www.bea.gov/

For N we use FRED:http://research.stlouisfed.org/fred2/series/CE16OV?cid=12

Slide 37 of 41

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Changes in TFP

Suppose there is an increase in TFP: ∆z > 0

Slide 38 of 41

Changes in TFP

Summarizing:

1 z1 ⇒ z2 with z2 > z1

2 Wage increases w2 > w1

3 Consumption increases C1 ⇒ C2

4 Hours worked? depends on Income and Substitution effects

Slide 39 of 41

Separating Income and Substitution Effects

PPF3 is PPF2 adjusting the income of the HH so that it’s indifferentbetween new and old equilibrium

Slide 40 of 41

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Testing the prediction of the model: ∆z

• Look at the relation between ∆z and ∆C(we expect a positive correlation)

• Look at the relation between ∆z and ∆N(we expect a positive correlation)

For G and C we use NIPA table 1.1.6:http://www.bea.gov/

For N we use FRED:http://research.stlouisfed.org/fred2/series/CE16OV?cid=12

For K use Private nonresidential fixed assets:line 1 of Table 4.1 of the NIPA fixed asset tables:http://www.bea.gov/national/FA2004SelectTable.asp

Slide 41 of 41

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Chapter 7

Optimality

104 of 260

Efficiency: Pareto Optimality

Slide 4 of 39

Efficiency

Idea:

• Up to now we showed what is going to happen in equilibrium.

• Now we determine what should happen in equilibrium.

Why do we care? Think about a role for the government.

Slide 5 of 39

Definition

Pareto Optimality

An equilibrium is Pareto optimal if there is no rearrangement ofproduction or consumption that makes the consumer better off.

The Pareto optimum is chosen by a social planner that:

1 Allocates factors to production, consumption and leisureto maximize the utility of the household.

2 Does not use markets.

3 Is only subject to feasibility.

Slide 6 of 39

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The Planner Problem

The planner solvesmaxC,l

U(C, l)

subject toC = zF (k, h− l)−G

Optimality implies:

zFN (k, h− l) =UL(C, l)

UC(C, l)

C = zF (k, h− l)−G

Those equations also characterize a competitive equilibrium, so...

Slide 7 of 39

Pareto Optimality

Theorem

First Welfare Theorem First welfare theorem: a competitive equilibriumis Pareto optimal.

Slide 8 of 39

The First Welfare Theorem

A.k.a: why do we like markets so much

• Competitive markets achieves the optimal allocation⇒ It seems that government are at best useless.

• However, how many assumptions did we use to get here?⇒ Government might have a role after all.

• When do we fail to have Pareto optimality?

1 Externalities (pollution)

2 Missing markets (financing frictions, moral hazard)

3 Non competitive firms

Slide 9 of 39

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Pareto Optimality

Theorem (Second Welfare Theorem)

Second welfare theorem: a Pareto optimum is a competitive equilibrium

This last theorem would not be so obvious if you had two typesof consumers.

Slide 10 of 39

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7.1 Optimal Taxation

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Optimal Taxation

Slide 11 of 39

Optimal Taxation

1 General Principles

2 Distortionary effects of taxation

3 Optimal taxes at the top

4 The Laffer Curve

Great Source for Data:http://www.taxpolicycenter.org/taxfacts/

Let’s begin with an example:http://users.nber.org/ taxsim/taxsim-calc9/index.html

Slide 12 of 39

Federal Taxes

What is the profile of taxes in the data?

2. Federal Average Tax Rates by Income Groups (individual+corporate+payroll+estate taxes)

0%

10%

20%

30%

40%

50%

60%

70%

80%

P0-2

0

P20-

40

P40-

60

P60-

80

P80-

90

P90-

95

P95-

99

P99-

99.5

P99.

5-99

.9

P99.

9-99

.99

P99.

99-1

00

1970

2000

2005

Source: Piketty and Saez JEP'07Source: Piketty and Saez (2007)

Note: Missing State and Local and FICA.Slide 13 of 39

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Optimal Taxation

• In the rest of the lecture we will study marginal taxes on income.

• Let’s be concrete:

c = (1− τ︸︷︷︸tax rate

(z)) · w · (h− l)︸︷︷︸pretax income = z

+π

The tax rate τ(z) depends on labor income z.

• Some definitions:

1 Tax liability τ(z) · z.2 Marginal Tax Rate (MTR). The idea: MTR tells me what fraction

of one more dollar earned do I “take home”.

MTR = τ ′(z).

Slide 14 of 39

Optimal Taxation

Definition (Progressive/Regressive Tax System)

A Tax system is progressive (regressive) if the Marginal Tax Rate isincreasing (decreasing) in income: τ ′(z) increasing (decreasing) in z.

+ A Progressive tax system reduces after tax income inequality.

Slide 15 of 39

Marginal Rates

Is The U.S Federal Tax Code Progressive of Regressive ?

7-Feb-14

2014 Individual Income Tax Rates, Standard Deductions,Personal Exemptions, and Filing Thresholds

But not But not Over --- over --- Over --- over ---

$0 $9,075 10% $0 $18,150 10%$9,075 $36,900 15% $18,150 $73,800 15%

$36,900 $89,350 25% $73,800 $148,850 25%$89,350 $186,350 28% $148,850 $226,850 28%

$186,350 $405,100 33% $226,850 $405,100 33%$405,100 $406,750 35% $405,100 $457,600 35%$406,750 and over 39.6% $457,600 and over 39.6%

But not But not Over --- over --- Over --- over ---

$0 $12,950 10% $0 $9,075 10%$12,950 $49,400 15% $9,075 $36,900 15%$49,400 $127,550 25% $36,900 $74,425 25%

$127,550 $206,600 28% $74,425 $113,425 28%$206,600 $405,100 33% $113,425 $202,550 33%$405,100 $432,200 35% $202,550 $228,800 35%$432,200 and over 39.6% $228,800 and over 39.6%

Standard Deduction Standard Deduction for DependentsStandard Blind/Elderly

Single $6,200 $1,550 Married filing

jointly $12,400 $1,200 Personal Exemption $3,950Head of

Household $9,100 $1,550 Married filing

separately $6,200 $1,200 $3,000

Filing ThresholdNumber of Blind / Elderly Exemptions

0 1 2 3 4Single 10,150 11,700 13,250Head of Household 13,050 14,600 16,150Married filing jointly 20,300 21,500 22,700 23,900 25,100

Source: Internal Revenue Service, Revenue Procedure 2013-35, downloaded February 7, 2014 from http://www.irs.gov/pub/irs-drop/rp-13-35.pdf

Greater of $1000 or sum of $350 and individual's earned income

Threshold for Refundable Child Tax Credit

If your filing status is Head of HouseholdIf your filing status is Married filing separately

Taxable Income Taxable Income

Marginal Rate Marginal Rate

If your filing status is Single If your filing status is Married filing jointlyTaxable Income Taxable Income

Marginal Rate Marginal Rate

Source: IRS (2014)

Slide 16 of 39

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Optimal Taxation

Why does the government use proportional taxes?

• Easy to administer.

• Allows for redistribution of resources (progressive vs. regressive)

A major downside:

• Are taxes efficient? Do the welfare theorems hold?

Slide 17 of 39

The Distortionary Effects of Taxation

• Government expenditure is to be financed through tax τ

• Does the first welfare theorem hold?

• The Household’s maximization problem is now:

maxc,l

u(c, l) + λ [(1− τ)w(h− l) + π − c]︸︷︷︸Budget Constraint

Slide 18 of 39

The Distortionary Effects of Taxation

Optimality conditions for the household:

(C) : Uc(c, l)− λ = 0

(l) : Ul(c, l)− λ(1− τ)w = 0

(λ) : (1− τ)w(h− l) + π − c = 0

So thatUl(c, l)

Uc(v, l)= (1− τ)w

Substituting

MRSl,c = (1− τ)MPN ⇒MRSl,c < MPN

The competitive equilibrium is not Pareto optimal!

Slide 19 of 39

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Optimal Taxation

Why does the government use proportional taxes?

• Easy to administer.

• Allows for redistribution of resources (progressive vs. regressive)

A major downside:

• Are taxes efficient? Do the welfare theorems hold?

+ The answer to both questions is NO! Proportional taxes shouldthen be used in “moderation”.

Slide 20 of 39

What Should Taxes Be?

Slide 21 of 39

An Utopian Goal

• Suppose there are N individuals with incomes z1 < z2 < . . . < zN

• Suppose the government cares equally about all of them.Social welfare is:

W =

N∑

i=1

u(ci), s.t. ci = (1− τ(zi))zi.

and subject to government budget constraint:

N∑

i=1

τ(zi)zi = G.

Where ci is consumption and τ(·) are taxes on zi.

• What should taxes be?Slide 22 of 39

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An Utopian Goal: Optimal Taxation

• Planning Problem choose taxes to maximize welfare :

maxτ(zi)

N∑

i=1

u((1− τ(zi))zi), s.t.

N∑

i=1

τ(zi)zi = G

• What should taxes be?

• From first order conditions (λ multiplier on budget constraint)

u′((1− τ(zi))zi) = λ

The above implies that for all i and j:

(1− τ(zi))zi = (1− τ(zj))zj

+ Full redistribution. What is the problem with this?

Slide 23 of 39

General Principles

• What are the tradeoffs for choosing taxes?

1 Equity Considerations.

+ For example the relative welfare weights of top earners v.s. therest.

2 Efficiency Considerations.

+ Behavioral responses from high taxes.

Slide 24 of 39

Behavioral Effects

In Data do we observe behavioral responses from taxation?

Source: Prescott (2004)Slide 25 of 39

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Ok...but what Should Taxes Be?

Slide 26 of 39

Taking Stock

Some lessons learned from optimal taxation:

1 In the U.S. and most countries taxes on income are proportional.(sometimes referred as marginal taxes)

2 The U.S. tax system is in most part progressive.

3 Proportional taxes make the equilibrium inefficient.

4 If we ignore individual responses, then optimal taxes should becompletely redistributive.

Slide 27 of 39

Tax Reform

• The goal is to now derive a simple formula for optimal taxes.

• A “Tax Reform”: suppose the government increases taxesby ∆τ on individual earning more than z∗.

• What happens to revenues? how do tax payer respond?

Definition (“e”)

Elasticity of reported income with respect to the net-of-tax rate 1− τ .

e =1− τz

dz

d(1− τ)

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Online Survey!

Q: In your opinion what is a reasonable value for “e”.That is, if taxes go up by 1% by how much would yourincome go down by?


Slide 29 of 39

Tax Reform

• Any individual with income z > z∗ changes taxes paid by:

Benefit + ∆τ(z − z∗).

• Due to behavioral responses income changes by:

Cost + τ∆z = −∆τ · e · z · τ

1− τ .

• Combining the two effects so that cost and benefit are zero:

∆τ

[(z − z∗)− e · z · τ

1− τ

]= 0

Slide 30 of 39

Tax Reform

31

Disposable Incomec=z-T(z)

Pre-tax income zz*

z*-T(z*)

0

Mechanical tax increase:'W[z-z*]

Behavioral response tax loss: W 'z = - 'W e z W/(1-W)

z

Top bracket: slope 1-W above z* Reform: slope 1-W�'W�above z*

Figure 1 Optimal Top Tax Rate Derivation Note. The figure depicts the derivation of the optimal top tax rate W*=1/(1+a e) by considering a small reform around the optimum which increases the top marginal tax rate W by 'W above z*. A taxpayer with income z mechanically pays dW [z-z*] extra taxes but, by definition of the elasticity e of earnings with respect to the net-of-tax rate 1-W, also reduces his income by 'z=e z 'W/(1-W) leading to a loss in tax revenue equal 'W e z W/(1-W). Summing across all top bracket taxpayers and denoting by zm the average income above z* and a=zm/(zm-z*)), we obtain the revenue maximizing tax rate W*=1/(1+a e). This is the optimum tax rate when the government sets zero marginal welfare weights on top income earners.

Source: Diamond, Saez (2011)

Slide 31 of 39

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Tax Reform

• Combining the two effects so that cost and benefit are zero

∆τ

[(z − z∗)− e · z · τ

1− τ

]= 0

Algebra...1− ττ

=e · zz − z∗

Let a = z/z − z∗, more algebra...

τ =1

1 + a · e

Slide 32 of 39

Tax Reform: A formula

Definition (“e”)

Elasticity of reported income with respect to the net-of-tax rate 1− τ .

e =1− τz

dz

d(1− τ)

• Balancing the tax increase and behavioral response we get:

τ =1

1 + a · e

• The value of a = 1.5 is not controversial(connected with the Pareto distribution of income).

• The values of e is controversial (estimates range from 0.25 to 2).

• Taxes ranges from ?? to ??

Back To a “Simple” Case

Slide 34 of 39

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Optimal Taxation: Maximizing Revenue

We now simplify the analysis assuming everybody is the same andgovernment wishes to maximize revenue.

• Household preferences: U(c, l) = log(v) + log(l)

• Household budget constraint: c = (1− τ) · w · (h− l) + π

• Assume F (K,N) = zN ⇒ wages are fixed!

Government revenues are

R(τ) = τ · w · (h− l)

Suppose the government has the goal of maximizing revenues.

Slide 35 of 39


• From first order conditions of households we get

c = (1− τ) · w · l

• Substituting the above in the budget constraint

wl =wh

2+

π

2(1− τ)

• Substituting the above in the expression for revenues R(τ) we get

R(τ) = τwh− τwl⇒ τhw

2− τ

1− τπ

2

Slide 36 of 39


• Revenues:

R(τ) =τhw

2− τ

1− τπ

2

• The objective of the government can be written as

Set τ so that R(τ) = G

• Note that R(0) = R(1) = 0... must be curved!

• R(τ) is also called in a different way:

+ http://www.youtube.com/watch?v=dxPVyieptwA

Slide 37 of 39

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The Laffer Curve

R(τ) =τhw

2− τ

1− τπ

2

• KEY: besides the maximum revenue there are alwaystwo tax rates that provide the same revenue.

• Since tax are distortionary is alwaysbetter to choose a small τ .

Slide 38 of 39

Taking Stock

Some lessons learned from optimal taxation:

1 In the U.S. and most countries taxes on income are proportional.(sometimes referred as marginal taxes)

2 The U.S. tax system is in most part progressive.

3 Proportional taxes make the equilibrium inefficient.

4 If we ignore individual responses, then optimal taxes should becompletely redistributive.

5 Quantitatively taxes at the top should be fairly high!

6 But not so high as being on the “wrong side” of the Laffer Curve.

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Chapter 8

Growth

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Income Per Capita Across Countries

In 2008:

Slide 4 of 32

Income Per Capita Over Time

As a histogram:

Density of countries

1960

1980

2000

6 8 10 12 Log GDP per capita

FIGURE 1.2 Estimates of the distribution of countries according to log GDP per capita (PPP adjusted) in 1960, 1980, and 2000.

Density of countries (weighted by population)

1960

1980

2000

6 8 10 12 Log GDP per capita

FIGURE 1.3 Estimates of the population-weighted distribution of countries according to log GDP per capita (PPP adjusted) in 1960, 1980, and 2000.

Source: Acemoglu (2008).Slide 5 of 32


How did we get there:1.4 Today’s Income Differences and World Economic Growth . 11

Log GDP per capita

United States

United Kingdom

Spain

Singapore Brazil

South Korea

Botswana

Guatemala

Nigeria

India

7

8

9

10

11

1960 1970 1980 1990 2000

FIGURE 1.8 The evolution of income per capita in the United States, the United Kingdom, Spain, Singapore, Brazil, Guatemala, South Korea, Botswana, Nigeria, and India, 1960–2000.

40 years? Why did Spain grow relatively rapidly for about 20 years but then slow down? Why did Brazil and Guatemala stagnate during the 1980s? What is responsible for the disastrous growth performance of Nigeria?

1.4 Origins of Today’s Income Differences and World Economic Growth

The growth rate differences shown in Figures 1.7 and 1.8 are interesting in their own right and could also be, in principle, responsible for the large differences in income per capita we observe today. But are they? The answer is largely no. Figure 1.8 shows that in 1960 there was already a very large gap between the United States on the one hand and India and Nigeria on the other.

This pattern can be seen more easily in Figure 1.9, which plots log GDP per worker in 2000 versus log GDP per capita in 1960 (in both cases relative to the U.S. value) superimposed over the 45! line. Most observations are around the 45! line, indicating that the relative ranking of countries has changed little between 1960 and 2000. Thus the origins of the very large income differences across nations are not to be found in the postwar era. There are striking growth differences during the postwar era, but the evidence presented so far suggests that world income distribution has been more or less stable, with a slight tendency toward becoming more unequal.

Source: Acemoglu (2008).

Slide 6 of 32

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Growth In the Last 35 Years

• Existence of large and sustained growth:(recall the 2% per year for the US)

• Existence of growth miracles:(South Korea, Singapore, Japan)

• Existence of growth disasters:(Venezuela, Norh Korea, Most of South Saharan Africa)

Slide 7 of 32

Modern Growth Rates

The distribution of growth rates:.10 Chapter 1 Economic Growth and Economic Development: The Questions

Density of countries

19601980

2000

–0.1 0.0 0.1 0.2 Average growth rate of GDP per worker

FIGURE 1.7 Estimates of the distribution of countries according to the growth rate of GDP per worker (PPP adjusted) in 1960, 1980, and 2000.

grows rapidly, and by the mid-1990s it has become richer than both. South Korea has a similar trajectory, though it starts out poorer than Singapore and grows slightly less rapidly, so that by the end of the sample it is still a little poorer than Spain. The other country that has grown very rapidly is the “African success story” Botswana, which was extremely poor at the beginning of the sample. Its rapid growth, especially after 1970, has taken Botswana to the ranks of the middle-income countries by 2000.

The two Latin American countries in this picture, Brazil and Guatemala, illustrate the often-discussed Latin American economic malaise of the postwar era. Brazil starts out richer than South Korea and Botswana and has a relatively rapid growth rate between 1960 and 1980. But it experiences stagnation from 1980 on, so that by the end of the sample South Korea and Botswana have become richer than Brazil. Guatemala’s experience is similar but even more bleak. Contrary to Brazil, there is little growth in Guatemala between 1960 and 1980 and no growth between 1980 and 2000.

Finally, Nigeria and India start out at similar levels of income per capita as Botswana but experience little growth until the 1980s. Starting in 1980, the Indian economy experiences relatively rapid growth, though this has not been sufficient for its income per capita to catch up with the other nations in the figure. Finally, Nigeria, in a pattern that is unfortunately all too familiar in sub-Saharan Africa, experiences a contraction of its GDP per capita, so that in 2000 it is in fact poorer than it was in 1960.

The patterns shown in Figure 1.8 are what we would like to understand and explain. Why is the United States richer in 1960 than other nations and able to grow at a steady pace thereafter? How did Singapore, South Korea, and Botswana manage to grow at a relatively rapid pace for


A Useful Formula

• How to visualize growth rates more directly?

• Let’s determine the time to double in size. Recall:

xt = x0eγt

where γ is the growth rate (not in %).

• Let T the time required to go from x0 → 2x0

2x0 = x0eγT ⇒ T =

ln 2

γ

• Also know as rule of 70:

T =ln 2

γ≈ .7

γ≈ 70

γ%

Where γ% is now in percentage terms

Slide 9 of 32

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Modern Growth Rates

The distribution of growth rates:

Slide 10 of 32

Historical Growth

Slide 11 of 32


How did we get there:.14 Chapter 1 Economic Growth and Economic Development: The Questions

Log GDP per capita

Western offshoots

Western Europe

Africa

Asia

Latin America

6

7

8

9

10

1000 1200 1400 1600 1800 2000

FIGURE 1.11 The evolution of average GDP per capita in Western offshoots, Western Europe, Latin America, Asia, and Africa, 1000–2000.

terms “takeoff” or “industrial revolution.” This debate is again secondary to our purposes. Whether or not the change was discontinuous, it was present and transformed the functioning of many economies. As a result of this transformation, the stagnant or slowly growing economies of Europe embarked upon a path of sustained growth. The origins of today’s riches and also of today’s differences in prosperity are to be found in this pattern of takeoff during the nineteenth century. In the same time that Western Europe and its offshoots grew rapidly, much of the rest of the world did not experience a comparable takeoff (or did so much later). Therefore an understanding of modern economic growth and current cross-country income differences ultimately necessitates an inquiry into the causes of why the takeoff occurred, why it did so about 200 years ago, and why it took place only in some areas and not in others.

Figure 1.12 shows the evolution of income per capita for the United States, the United Kingdom, Spain, Brazil, China, India, and Ghana. This figure confirms the patterns shown in Figure 1.10 for averages, with the United States, the United Kingdom, and Spain growing much faster than India and Ghana throughout, and also much faster than Brazil and China except during the growth spurts experienced by these two countries.

Overall, on the basis of the available information we can conclude that the origins of the current cross-country differences in income per capita are in the nineteenth and early twentieth centuries (or perhaps even during the late eighteenth century). This cross-country divergence took place at the same time as a number of countries in the world “took off” and achieved sustained economic growth. Therefore understanding the origins of modern economic growth are not only interesting and important in their own right, but also holds the key to understanding the causes of cross-country differences in income per capita today.


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Growth Before 1800

What happened before 1800?

• Growth Was Slow! World GDP growth was:

1 Between 1700-1820: 0.07%

2 Between 1500-1700: 0.04%

• Long-term cycles.

• Huge changes in relative rankings (Rome, China, Incas, Haiti).

• Little difference between countries:(Rich to poor ratio ≈ 2)

Slide 13 of 32

Taking Stock

• So far the following questions have emerged:

1 How can some countries sustain stable growth?

2 Why do some country go much faster than others?

3 Why are some countries not growing?

4 Why was the world not growing before the 19th century?

Question for review:

• Is the World accelerating?

• Is there a Widening gap between rich and poor?

Slide 14 of 32

What Determines Growth?

Slide 15 of 32

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• First step find the data!

• Great sources:

1 Penn World Tables:https://pwt.sas.upenn.edu/php site/pwt71/pwt71 form.php

2 IMF World Economic Outlook Database:http://www.imf.org/external/pubs/ft/weo/2013/02/weodata/index.aspx

Slide 16 of 32


We need a model, but what matters? what should we model?

Investment is positively correlated with GDP levels.

Slide 17 of 32


More on investment:

.18 Chapter 1 Economic Growth and Economic Development: The Questions

1.6 Correlates of Economic Growth

The previous section emphasized the importance of certain country characteristics that might be related to the process of economic growth. What types of countries grow more rapidly? Ideally, this question should be answered at a causal level. In other words, we would like to know which specific characteristics of countries (including their policies and institutions) have a causal effect on growth. “Causal effect” refers to the answer to the following counterfactual thought experiment: if, all else being equal, a particular characteristic of the country were changed exogenously (i.e., not as part of equilibrium dynamics or in response to a change in other observable or unobservable variables), what would be the effect on equilibrium growth? Answering such causal questions is quite challenging, precisely because it is difficult to isolate changes in endogenous variables that are not driven by equilibrium dynamics or by omitted factors.

For this reason, let us start with the more modest question of what factors correlate with postwar economic growth. With an eye to the theories to come in the next two chapters, the two obvious candidates to look at are investments in physical and human capital (education).

Figure 1.15 shows a positive association between the average investment to GDP ratio and economic growth between 1960 and 2000. Figure 1.16 shows a positive correlation between average years of schooling and economic growth. These figures therefore suggest that the countries that have grown faster are typically those that have invested more in physical and human capital. It has to be stressed that these figures do not imply that physical or human capital investment are the causes of economic growth (even though we expect from basic economic theory that they should contribute to growth). So far these are simply correlations, and they

Average growth rate of GDP per capita, 1960–2000

ARG

AUS

AUT BEL

BEN

BOL

BRA

BFA

CANCHL

CHN

COL CRI

DNK

DOM

ECU

EGY

SLV

ETH

FINFRA

GHA

GRC

GTM

GIN

HND

ISLIND

IRN

IRL

ISRITA

JAM

JPN

JOR

KEN

KOR

LUX

MWI

MYS

MUS

MEX

MAR NLD

NZL

NIC

NGA

NOR

PAK

PAN

PRY

PER

PHL

PRT

ZAF

ESP

LKA

SW E

CHE

TWN

THA

TTO TUR

UGA

GBR USA

URY

VENZMB

ZWE

0.00

0.02

0.04

0.06

0.08

0.0 0.1 0.2 0.3 0.4 Average investment rate, 1960–2000

FIGURE 1.15 The relationship between average growth of GDP per capita and average growth of investments to GDP ratio, 1960–2000.

Source: Acemoglu (2008)Slide 18 of 32

124 of 260


Population growth?

Population growth is negatively correlated with GDP levels.

Slide 19 of 32


Levels of GDP?

Levels of GDP are not correlated with GDP growth rates.

Slide 20 of 32


Schooling 1.7 From Correlates to Fundamental Causes . 19


0.06

0.04

0.02

0.00

–0.02

TWN

CHN

RWA

KOR

HKG THAMYS

SGP IRL JPN

LKA

EGY IDN

PAK GHA LSO IND

PRT

SYR

TUN TUR MUS

ESP

ITA

PAN FRA

GRC AUT

BEL FIN NORISR

BDI

BEN

MLIGMBMOZ

NPL

SLV BOL PER

MWI BRA

CMR ZAF COG

ZWE COL MEXECU

UGADZA CRI

DOM

GTM

HND

IRN

TGO KEN ZMBJAM

PRY

ARG

CHL

ISL

PHLTTO URY BRB

NLD GBR

AUS CAN

CHE

DNK SWE

NZL

USA

SEN VEN

JOR NER

NIC

0 2 4 6 8 10 12 Average years of schooling, 1960–2000

FIGURE 1.16 The relationship between average growth of GDP per capita and average years of schooling, 1960–2000.

are likely driven, at least in part, by omitted factors affecting both investment and schooling on the one hand and economic growth on the other.

We investigate the role of physical and human capital in economic growth further in Chapter 3. One of the major points that emerges from the analysis in Chapter 3 is that focusing only on physical and human capital is not sufficient. Both to understand the process of sustained economic growth and to account for large cross-country differences in income, we also need to understand why societies differ in the efficiency with which they use their physical and human capital. Economists normally use the shorthand expression “technology” to capture factors other than physical and human capital that affect economic growth and performance. It is therefore important to remember that variations in technology across countries include not only differences in production techniques and in the quality of machines used in production but also disparities in productive efficiency (see in particular Chapter 21 on differences in productive efficiency resulting from the organization of markets and from market failures). A detailed study of technology (broadly construed) is necessary for understanding both the worldwide process of economic growth and cross-country differences. The role of technology in economic growth is investigated in Chapter 3 and later chapters.

1.7 From Correlates to Fundamental Causes

The correlates of economic growth, such as physical capital, human capital, and technology, is our first topic of study. But these are only proximate causes of economic growth and economic success (even if we convince ourselves that there is an element of causality in the correlations

Schooling levels are positively correlated with GDP growth rates.Slide 21 of 32

125 of 260


This is why we need a model!!! Latitude is positively correlatedwith GDP levels and growth rates!

Slide 22 of 32

Welfare And Inequality

Slide 23 of 32

Growth and Welfare

• Does growth Increase Welfare?

• Economists define welfare as the expected lifetime utility for allindividuals in a country.

• To make things simple suppose that welfare depends on:(i) life expectancy (H) and (ii) income (y). We have:

W = H · E[u(y)]

where W is average welfare. E[·] is an expectation.

Slide 24 of 32

126 of 260

Growth and Welfare

• Let y be the average income in a country.

• We can approximate E[u(y)] taking second order Taylor expansionsaround y. We have:

E[u(y)] = u(y) + u′(y) · E[(y − y)] +u′′(y)

2E[(y − y)2]

Slide 25 of 32

Growth and Welfare

• Simplifying

E[u(y)] = u(y) + u′(y) · E[(y − y)]︸︷︷︸=0 by definition

+u′′(y)

2E[(y − y)2]︸︷︷︸

=Variance of income

• So that welfare is

W = H · [u(y) +u′′(y)

2V ar[y]]

• This implies that Welfare:

1 Is increasing in life expectancy

2 Is increasing in income per capita

3 Is decreasing in the variance of income (recall u′′ is negative!)

Slide 26 of 32

Welfare: Consumption

Relationship with consumption:

.1.2 Income and Welfare 7

1.2 Income and Welfare

Should we care about cross-country income differences? The answer is definitely yes. High income levels reflect high standards of living. Economic growth sometimes increases pollution or may raise individual aspirations, so that the same bundle of consumption may no longer satisfy an individual. But at the end of the day, when one compares an advanced, rich country with a less-developed one, there are striking differences in the quality of life, standards of living, and health.

Figures 1.5 and 1.6 give a glimpse of these differences and depict the relationship between income per capita in 2000 and consumption per capita and life expectancy at birth in the same year. Consumption data also come from the Penn World tables, while data on life expectancy at birth are available from the World Bank Development Indicators.

These figures document that income per capita differences are strongly associated with differences in consumption and in health as measured by life expectancy. Recall also that these numbers refer to PPP-adjusted quantities; thus differences in consumption do not (at least in principle) reflect the differences in costs for the same bundle of consumption goods in different countries. The PPP adjustment corrects for these differences and attempts to measure the variation in real consumption. Thus the richest countries are not only producing more than 30 times as much as the poorest countries, but are also consuming 30 times as much. Similarly, cross-country differences in health are quite remarkable; while life expectancy at birth is as

Log consumption per capita, 2000

15

14

13

12

11

10

AFG

ALB

DZA

AGO

ATG

ARG

ARM

AUSAUT

AZE

BHS

BHR

BGD

BRB

BLR

BEL

BLZ

BEN

BMU

BTN

BOL BIH

BWA

BRA BRN

BGR

BFA

BDI

KHM

CMR

CAN

CPV

CAF

TCD

CHL

CHN

COL

COM

ZAR

COG

CRI

CIV

HRV

CUB

CYP

CZE

DNK

DJI DMA

DOM

ECU

EGYSLV

GNQ

ERI

EST

ETH

FJI

FIN

FRA

GAB

GMB

GEO

GER

GHA

GRC

GRD

GTM

GIN

GNB

GUYHTI HND

HKG

HUN

ISL

IND

IDN

IRN

IRQ

IRLISR

ITA

JAM

JPN

JOR

KAZ

KEN

KIR

PRK

KOR

KWT

KGZ

LAO

LVA

LBN

LSO

LBR

LBY LTU

LUX

MAC

MKD

MDGMWI

MYS

MDV

MLI

MLT

MRT

MUS

MEX

FSMMDA

MNG

MAR

MOZ

NAM

NPL

NLD

ANT

NZL

NIC

NER NGA

NOR

OMN

PAK

PLWPAN

PNG

PRY

PERPHL

POL

PRT PRI

QAT

ROM RUS

RWA

WSM

STP

SAU

SEN SCG

SYC

SLE

SGP

SVK

SVN

SLB

SOM

ZAF

ESP

LKA

KNA

LCA

VCT

SDN

SUR

SW Z

SWE

CHE

SYR

TWN

TJK

TZA

THA

TGO

TON

TTO

TUN

TUR

TKM

UGA

UKR

AREGBR

USA

URY

UZB VUT

VEN

VNM

YEM

ZMB

ZWE

6 7 8 9 10 11 Log GDP per capita, 2000

FIGURE 1.5 The association between income per capita and consumption per capita in 2000. For a definition of the abbreviations used in this and similar figures in the book, see http://unstats.un.org/unsd /methods/m49/m49alpha.htm. Source: Acemoglu (2008).

Slide 27 of 32

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Welfare: Life Expectancy

Relationship with life expectancy:8 . Chapter 1 Economic Growth and Economic Development: The Questions

Life expectancy, 2000 (years)

AFG

AGO

ALB

ANT

ARE

ARG

ARM

AUS AUT

AZE

BDI

BEL

BEN

BFA

BGD

BGR

BHR

BHS

BIH

BLR

BLZ

BOL

BRA

BRB

BRN

BTN

BWA

CAF

CANCHE

CHL

CHN

CIV CMR

COG

COL

COM

CPV

CRICUB

CYP

CZE

DJI

DNK

DOM

DZA

ECU

EGY

ERI

ESP

EST

FIN

FJI

FRA

FSM

GAB

GBR

GEO

GHA

GIN GMB

GNB GNQ

GRC

GTM

GUY

HKG

HND

HRV

HTI

HUN

IDN

IND

IRL

IRN

IRQ

ISL ISRITA

JAM JOR

JPN

KAZ

KEN

KGZ

KHM

KOR

KWT

LAO

LBN

LBR

LBYLCALKA

LSO

LTU

LUX

LVA

MAC

MAR

MDA

MDG

MDV

MEX MKD

MLI

MLT

MNG

MOZ

MRT

MUS

MWI

MYS

NAM

NER NGA

NIC

NLD NOR

NPL

NZL

OMN

PAK

PAN

PERPHL

PNG

POL

PRI

PRK

PRT

PRY

QAT

ROM

RUS

RWA

SAU SCG

SDN SEN

SGP

SLB

SLE

SLV

SOM

STP

SUR

SVK

SVN

SWE

SW Z

SYR

TCD

TGO

THA

TJK

TKM

TON

TTO

TUN

TUR

TZA

UGA

UKR

URY

USA

UZB

VCT

VEN

VNM

VUTWSM

YEM ZAF

ZMB

ZWE

ETH

GER

30

40

50

60

70

80

6 7 8 9 10 11 Log GDP per capita, 2000

FIGURE 1.6 The association between income per capita and life expectancy at birth in 2000.

high as 80 in the richest countries, it is only between 40 and 50 in many sub-Saharan African nations. These gaps represent huge welfare differences.

Understanding why some countries are so rich while some others are so poor is one of the most important, perhaps the most important, challenges facing social science. It is important both because these income differences have major welfare consequences and because a study of these striking differences will shed light on how the economies of different nations function and how they sometimes fail to function.

The emphasis on income differences across countries implies neither that income per capita can be used as a “sufficient statistic” for the welfare of the average citizen nor that it is the only feature that we should care about. As discussed in detail later, the efficiency properties of the market economy (such as the celebrated First Welfare Theorem or Adam Smith’s invisible hand) do not imply that there is no conflict among individuals or groups in society. Economic growth is generally good for welfare but it often creates winners and losers. Joseph Schumpeter’s famous notion of creative destruction emphasizes precisely this aspect of economic growth; productive relationships, firms, and sometimes individual livelihoods will be destroyed by the process of economic growth, because growth is brought about by the introduction of new technologies and creation of new firms, replacing existing firms and technologies. This process creates a natural social tension, even in a growing society. Another source of social tension related to growth (and development) is that, as emphasized by Simon Kuznets and discussed in detail in Part VII, growth and development are often accompanied by sweeping structural transformations, which can also destroy certain established relationships and create yet other winners and losers in the process. One of the important questions of


Inequality Over Time

Decomposing inequality between and within countries:2

• Inequality between countries in increasing

• Inequality within countries is decreasing2See appendix for formal definition of inequality

Wealth Share at the Top

• What about inequality the US?

Source: Piketty and Saez (2009)Slide 30 of 32

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8.1 Malthus and Solow

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Two Models of Growth

Two model main difference is in the production function:

• MalthusY = zF ( L︸︷︷︸

land

, N)

• SolowY = zF ( K︸︷︷︸

capital

, N)

N = labor

L = land

K = capital

z = productivity (TFP)

Note: new ingredient Ü land

Slide 5 of 1

Two Models of Growth

Key difference:

L = land is in fixed supply

K = can be accumulated over time

• We will use two models to describe growth facts both ancient(Malthus) and modern (Solow).

• Hansen-Prescott in the paper entitled Malthus to Solow describehow society switched from one regime to the other.

Slide 6 of 1

Malthusian Model

1 Technology: Y = zF (L,N)

• assume constant return to scale

2 Preferences: fixed labor supply (we normalize to 1 unit)

3 Population = number of workers

• Use N to denote number of workers today;

• Use N ′ to denote number of workers tomorrow;

Question: what determines population growth?

Slide 7 of 1

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Malthusian Model: Population Growth

• Key assumption:

Growth rate of population depends on living standards.

• Living standard are related to consumption per capita:

living standards =C

N

• We have:N ′

N= g

(C

N

)

g(·) increasing and concave function;

Slide 8 of 1

Equilibrium in the Malthusian Model

Equilibrium is standard: Agents and firm optimize, market clearing...plus: steady state in the population N ′ = N = N∗

Equilibrium is determined by:

1 Market Clearing for goods market:

C = Y = zF (L,N)

2 Steady State condition:N ′ = N (A)

3 Population growth equation:

N ′

N= g

(C

N

).

Slide 9 of 1


• Substitute C in population growth equation:

N ′

N= g

(zF (L,N)

N

)

• Using our constant return to scale assumption:

N ′

N= g

(zF

(L

N, 1

))(B)

where L/N = land per capita

Slide 10 of 1

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• We now have two equilibrium conditions:

(A)⇒ N ′ = N

(B)⇒ N ′

N= g

(zF

(L

N, 1

))

• Combining (A) and (B):

g

(zF

(L

N, 1

))= 1

Slide 11 of 1

Equilibrium: Example

• Let F (L,N) = zLαN1−α and g(·) = (·)γ , then

N ′ = zγLαγN1−αγ

recall α < 1 and γ < 1.• Equilibrium exist: N∗

(intersection of 45 degree line and concave curve)

• Note: is there another equilibrium?Slide 12 of 1

Malthusian Model: Analysis and Policy

Slide 13 of 1

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Malthusian Model: Policy

• We have large technology developments prior to industrialrevolution

• If z has always been increasing, why have standard of living beenstagnating for centuries?

Slide 14 of 1

Malthusian Model: Analysis

What happens if z increases at a time T = 1?

Recall that in steady state :

g

(C∗1N∗1

)= 1 (B)

C∗1 = z1F (L,N∗1 )

If z1 ↑ z2 (with z1 < z2) then :

1 C∗1 < z2F (L,N∗1 ), so C∗1 must increase to C∗2

2 From equation (B): g(C∗

2N∗

1

)> 1 so N∗1 must increase to N∗2

3 Converge to new steady state with C∗2 = z2F (L,N∗2 )

Slide 15 of 1

Malthusian Model: Analysis

Slide 16 of 1

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• How can we increase standard of living? Population Control

+ Cut population growth by factor δ < 1

• New equilibrium conditions become:

δ · g(C∗

N∗

)= 1 (C)

C∗ = zF (L,N∗)

Compare equation (B) with equation (C).

Slide 17 of 1


Cutting population growth rates:

Slide 18 of 1

Malthusian Model: Taking Stock

1 The Malthusian model achieve stagnation in growth.

2 Any technological development gets absorbed by larger populations.

3 Land seems to play a key role in depressing growth.

Slide 19 of 1

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The Solow Growth Model

Slide 20 of 1

The Solow Growth Model: Introduction

• Key difference with Malthus: the use of capital

• New Ingredients:

• Exogenous population growth.

• Saving (S).

Slide 21 of 1

The Household

• Exogenous population growth:

N ′ = (1 + n)N

n is the growth rate and n > −1

• Households care about consumption, leisure and the futurethe budget constraint is:

C + S︸︷︷︸Saving

= Y︸︷︷︸Income

• For now: “rule of thumb” for saving

S = sY ⇒ C = (1− s)Y

household save a constant fraction of their incomeSlide 22 of 1

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Saving Rate in the US

Fraction of disposable income saved:

Slide 23 of 1

Saving Rate in the US

Historical:

Slide 24 of 1

Capital and the Firm

• Production function:

Y = zF (K,N)

Note for now z is exogenous.

• New ingredient: law for capital accumulation

K ′︸︷︷︸Capital tomorrow

= (1− d) K︸︷︷︸Capital today

+I

where I is investment and d is the depreciation rate: 0 < d < 1

Slide 25 of 1

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Depreciation Rates in the US

What is the value of d for the US?

Data: http://www.bea.gov/scb/pdf/national/niparel/1997/0797fr.pdf

Type of asset Depreciation rate Service life

Computing equipment .3119 7Aircrafts 1960 and later .0660 25

General industrial equipment .1072 16Agricultural machinery .1179 14

Industrial buildings .0314 31Submarines .0825 20

Slide 26 of 1

The Firm

• Maximizes profits:

π(K) = maxI,N

Y − wn− I + π(K ′)︸︷︷︸

Profits Tomorrow

Subject toY = zF (K,N)

AndK ′ = (1− d)K + I

Slide 27 of 1

Equilibrium and Steady State

1 Firm and Household optimize.

2 Market clearing for goods:

Y = C + S

3 Market clearing for assets (NEW!):

S = I

This implies that all investments comes from saving.

Slide 28 of 1

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Steady State

• In Malthus steady state was N = N ′ = N∗

• In Solow population always grows,

Ü use notion of per capita steady state

K ′

N ′=K

N= k∗ ⇒ k′ = k = k∗

Y ′

N ′=Y

N= y∗ ⇒ y′ = y = y∗

• From now on lower case letters denote per-capita quantities, also

F (K,N)

N= F

(K

N, 1

)= f(k)

Slide 29 of 1

Kaldor Facts

Facts about economic growth proposed by Kaldor in 1961

1YN increases at a constant rate over time

2KN increases at a constant rate over time

3KY remains constant

Steady state assumption seems justified...

+ Can one of the above help me figure out K?

Slide 30 of 1

Solving For the Steady State

• Our goal is now to derive a condition for equilibrium value of k.

This is important to understand questions like:

1 How to foster growth?

2 Why is the saving rate important?

3 Is a capital tax good or bad?

• Algebra ahead: take a deep breath!!

Slide 31 of 1

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Solving For the Steady State

Start:K ′ = (1− d)K + I

Substitute I from market clearing for goods and assets:

Y = C +K ′ − (1− d)K

Substitute rule of thumb for saving and production function:

Y = (1− s)Y +K ′ − (1− d)K ⇒ K ′ = szF (K,N) + (1− d)K

Divide by NK ′

N

N ′

N ′=szF (K,N)

N+

(1− d)K

NRecall that N ′ = (1 + n)N

k′(1 + n) = szf(k) + (1− d)k

since in steady state k = k′

szf(k) = (n+ d)k

Slide 32 of 1

Analysis of the Steady State

Key equilibrium condition:

szf(k∗) = (n+ d)k∗

To understand it, graph both sides of the equation:

What happens if s, n, d, z changes?Slide 33 of 1

Changing the Saving Rate

• Suppose s changes: s1 to s2 (s2 > s1)

• k1 increases to k2

• Question: what happens to y1?Slide 34 of 1

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From Data Lecture

Recall that in equilibrium saving = investment.

Investment is positively correlated with GDP levels.

Slide 35 of 1

Changing the Population Growth Rate

• Suppose n changes: n1 to n2 (n2 > n1)

• k1 decreases to k2

Slide 36 of 1

From Data Lecture

Population growth is negatively correlated withGDP levels.

Slide 37 of 1

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Growth

Slide 38 of 1

Growth Rates

• In Malthus consumption per capita is constant over time.

• Question 1: how is consumption, output andcapital growing over time?

• Question 2: how is consumption, output andcapital per capita growing over time?

Slide 39 of 1

Growth Rates

What is the growth rate of K,C, Y in steady state?

k′ = k ⇒ K ′

N ′=K

N

so that

K ′ =N ′

NK = (1 + n)K

growth rate is the population growth rate!

(Same for Y and C)

Question: how do you show it for Y ?(hint you will need CRS assumption for F)

Slide 40 of 1

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Growth Rates

• Question 1: how is consumption, output andcapital growing over time?

• Answer 1:Y,C,K grow at rate n, the population growth rate.

• Question 2: how is consumption, output andcapital per capita growing over time?

• Answer 2:The above implies that K/N is constant over time...as Malthus?

Something is now very different than Malthus...

Slide 41 of 1

Sustaining Growth

To sustain growth over time we need something other than s and n: z!

Increasing z1 Ü z2 Ü z3 generates long term growth!

Slide 42 of 1

The Solow Residual

• We have identified z as a key source for growth.z is sometimes called the Solow Residual

• Key question, what is z in the data, how do we calculate it?

• From equilibrium condition:

Y = zF (K,N) = zKαN1−α

hence

z =Y

F (K,N)=

Y

KαN1−α

• We need information on: GDP (Y )...easy, Workers (N)...easy,α not easy but done, K hard.

Slide 43 of 1

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Measuring K

• Starting point to determine Kt+1 (at time t+ 1) is:

Kt+1 = (1− d)Kt + It

• We have information on It since 1947 but we do not know K1947

• Idea from Kaldor: set K1947 so that over time Kt/Yt is roughlyconstant

• If K1947 is set too high then Kt/Yt will decrease over time.If K1947 is set too low then Kt/Yt will grow over time.

• As a rule of thumb it is ok to set K1947 so that K1947/Y1947 = 3.

Slide 44 of 1

The Solow Residual

Plotting z (the Solow residual) for the US

Slide 45 of 1

Cross Country Convergence

Slide 46 of 1

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• Q: If the world was described by a Solow model, what wouldhappen eventually to identical countries with different level of GDPper capita ypoor and yrich today?

•ypoor = zf(kpoor) yrich = zf(krich)

If today ypoor < yrich it implies kpoor < krich...

what happens in steady state?

• Key equation:szf(k) = (n+ d)k

Slide 47 of 1


A: In the long run, they will have the same level of gdp per capita

Is this happening?

Slide 48 of 1

Cross Country Convergence: Eastern Europe

Source: http://www.voxeu.org/index.php?q=node/7740

Here is an example of countries converging.However looking across all countries...

144 of 260


...not quite

Levels of GDP are not correlated with GDP growth rates.

Slide 50 of 1

Convergence: An Explanation

What is wrong with the model?

1 Maybe all the countries are not the same

2 Barriers to technology adoption

3 Barriers to investment

4 Non optimizing firms?

If interested, see also Parente, Prescott (2000).

If really Interested take my class in the Fall: Emerging Markets.

Slide 51 of 1

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8.2 Endogenous Growth Model

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Education and Growth

Slide 2 of 14

Endogenous Growth

• Solow explains why we have growth: it’s either z or n

• Does not tell us what to do to improve long run growth:i.e how does z go up?

Ü we need to go further and introduce: human capital

Slide 3 of 14

Schooling Years

Source: World Bank

Ü What can we learn from the above?Slide 4 of 14

147 of 260

Education and growth1.7 From Correlates to Fundamental Causes . 19


0.06

0.04

0.02

0.00

–0.02

TWN

CHN

RWA

KOR

HKG THAMYS

SGP IRL JPN

LKA

EGY IDN

PAK GHA LSO IND

PRT

SYR

TUN TUR MUS

ESP

ITA

PAN FRA

GRC AUT

BEL FIN NORISR

BDI

BEN

MLIGMBMOZ

NPL

SLV BOL PER

MWI BRA

CMR ZAF COG

ZWE COL MEXECU

UGADZA CRI

DOM

GTM

HND

IRN

TGO KEN ZMBJAM

PRY

ARG

CHL

ISL

PHLTTO URY BRB

NLD GBR

AUS CAN

CHE

DNK SWE

NZL

USA

SEN VEN

JOR NER

NIC

0 2 4 6 8 10 12 Average years of schooling, 1960–2000

FIGURE 1.16 The relationship between average growth of GDP per capita and average years of schooling, 1960–2000.

are likely driven, at least in part, by omitted factors affecting both investment and schooling on the one hand and economic growth on the other.

We investigate the role of physical and human capital in economic growth further in Chapter 3. One of the major points that emerges from the analysis in Chapter 3 is that focusing only on physical and human capital is not sufficient. Both to understand the process of sustained economic growth and to account for large cross-country differences in income, we also need to understand why societies differ in the efficiency with which they use their physical and human capital. Economists normally use the shorthand expression “technology” to capture factors other than physical and human capital that affect economic growth and performance. It is therefore important to remember that variations in technology across countries include not only differences in production techniques and in the quality of machines used in production but also disparities in productive efficiency (see in particular Chapter 21 on differences in productive efficiency resulting from the organization of markets and from market failures). A detailed study of technology (broadly construed) is necessary for understanding both the worldwide process of economic growth and cross-country differences. The role of technology in economic growth is investigated in Chapter 3 and later chapters.

1.7 From Correlates to Fundamental Causes

The correlates of economic growth, such as physical capital, human capital, and technology, is our first topic of study. But these are only proximate causes of economic growth and economic success (even if we convince ourselves that there is an element of causality in the correlations

Slide 5 of 14

Schooling: Spending

Country % of GDP

Yemen 9.5%Mongolia 9%

Kenya 7%Switzerland (U.S) 5.8% (5.7%)

Italy 4.7%Zambia 2%Ecuador 1%

Source: United Nations

Ü What can we learn from the above?

Slide 6 of 14

Endogenous Growth:The relation between z and education

Slide 7 of 14

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Endogenous Growth: Human Capital

Human Capital:

The stock of skills and education that workers have at a point in time

Properties:

1 It grows

2 It does not depreciate

3 Technologies using it do not exhibit decreasing returns

4 Is non-rivalrous

Slide 8 of 14

A Simple Model: The Consumer

Suppose :

1 There is no leisure:

Ü Workers divide their time between workand human capital accumulation.

Let N denote time at work. (1−N) time at school.

2 Human capital Hs increase effective time at work: more humancapital = more output for the same amount of hours.

3 There is no capital.

Slide 9 of 14

A Simple Model: The Consumer

• Budget constraint:

C = w︸︷︷︸Wage

· N ·H︸︷︷︸Effective labor

Note that effective amount of labor is now N ·H not N .

• Human capital accumulation

H′

= b(1−N)H

b is efficiency of human capital accumulation (quality of schools)

Slide 10 of 14

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A Simple Model: The Firm

• Firm maximize profits choosing effective labor N ·H

maxN ·H

zN ·H︸︷︷︸technology

−wN ·H

Note: we assumed linear firm technology

• Since problem of the firm is linear:

1 Equilibrium wage is z.

2 Firm is indifferent in choice of N ·H.

Slide 11 of 14

A Simple Model: The Equilibrium

Let’s determine the consumption growth rate

• From budget constraint and firm maximization problem:

C = zN ·H

(note w = z) and

H ′ = b(1−N)H ⇒ H ′

H− 1 = b(1−N)− 1

• Computing growth rates of consumption:

C ′

C− 1 =

zNH ′

zNH− 1 =

H ′

H− 1 =

= b︸︷︷︸efficiency

· (1−N)︸︷︷︸intensity

−1

Slide 12 of 14

A Simple Model: Summary

1 Economy grows indefinitely because of human capitalaccumulation.

2 Rate of growth determined by intensity and efficiencyof human capital accumulation.

Slide 13 of 14

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A Simple Model: Policy

What are good policies?

1 Increase schooling

2 Increase efficiency of schooling

+ http://www.worldbank.org/education

Slide 14 of 14

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Chapter 9

Dynamic Model

9.1 Forecasting: Part 2

152 of 260

Forecasting Part II: Leading Indicators

Slide 2 of 22

This Lecture

• Leading Indicators

• Application to Employment Forecasting:

1 ADP employment Survey

2 Vacancies

• Application to GDP Forecasting:

1 Heavy truck sales

Slide 3 of 22

Forecasting: Information Sets

Definition (Information Sets)

Let It be the set of information available at time t for a forecast.

• In previous lecture we used past information on the variable ofinterest (xt) to forecast it’s feature.

• In particular we used all of the available past information toforecast via a linear trend. Formally It = {xn}t−1

n=1

• In this lecture we will use other variables to help us forecast xt sothat: It = {zn}t−1

n=1

Slide 4 of 22

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Leading Indicators

• Setting It = {zn}t−1n=1 is particularly useful if zt−1 “predicts” xt.

• In this case we will call zt a leading indicator of xt.

• Recall that a leading indicator (zt in our case) is a variable thatover the cycle anticipates the changes of another variable (xt).

• Examples:

1 Earnings Ü Dividends;

2 Monetary base Ü Inflation;

3 ?? Ü Employment;

4 ?? Ü GDP.

Slide 5 of 22

A Simple Model

• Suppose we knew that:

xt = b0 + b1 · zt−1 + εt︸︷︷︸error

(1)

• Suppose today we observe zt; Then today we can forecast thefuture value of xt+1 by:

xt+1 = b0 + b1 · zt

+ Goal: find b0 and b1.

Slide 6 of 22

A General Model

• The previous model only consider 1 explanatory variable z.We can generalize:

xt = b0 + b1 · zt−1 + b2 · xt−1 + b3 · wt−1 + . . . + εt.

• We now also consider:

1 Past realization of the variable xt−1;(for example if x is GDP is natural to include past values)

2 Additional explanatory variables wt−1.

• The generalization to include additional explanatory variables isconceptually easy. Is harder to implement quantitatively.

+ Refer to your econometrics class

Slide 7 of 22

154 of 260

Appendix: Which Model to Choose?

• The previous and this lecture point to a variety of modelingapproaches. Including different leading indicators or laggedvariables.

• Natural question, which is the “best model”?

• Many formal ways to answer this.A simple approach is to look at εt the error term.

• In particular we are interested to see if the series εt has “patterns”.

Slide 8 of 22

Appendix: Durbin-Watson

• The Durbin-Watson Statistic (d) is given by(assuming ε is of length T ):

d =

∑Tt=2(εt − εt−1)

2

∑Tt=1 ε

2t

• d determines how correlated are the error over time. If errors arecorrelated then one could used past errors to reduce future errors.

• Rule of thumb: the closer d is to 2 the better the model.

Slide 9 of 22

A Word of Caution: Lucas 1976

• Consider a simple “econometric” model of the household:

ct = b0 + b1 · yt︸︷︷︸Income

+b2 · Tt︸︷︷︸Transfers

parameters b0, b1 and b2 can be estimated looking at past data.

• Suppose a policy maker is considering changing Tt or Tt+1.What mistake he would be making relying on the above model?

The mistake would be considering (b0, b1, b2) as fixed rather thandependent on policy itself. Households are “smart” and haveexpectations about future policies!

• Lucas (1976) “Econometric Policy Evaluation: A Critique” makesthis points with multiple examples. Since this critiques has bereferred to as: The Lucas Critique

155 of 260

Application to Employment Forecasting

Slide 11 of 22

BLS Employment Survey

• Policy maker and market pay close attention to the behavior of thelabor market as a good indicator of the state of the economy.

• From the BLS:Each month the Current Employment Statistics (CES) programsurveys approximately 144,000 businesses and government agencies,representing approximately 554,000 individual worksites, in order toprovide detailed industry data on employment, hours, and earningsof workers on nonfarm payrolls.

• Note: The CES is an estimate on the number of salary jobs: anindividual with two jobs is counted twice by the payroll survey.

• The CES releases monthly, next releases are April 4th and May 2nd.

ADP Employment Report

• ADP (Automatic Data Processing) is a private firm that offerspayroll services to other companies.

• ADP process approximately 411,00 US firms (20% of the privatesector). This puts ADP on similar footing to the BLS in terms ofdata owned.

• Every month shortly (few days) before the CES report, ADPreleases the National Employment Report.

• Next release dates are April 2nd and April 30th.

Slide 13 of 22

156 of 260

ADP vs. CES

• Legend payems (BLS); nppttl (ADP).

• The two series track each other very closely.

Slide 14 of 22

Leading Indicator: Job Openings

• The ADP series is released only few days the CES series.

• Other leading indicators are available. A popular one: job openings

• The idea is simple to fill a job, a job must first become available.

• Job openings are published in the JOLTS(Job openings and labor turnover survey)

• The next release date is April 8th.

Slide 15 of 22

Vacancies vs. CES

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• Job opening “anticipates” the behavior of payroll employment.

Slide 16 of 22

157 of 260

Results

• The previous two graphs are displayed as:differences from a year ago.

• This is done to remove possible seasonality effects.

• We compute b0 and b1 in (1) using Excel.

• As before we can use Slope to compute b1 andIntercept to compute b0.

• We find:

b0 = −75.11; b1 = 0.186; d = 0.5

• If we use 1 lag of CES as explanatory variable then d = 2.7.

Slide 17 of 22

Application to GDP Forecasting

Slide 18 of 22

Truck Sales

• We now look at GDP more closely.

• The idea is to look at the behavior of firms. Firm, as a whole caninternalize the current conditions. of the economy

• In the next class we will see that investment is an importantforward looking variable.

• Today we look at one particular investment heavy trucks.2

2Heavy trucks are trucks with more than 14,000 pounds gross vehicle weight.Slide 19 of 22

158 of 260

Historical Truck Sales

• There appears to be a negative relationship betweenshaded areas and truck sales.

Slide 20 of 22

GDP vs. Truck Sales

• Truck Sales is a good leading Indicator for GDPfor the current recession...

Slide 21 of 22

Historical Relationship

• ...the relationship seem to be also present in historical data.

Slide 22 of 22

159 of 260

9.2 The Household

160 of 260

News of the Week

• The Federal Open Market Committee (FOMC) meets 8 times ayear to set monetary policy for the US.

• On March 19th the FOMC released a statement concerning thelatest meeting.

• This Meeting was important as it marks the first one chaired byJanet Yellen.

• The statement can be found here:http://www.federalreserve.gov/newsevents/press/monetary/20140319a.htm

Slide 2 of 44

Reading FOMC Statements

• FOMC statement have a precise structure:

1 Start with an overview of the current economic conditions

2 Relate conditions with the FED mandate

3 Describe the policy taken and how they might impact

• Key information that economist look for in FOMC statement isForward guidance:

Through ”forward guidance,” the Federal Open Market Committeeprovides an indication to households, businesses, and investorsabout the stance of monetary policy expected to prevail in the future.

Source: http://www.federalreserve.gov/faqs/money 19277.htm

Slide 3 of 44

Forward Guidance?

• In January:Committee today reaffirmed its view that a highly accommodative stance of

monetary policy will remain appropriate for a considerable time after the asset

purchase program ends and the economic recovery strengthens. The Committee

also reaffirmed its expectation that the current exceptionally low target range for

the federal funds rate of 0 to 1/4 percent will be appropriate at least as long as

the unemployment rate remains above 6-1/2 percent

• In March:Committee currently anticipates that, even after employment and inflation are

near mandate-consistent levels, economic conditions may, for some time,

warrant keeping the target federal funds rate below levels the Committee views as

normal in the longer run.161 of 260

Online Survey!

Q: Suppose this year the economy is in a recession.When should the government levy more taxes?


1 This year

2 Next year

3 At the end of the recession

Slide 5 of 44


1 The two period model: the consumer

• Inter-temporal budget constraints

• Household savings data

2 The two period model: comparative statics

• Changes in wealth

• Changes in interest rates

3 The two period model: the government

• Ricardian Equivalence

Slide 6 of 44

Two Period Model

Slide 7 of 44

162 of 260

Two Period Model: Consumer

• Consumers live two periods

• New trade-off: consumption today vs consumption tomorrow(add this to the consumption leisure trade-off studied in part I)

• New instrument: bonds s

1 All bonds are identical

2 All bonds are safe

3 No intermediaries

• New price: interest rate r (1 bond today, pays 1 + r tomorrow)

4 Borrowers and lenders face the same r

Slide 8 of 44

Two Period Model: Budget Constraints

• Budget constraint today:

c+ s = y − t

• Budget constraint tomorrow: (recall ′ denotes tomorrow’s variable)

c′ = y′ − t′ + (1 + r)s

• Define lifetime wealth (today) as:

we = y +y′

1 + r− t− t′

1 + r

then c′ = −(1 + r)c+ we(1 + r)

Slide 9 of 44

Two Period Model: Budget Constraints

Plotting the budget constraint

E = (y − t, y′ − t′) used to determine how income isdistributed during the lifetime

Slide 10 of 44

163 of 260

Two Period Model: Optimality

• Households enjoy consumption today and tomorrow

• Households enjoy more the present

• Preferences :u(c) + βu(c′)

0 < β < 1: time discount factor; u(·): standard utility function

• Problem of the household:

maxc,c′

u(c) + βu(c′)

Subject to (1 + r)c+ c′ = we(1 + r)

Slide 11 of 44


From first order conditions:

uc(c) = (1 + r)βuc(c′)

Optimality:

uc(c)

βuc′(c′)= (1 + r)

+ MRSc,c′ = 1 + r

Intuition:

Give up one consumption today (valued at uc′(c′)) for (1 + r) units

of consumption tomorrow (valued at uc′(c′) and discounted by β)

Slide 12 of 44


• The case of borrowers and lenders

(a) Lender (b) Borrower

• Note slope of indifference curves = 1 + r

• Note the different position relative to E!

Slide 13 of 44

164 of 260

Two Period Model: Saving

What are the implication for saving?

1 flat income profile (y − t = y′ − t′) : optimal saving is 0.2 increasing income (y − t < y′ − t′) : optimal saving is < 0.3 decreasing income (y − t > y′ − t′) : optimal saving is > 0 .

(c) Positive saving (d) Negative savingSlide 14 of 44

Two Period Model: Consumption Smoothing

Question: what are the implications for consumption?

• A simple case: let β = 11+r . Optimal solution is given by:

uc(c) = uc′(c′)⇒ c = c′ (1)

• Household seeks to equalize his marginal utility over both periods.

• This property is called consumption smoothing

Slide 15 of 44

165 of 260

Negative Saving Rate: Panic?

Is there a problem with a negative national saving rate?

• This aggregate measure leaves out realized earning in other assets

• This is important especially thinking about retirement(if your stock portfolio goes well, you save less)

• Is this impacting the business sector?

A nice article:http://www.clevelandfed.org/research/trends/2010/0410/01ecoact.cfm

Slide 23 of 44

Two Period Model: The Government

Slide 24 of 44

The Dynamic Government

• Government spends and taxes in two periods

• NEW: now it can borrow and save!

• Budget constraint today

G = T +B

• Budget constraint tomorrow

G′ + (1 + r)B = T ′

• Life-time budget

G+G′

1 + r= T +

T ′

1 + r

Slide 25 of 44

166 of 260

Ricardian Equivalence

Slide 26 of 44

Ricardian Equivalence

• Punchline: the timing of taxes is irrelevant

• Key equation: lifetime budget constraint (in today’s $)

c+c′

1 + r︸︷︷︸present value of consumption

= y +y′

1 + r︸︷︷︸...of income

−(t+

t′

1 + r

)

︸︷︷︸...of taxes

Let T = t (assuming size of population equal 1, otherwise let T = N · t)

t+t′

1 + r= G+

G′

1 + r

substituting in consumer lifetime budget

c+c′

1 + r= y +

y′

1 + r−(G+

G′

1 + r

)

Note: if r is constant changes in t and t′ don’t matter

Slide 27 of 44

Ricardian Equivalence: In words

Suppose the government today lowers T by 100$ and raises B by 100$

• If r = 3%, tomorrow the government owes 103$Ü taxes tomorrow go up by 103$.

• Household has two course of actions:

1 Keep same spending on C, today save 100$,tomorrow earn 103$ and use to pay increased taxes.

2 Spend today the extra 100$, today save 0$,tomorrow lower consumption by 103$ to pay for taxes.

• What would the household do?

Slide 28 of 44

167 of 260

Ricardian Equivalence: Credit Markets

• Does r change?

Ü No: since demand and supply of assets cancels out

• Think about the previous example

Note: SP is private demand for savingSlide 29 of 44

Ricardian Equivalence: Assumptions

1 Taxes are equal for all populations (no redistribution)

2 Debt repaid while you are alive

3 Lump sum taxes

4 Credit markets without frictions

Slide 30 of 44

Data on Interest Rates

Slide 31 of 44

168 of 260

Household Savings: Interest Rates

The closest parallel in data of the bond in our model is the:3 month T-bill

Source: St. Louis Fed http://research.stlouisfed.org/fred2/series/WTB3MS

Slide 32 of 44

Bonds: Model vs Data

The bond in the model has two special features:

1 It cannot be defaulted on

2 Is available in one maturity

In data...

Slide 33 of 44

Bonds: Maturity

In data we have different maturities:

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%"

%#$"

&"

&#$"

'"

'#$"

%"()" '"()" *"()" %"+," &"+," '"+," $"+," -"+," %!"+," &!"+," '!"+,"

!"#$"%

&'(")

*+,")&-).'&/#+&0))

*#"'1/#0)2+"34)5/#6")7-#).'#$8)9:;)9<=9)

Source: http://www.treasury.gov/resource-center/data-chart-center/interest-

rates/Pages/TextView.aspx?data=yield

Slide 34 of 44

169 of 260

Bonds: Maturity

• Question: how would the model price different maturities?

• Answer: let’s assume that by the time the bonds matures, thereturn is the same even if you had rolled over bonds of shortermaturities

Let rm = return of bond of maturity m

(1 + rm)m = (1 + r)× · · · × (1 + r)︸︷︷︸m times

• Yield curve should be flat... what is missing?

Slide 35 of 44

Bonds: Default

In data we have bonds with different default risk:

Source: http://markets.ft.com/RESEARCH/Markets/Government-Bond-Spreads

Bonds: Default

• Question: how would the model price different default risks?

• Answer: let’s assume that the return on each bond is the same(In finance you will study the efficient market hypothesis)

Let pi =probability that country i defaults

(1− pi) ri︸︷︷︸return on bonds of i

= r︸︷︷︸return on US bonds

Slide 37 of 44

170 of 260

Two period model:Comparative statics

Slide 38 of 44

Comparative Statics

We look at the following cases:

1 Temporary changes in income: either today or tomorrow.

2 Permanent changes in income.

3 Changes in interest rate.

Slide 39 of 44

Comparative Statics: Change in Income

Increase in today’s income: y1 ⇒ y2 with y2 > y1

• Recall wei = yi + y′1+r − t− t′

1+r

• Change in wealth: ∆we = (we2 − we1) = y2 − y1 > 0

• So that: outward shift in budget constraint

• Consumption increases today and tomorrow!(remember income effects)

Slide 40 of 44

171 of 260


• Don’t forget consumption smoothing!

• Our model of C does not include durables,how would you model them?


• Suppose permanent increase in income y1 ⇒ y2 and y′1 ⇒ y′2

• In the picture optimal choice moves from H ⇒ K

• Difference with respect to temporary changes?Larger effect on consumption since savings maynot increase

Slide 42 of 44

172 of 260

9.3 The Government

173 of 260

Deviation From Trend Consumption vs. GDP

From Lecture 3:

• Consumption is: slightly less variable

Slide 16 of 44

Two Period Model: Saving

Question: how much does a household save?

• Recall saving equalss = y − t− c

• Using equation (1) the budget constraint is

c(2 + r) = y(1 + r) + y′ + t(1 + r) + t′

So that

s =(y − t)(2 + r)− [y(1 + r) + y′ + t(1 + r) + t′]

2 + r

s =(y − t)− (y′ − t′)

2 + r

Slide 17 of 44

Data on Saving

Slide 18 of 44

174 of 260

Household Balance-sheet: Flow of Funds

• Federal Reserve provides all information on who saves where...104 Z.1, September 17, 2009

B.100 Balance Sheet of Households and Nonprofit Organizations (1)Billions of dollars; amounts outstanding end of period, not seasonally adjusted

2003 2004 2005 2006 2007 2008 2009 Q1 Q2 Q3 Q4 Q1 Q2

1 Assets 56744.9 63506.2 70987.5 76749.0 78228.8 75868.6 74945.9 72339.4 67134.0 65244.0 67207.9 1

2 Tangible assets 21437.7 24270.7 27719.1 28724.2 27525.6 26863.9 26541.9 26051.2 25177.0 24660.1 24847.1 2

3 Real estate 17599.0 20214.4 23458.4 24259.6 22880.2 22154.7 21785.0 21261.5 20397.7 19869.0 20025.9 3 4 Households (2,3) 16170.3 18629.4 21427.7 21948.2 20477.4 19803.5 19538.7 19036.3 18317.1 17948.6 18272.0 4 5 Nonprofit organizations 1428.7 1585.0 2030.7 2311.4 2402.8 2351.2 2246.2 2225.3 2080.5 1920.4 1753.9 5 Equipment and software owned by 6 nonprofit organizations (4) 160.7 173.2 183.7 196.5 207.9 210.4 214.0 218.1 220.9 221.0 220.5 6 7 Consumer durable goods (4) 3678.0 3883.1 4077.0 4268.1 4437.5 4498.9 4542.9 4571.5 4558.5 4570.1 4600.8 7

8 Financial assets 35307.2 39235.5 43268.4 48024.8 50703.1 49004.7 48404.0 46288.2 41957.0 40583.8 42360.8 8

9 Deposits 5350.4 5742.5 6153.6 6779.0 7381.3 7579.1 7420.3 7566.4 7827.4 7848.9 7760.2 910 Foreign deposits 52.1 57.5 59.9 65.2 81.0 74.5 68.3 63.9 59.8 55.7 50.6 1011 Checkable deposits and currency 399.1 370.3 256.8 236.4 156.9 87.8 98.5 64.7 236.7 241.7 300.1 1112 Time and savings deposits 3939.0 4410.6 4887.6 5363.0 5796.7 5958.9 5859.8 5991.7 5949.2 5988.8 5913.8 1213 Money market fund shares 960.2 904.1 949.2 1114.5 1346.8 1457.9 1393.7 1446.1 1581.7 1562.7 1495.7 13

14 Credit market instruments 2755.2 3075.8 3426.8 3553.5 4113.4 4077.9 4138.8 4218.5 4054.5 4536.2 4326.6 1415 Open market paper 105.9 136.1 164.2 187.7 149.7 117.5 82.7 39.1 10.4 7.3 8.9 1516 Treasury securities 438.6 532.2 507.5 433.1 252.3 322.1 368.1 386.8 240.0 576.4 605.9 1617 Savings bonds 203.8 204.4 205.1 202.4 196.4 195.3 194.9 194.2 194.0 193.9 193.5 1718 Other Treasury 234.8 327.8 302.4 230.7 55.9 126.8 173.2 192.6 46.0 382.5 412.4 1819 Agency- and GSE-backed securities 421.2 390.0 488.3 412.6 689.8 657.0 675.5 820.1 711.3 439.6 129.5 1920 Municipal securities 703.8 742.4 821.0 871.8 895.9 883.3 894.5 910.1 938.0 954.5 996.8 2021 Corporate and foreign bonds 964.2 1135.6 1294.1 1517.7 2001.7 1971.0 1979.9 1919.2 2010.9 2415.4 2443.6 2122 Other loans and advances (5) 3.1 5.9 8.7 8.3 17.4 20.1 22.3 27.5 27.9 28.5 29.2 2223 Mortgages 118.5 133.6 143.0 122.4 106.5 107.0 115.8 115.7 116.0 114.5 112.7 23

24 Corporate equities (2) 6749.9 7491.0 7999.5 9488.0 9453.0 8759.6 8449.1 7442.0 5878.7 5150.3 6266.3 2425 Mutual fund shares (6) 2904.3 3417.4 3839.3 4387.6 4832.0 4575.2 4662.8 4111.1 3444.7 3254.7 3740.5 2526 Security credit 475.4 578.3 575.3 655.7 866.4 984.5 992.1 998.6 742.7 667.0 649.2 2627 Life insurance reserves 1013.2 1060.4 1082.6 1163.7 1201.5 1187.2 1196.4 1197.7 1179.8 1181.1 1197.6 2728 Pension fund reserves 9718.9 10635.5 11373.7 12696.2 13375.9 12566.7 12476.1 11832.5 10442.6 9913.8 10656.3 2829 Equity in noncorporate business (7) 5838.7 6680.9 8208.9 8655.0 8767.3 8548.5 8335.1 8170.3 7618.4 7266.7 6995.7 2930 Miscellaneous assets 501.3 553.8 608.7 646.1 712.2 725.9 733.5 751.3 768.2 765.1 768.4 30

31 Liabilities 9842.8 11012.1 12164.2 13414.0 14318.1 14416.4 14368.2 14514.8 14216.9 14102.5 14068.0 31

32 Credit market instruments 9482.6 10552.4 11723.1 12899.2 13754.2 13807.5 13828.9 13860.9 13794.8 13709.6 13661.8 3233 Home mortgages (8) 6871.9 7819.3 8855.3 9832.8 10485.2 10547.9 10544.3 10503.5 10430.7 10431.0 10401.7 3334 Consumer credit 2102.5 2219.5 2319.8 2415.0 2551.9 2529.6 2555.6 2588.0 2592.1 2517.0 2475.5 3435 Municipal securities (9) 178.3 188.6 205.1 226.9 249.5 252.3 261.6 265.2 269.6 273.0 281.9 3536 Bank loans n.e.c. 49.8 26.7 36.4 86.4 99.7 104.9 89.2 121.4 117.7 104.0 118.5 3637 Other loans and advances 118.7 119.0 119.0 123.8 127.0 128.0 129.7 130.7 133.2 133.5 134.0 3738 Commercial mortgages (9) 161.4 179.2 187.4 214.3 240.8 244.9 248.4 252.1 251.5 251.0 250.1 38

39 Security credit 182.5 264.0 232.4 292.1 325.5 365.3 291.5 402.3 164.8 134.6 147.6 3940 Trade payables (9) 156.8 173.3 186.3 199.9 214.5 218.4 222.2 226.2 230.2 231.8 233.8 40 Deferred and unpaid41 life insurance premiums 20.9 22.5 22.4 22.8 23.9 25.2 25.5 25.3 27.0 26.5 24.8 41

42 Net worth 46902.1 52494.0 58823.3 63334.9 63910.6 61452.2 60577.8 57824.7 52917.1 51141.5 53139.9 42

Memo: Replacement-cost value of structures:43 Residential 10679.9 12030.3 13475.1 14440.6 14643.0 14587.2 14523.6 14359.8 13981.2 13776.4 13831.2 4344 Households 10513.7 11848.9 13275.9 14229.3 14430.3 14375.4 14313.0 14151.6 13778.7 13577.1 13631.3 4445 Nonprofit organizations 166.1 181.4 199.3 211.3 212.7 211.7 210.6 208.2 202.5 199.4 199.9 4546 Nonresidential (nonprofits) 955.5 1058.3 1174.8 1279.5 1352.6 1356.9 1368.9 1394.2 1424.0 1412.1 1379.2 46

47 Disposable personal income 8377.8 8889.4 9277.3 9915.7 10403.1 10610.4 10966.7 10849.3 10799.1 10765.4 10902.9 47 Household net worth as percentage of48 disposable personal income 559.8 590.5 634.1 638.7 614.3 579.2 552.4 533.0 490.0 475.1 487.4 48 Owners’ equity in household real49 estate (10) 9298.4 10810.1 12572.5 12115.4 9992.2 9255.6 8994.4 8532.8 7886.4 7517.7 7870.4 49 Owners’ equity as percentage of50 household real estate (11) 57.5 58.0 58.7 55.2 48.8 46.7 46.0 44.8 43.1 41.9 43.1 50

(1) Sector includes farm households and domestic hedge funds.(2) At market value.(3) All types of owner-occupied housing including farm houses and mobile homes, as well as second homes that are not rented, vacant homes for sale, and vacant land.(4) At replacement (current) cost.(5) Syndicated loans to nonfinancial corporate business by nonprofits and domestic hedge funds.(6) Value based on the market values of equities held and the book value of other assets held by mutual funds.(7) Net worth of noncorporate business (table B.103, line 31) and owners’ equity in farm business and unincorporated security brokers and dealers.(8) Includes loans made under home equity lines of credit and home equity loans secured by junior liens, shown on table L.218, line 22.(9) Liabilities of nonprofit organizations.(10) Line 4 less line 33.(11) Line 49 divided by line 4.

Slide 19 of 44

Household Savings: Rates

Source: St. Louis Fedhttp://research.stlouisfed.org/fred2/series/PSAVERT/Slide 20 of 44

International Rates

“consumption boom” that has at the same timecharacterized the behavior of U.S. households.

A third argument refers mainly to FoF esti-mates of the personal saving rate and leads toconclude that such a measure—certainly to beconsidered superior to NIPA measures, the argu-ment goes—could be grossly underestimated atpresent. For instance, Hall (2000) has estimatedthat a large part of the increase in the net worthof U.S. households during the 1990s would havetaken the form of what he calls “e-capital,” a bodyof information-processing methods and organi-zational knowledge that has strongly increasedthe productivity of labor. Hall has argued that theaccumulation of such e-capital by householdswould have created a new, intangible type ofasset that should legitimately enter saving ratecalculations. Obviously, a similar phenomenonwould have involved U.S. firms that thereforewould have a much higher net saving rate thanrecorded by the BEA. From this perspective, the

recent decline in the U.S. personal saving ratewould simply hide a shift from savings in theform of accumulation of traditional assets (stocks,bonds, houses) to what we could call “e-assets.”In parallel, the net saving of U.S. businesses alsomight be substantially underestimated. Given thegrowing importance of information technologyin a globalized world, the decline in the personalsaving rate would actually reflect an encouragingdevelopment, likely to predict sustained produc-tivity growth. Although some of these innovativenotions of what constitutes an asset and whatconstitutes saving behavior are of key importance,at this point the estimates of the amount of annualinvestments as a percentage of GNP remain fairlyuncertain and probably insufficient to explainthe decline in the personal saving rate.

One final argument exploits the fact that therecent U.S. experience is not very different fromthe recent historical record of a number of devel-oped countries. Figure 12 shows the personal

Guidolin and La Jeunesse

FEDERAL RESERVE BANK OF ST. LOUIS REVIEW NOVEMBER/DECEMBER 2007 507

–5

0

5

10

15

20

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006

Percent

Australia

Canada

United Kingdom

Japan

United StatesFranceGermany

Figure 12International Household Saving Ratios (quarterly)

SOURCE: Organisation for Economic Co-operation and Development.

Source: St. Louis Fed: Guidolin, La Jeunesse (2007)Slide 21 of 44

175 of 260

National Savings

At a national level:

S︸︷︷︸National Saving

= Sp︸︷︷︸

Private Saving

+ Sg︸︷︷︸

Government SavingNational Economic Trendsupdated through03/05/14

15Research DivisionFederal Reserve Bank of St. Louis

88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13

Gross Govt. Saving

Gross Private Saving

BOCA

Percent of GDP

Gross Saving Rates and Balance on Current Account (NIPA)

-10

-5

0

5

10

15

20

25

88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14

2011 2012 2013

Compounded annual rates of change

Real Private Fixed Investment

-5

0

5

10

15

20

18628 18993 19359 19724

2011 2012 2013


Real Equipment Investment

-10

-5

0

5

10

15

20

25

18628 18993 19359 19724 2011 2012 2013


Real Nonresidential Fixed Investment

-10

-5

0

5

10

15

20

25

18628 18993 19359 19724

2011 2012 2013


Real Residential Fixed Investment

-15

-10

-5

0

5

10

15

20

25

18628 18993 19359 19724 2012 2013 2014

Millions, annual rate Millions, annual rate

Housing Starts(left scale)

New Home Sales(right scale)

Housing Starts and New Home Sales

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

18993 19359 19724 20089

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

0.60

2009 2010 2011 2012 2013 2014

Percent change from year ago, excluding aircraft

Orders

EquipmentInvestment

Nondefense Capital Goods Orders

-40

-30

-20

-10

0

10

20

30

17898 18263 18628 18993 19359 19724 20089

Source: http://research.stlouisfed.org/publications/net/page15.pdf

Slide 22 of 44

176 of 260

9.4 Elastic Labor

177 of 260

Extending the two period model

Slide 2 of 18

What is the two periods model missing so far?

1 Labor supply and wages

2 Firms

3 Investment decision

Slide 3 of 18

Consumption Today

Let consumption depend on wealth and interest rate: C(we, r)

Q: What happens when we change wealth and interest rates?

Effects on the consumption of goods:

• Demand of current consumption increases whenlifetime wealth increases (consumption is a normal good)

dC(we, r)

dwe> 0

• Current consumption decreases with interest rate increases(we assume substitution effect dominates)

dC(we, r)

dr< 0

Slide 4 of 18

178 of 260

The Elastic Consumer

Up to now y was exogenous ⇒ now introduce elastic labor:

• Today budget constraint:

c+ s = w(h− l) + π − T

• Tomorrow budget constraint:

c′ = w′(h− l′) + π′ − T + (1 + r)s

• Lifetime budget constraint:

c+c′

1 + r= w(h− l) + π − T +

w′(h− l′) + π′ − T1 + r

Slide 5 of 18

Optimality and Labor Supply

Optimality conditions:

• First period consumption-leisure trade-off: MRSl,c = w

• Second period consumption-leisure trade-off: MRSl′,c′ = w′

• Optimal consumption saving: MRSc,c′ = 1 + r

Slide 6 of 18

Interest Rates and Labor Supply

Let labor supply be N(we, r, w). Effects on the supply of labor:

• Current labor supply is increasing in real wage(from now on assume substitution larger than income effect)

dN(we, r, w)

dw> 0

• Current labor supply decreases if lifetime wealth increases

dN(we, r, w)

dwe< 0

• Current labor supply increases when the interest rate increases

dN(we, r, w)

dr> 0

Slide 7 of 18

179 of 260

9.5 The Firm

180 of 260

The Firm

Slide 8 of 18

US Firms: Data

Adding Investment decision:

Business Enterprise 515U.S. Census Bureau, Statistical Abstract of the United States: 2012

Table 784. Capital Expenditures: 2000 to 2009[In billions of dollars (1,161 represents $1,161,000,000,000). Based on a sample survey and subject to sampling error; see source for details]

ItemAll companies Companies with employees Companies without employees

2000 2005 2008 2009 2000 2005 2008 2009 2000 2005 2008 2009 Capital expenditures, total . . . 1,161 1,145 1,374 1,090 1,090 1,063 1,294 1,015 71 82 80 75 Structures . . . . . . . . . . . . . . . . . . . 364 402 562 448 338 369 529 413 26 33 33 35 New . . . . . . . . . . . . . . . . . . . . . . . 329 366 523 421 309 341 500 393 20 25 23 28 Used . . . . . . . . . . . . . . . . . . . . . . 35 36 39 27 29 28 29 19 6 8 10 8 Equipment and software . . . . . . . . 797 743 812 642 752 694 765 602 45 49 47 40 New . . . . . . . . . . . . . . . . . . . . . . . 751 701 765 607 718 665 728 577 32 37 37 30 Used . . . . . . . . . . . . . . . . . . . . . . 46 42 47 35 34 29 37 25 12 13 10 10 Capital leases . . . . . . . . . . . . . . . . 20 18 20 17 19 18 19 17 (Z) (Z) 1 1

Z Less than $500 million.Source: U.S. Census Bureau, “2009 Annual Capital Expenditures Survey,” February 2011, <http://www.census.gov/econ

/aces/>, and earlier reports.

Table 785. Capital Expenditures by Industry: 2000 and 2009[In billions of dollars (1,090 represents $1,090,000,000,000). Covers only companies with employees. Data for 2000 based on the North American Industry Classification System (NAICS), 1997; 2009 based on NAICS, 2007; see text this section. Based on a sample survey and subject to sampling error; see source for details]

Industry NAICS code 2000 2009 Industry NAICS

code 2000 2009 Total expenditures . . . . . . . . . . . . (X) 1,090 1,015

Professional, scientific, and technical services . . . . . . . . . . . . . . . . . . . . . . . . 54 34 27

Forestry, fishing, and agricultural services . . . . . . . . . . . . . . . . . . . . . . 113–115 1 2Mining . . . . . . . . . . . . . . . . . . . . . . . . 21 43 101 Management of companies and

enterprises . . . . . . . . . . . . . . . . . . . . . . 55 5 5Utilities . . . . . . . . . . . . . . . . . . . . . . . . 22 61 102Construction . . . . . . . . . . . . . . . . . . . 23 25 20 Admin/support waste mgt/remediation

services . . . . . . . . . . . . . . . . . . . . . . . . 56 18 19Manufacturing . . . . . . . . . . . . . . . . . . 31–33 215 156 Durable goods . . . . . . . . . . . . . . . . . 321, 327, 33 134 77 Educational services . . . . . . . . . . . . . . . 61 18 28 Nondurable goods . . . . . . . . . . . . . . 31, 322–326 81 79 Health care and social assistance . . . . . 62 52 79Wholesale trade . . . . . . . . . . . . . . . . . 42 34 25 Arts, entertainment, and recreation . . . . 71 19 16Retail trade . . . . . . . . . . . . . . . . . . . . 44–45 70 58 Accommodation and food services . . . . 72 26 26Transportation and warehousing . . . . 48–49 60 56 Other services (except public

administration) . . . . . . . . . . . . . . . . . . . 81 21 29Information . . . . . . . . . . . . . . . . . . . . . 51 160 88Finance and insurance . . . . . . . . . . . 52 134 100 Structure and equipment expenditures

serving multiple industry categories . . (X) 2 3Real estate and rental and leasing . . 53 92 73

X Not applicable.Source: U.S. Census Bureau, “2009 Annual Capital Expenditures Survey,” February 2011, <http://www.census.gov/econ


Table 786. Business Cycle Expansions and Contractions—Months of Duration: 1945 to 2009[A trough is the low point of a business cycle; a peak is the high point. Contraction, or recession, is the period from peak to subsequent trough; expansion is the period from trough to subsequent peak. Business cycle reference dates are determined by the National Bureau of Economic Research, Inc.]

Business cycle reference dateContraction

(Peak to trough)

Expansion (Previous trough to

peak)

Length of cyclePeak Trough Trough from

previous trough

Peak from previous

peakMonth Year Month YearFebruary . . . . . . . . . . . . . . . . . 1945 October . . . . . . 1945 8 1 80 1 88 2 93November . . . . . . . . . . . . . . . . 1948 October . . . . . . 1949 11 37 48 45July . . . . . . . . . . . . . . . . . . . . . 1953 May . . . . . . . . . 1954 10 45 55 56August . . . . . . . . . . . . . . . . . . . 1957 April . . . . . . . . . 1958 8 39 47 49April . . . . . . . . . . . . . . . . . . . . . 1960 February . . . . . 1961 10 24 34 32December . . . . . . . . . . . . . . . . 1969 November . . . . 1970 11 106 117 116November . . . . . . . . . . . . . . . . 1973 March . . . . . . . . 1975 16 36 52 47January . . . . . . . . . . . . . . . . . . 1980 July . . . . . . . . . 1980 6 58 64 74July . . . . . . . . . . . . . . . . . . . . . 1981 November . . . . 1982 16 12 28 18July . . . . . . . . . . . . . . . . . . . . . 1990 March . . . . . . . . 1991 8 92 100 108March . . . . . . . . . . . . . . . . . . . . 2001 November . . . . 2001 8 120 128 128December . . . . . . . . . . . . . . . . 2007 June . . . . . . . . . 2009 18 73 91 81

Average, all cycles: 1945 to 2009 (11 cycles) . . . . 11 59 73 66

1 Previous trough: June 1938. 2 Previous peak: May 1937.Source: National Bureau of Economic Research, Inc., Cambridge, MA, “Business Cycle Expansions and Contractions,”

<http://www.nber.org/cycles.html>, accessed May 2011.

• Source US Census: LINK

Slide 9 of 18

Online Survey!

Q: which industry does the bulk of investment?


1 Mining

2 Forestry and agricultural services

3 Manufacturing

4 Finance and Insurance

5 Health Care

Slide 10 of 18

181 of 260

US Firms: Data

Q: who does the bulk of investment?

Business Enterprise 515U.S. Census Bureau, Statistical Abstract of the United States: 2012

Table 784. Capital Expenditures: 2000 to 2009[In billions of dollars (1,161 represents $1,161,000,000,000). Based on a sample survey and subject to sampling error; see source for details]

ItemAll companies Companies with employees Companies without employees

2000 2005 2008 2009 2000 2005 2008 2009 2000 2005 2008 2009 Capital expenditures, total . . . 1,161 1,145 1,374 1,090 1,090 1,063 1,294 1,015 71 82 80 75 Structures . . . . . . . . . . . . . . . . . . . 364 402 562 448 338 369 529 413 26 33 33 35 New . . . . . . . . . . . . . . . . . . . . . . . 329 366 523 421 309 341 500 393 20 25 23 28 Used . . . . . . . . . . . . . . . . . . . . . . 35 36 39 27 29 28 29 19 6 8 10 8 Equipment and software . . . . . . . . 797 743 812 642 752 694 765 602 45 49 47 40 New . . . . . . . . . . . . . . . . . . . . . . . 751 701 765 607 718 665 728 577 32 37 37 30 Used . . . . . . . . . . . . . . . . . . . . . . 46 42 47 35 34 29 37 25 12 13 10 10 Capital leases . . . . . . . . . . . . . . . . 20 18 20 17 19 18 19 17 (Z) (Z) 1 1

Z Less than $500 million.Source: U.S. Census Bureau, “2009 Annual Capital Expenditures Survey,” February 2011, <http://www.census.gov/econ


Table 785. Capital Expenditures by Industry: 2000 and 2009[In billions of dollars (1,090 represents $1,090,000,000,000). Covers only companies with employees. Data for 2000 based on the North American Industry Classification System (NAICS), 1997; 2009 based on NAICS, 2007; see text this section. Based on a sample survey and subject to sampling error; see source for details]

Industry NAICS code 2000 2009 Industry NAICS

code 2000 2009 Total expenditures . . . . . . . . . . . . (X) 1,090 1,015

Professional, scientific, and technical services . . . . . . . . . . . . . . . . . . . . . . . . 54 34 27

Forestry, fishing, and agricultural services . . . . . . . . . . . . . . . . . . . . . . 113–115 1 2Mining . . . . . . . . . . . . . . . . . . . . . . . . 21 43 101 Management of companies and

enterprises . . . . . . . . . . . . . . . . . . . . . . 55 5 5Utilities . . . . . . . . . . . . . . . . . . . . . . . . 22 61 102Construction . . . . . . . . . . . . . . . . . . . 23 25 20 Admin/support waste mgt/remediation

services . . . . . . . . . . . . . . . . . . . . . . . . 56 18 19Manufacturing . . . . . . . . . . . . . . . . . . 31–33 215 156 Durable goods . . . . . . . . . . . . . . . . . 321, 327, 33 134 77 Educational services . . . . . . . . . . . . . . . 61 18 28 Nondurable goods . . . . . . . . . . . . . . 31, 322–326 81 79 Health care and social assistance . . . . . 62 52 79Wholesale trade . . . . . . . . . . . . . . . . . 42 34 25 Arts, entertainment, and recreation . . . . 71 19 16Retail trade . . . . . . . . . . . . . . . . . . . . 44–45 70 58 Accommodation and food services . . . . 72 26 26Transportation and warehousing . . . . 48–49 60 56 Other services (except public

administration) . . . . . . . . . . . . . . . . . . . 81 21 29Information . . . . . . . . . . . . . . . . . . . . . 51 160 88Finance and insurance . . . . . . . . . . . 52 134 100 Structure and equipment expenditures

serving multiple industry categories . . (X) 2 3Real estate and rental and leasing . . 53 92 73

X Not applicable.Source: U.S. Census Bureau, “2009 Annual Capital Expenditures Survey,” February 2011, <http://www.census.gov/econ


Table 786. Business Cycle Expansions and Contractions—Months of Duration: 1945 to 2009[A trough is the low point of a business cycle; a peak is the high point. Contraction, or recession, is the period from peak to subsequent trough; expansion is the period from trough to subsequent peak. Business cycle reference dates are determined by the National Bureau of Economic Research, Inc.]

Business cycle reference dateContraction

(Peak to trough)

Expansion (Previous trough to

peak)

Length of cyclePeak Trough Trough from

previous trough

Peak from previous

peakMonth Year Month YearFebruary . . . . . . . . . . . . . . . . . 1945 October . . . . . . 1945 8 1 80 1 88 2 93November . . . . . . . . . . . . . . . . 1948 October . . . . . . 1949 11 37 48 45July . . . . . . . . . . . . . . . . . . . . . 1953 May . . . . . . . . . 1954 10 45 55 56August . . . . . . . . . . . . . . . . . . . 1957 April . . . . . . . . . 1958 8 39 47 49April . . . . . . . . . . . . . . . . . . . . . 1960 February . . . . . 1961 10 24 34 32December . . . . . . . . . . . . . . . . 1969 November . . . . 1970 11 106 117 116November . . . . . . . . . . . . . . . . 1973 March . . . . . . . . 1975 16 36 52 47January . . . . . . . . . . . . . . . . . . 1980 July . . . . . . . . . 1980 6 58 64 74July . . . . . . . . . . . . . . . . . . . . . 1981 November . . . . 1982 16 12 28 18July . . . . . . . . . . . . . . . . . . . . . 1990 March . . . . . . . . 1991 8 92 100 108March . . . . . . . . . . . . . . . . . . . . 2001 November . . . . 2001 8 120 128 128December . . . . . . . . . . . . . . . . 2007 June . . . . . . . . . 2009 18 73 91 81

Average, all cycles: 1945 to 2009 (11 cycles) . . . . 11 59 73 66

1 Previous trough: June 1938. 2 Previous peak: May 1937.Source: National Bureau of Economic Research, Inc., Cambridge, MA, “Business Cycle Expansions and Contractions,”

<http://www.nber.org/cycles.html>, accessed May 2011.

• Source US Census: LINK

Slide 11 of 18

The Firm

• Introduce non linear technology and investment decision

• Output today: Y = zF (K,N)

• Output tomorrow: Y ′ = z′F (K ′, N ′)

• Firm invests I so that

K ′ = (1− d)K + I

• Note: we are modeling K as in Solow.

Slide 12 of 18

The Firm

• Firm maximize present discounted value of the firm

V = π +π′

1 + r

• Profits today: π = Y − wN−I

• Profits tomorrow: π′ = Y ′ − w′N ′+ (1− d)K ′︸︷︷︸Liquidation Value

• Note that now the firm owns the capital andliquidates it in the last period

Slide 13 of 18

182 of 260

The Firm and Labor Demand

• Optimality MPN = w (wage goes up labor demand goes down)

• If z or K increase Ü labor demand increases. Why?

Slide 14 of 18

The Firm and Investment Decision

We now calculate the optimal investment decision.

The problem of the Firm is:

maxN,N ′,I

zF (K,N)− wN − I +z′F (K ′, N ′)− w′N ′ + (1− d)K ′

1 + r

Optimality with respect to I gives

−1 +z′FK(

K′︷︸︸︷(1− d)K + I,N) + (1− d)

1 + r= 0

so thatz′FK(K ′, N ′)︸︷︷︸

MP ′K

−d = r

(net marginal product of capital tomorrow = interest rate)

Slide 15 of 18


• Suppose r1 ↓ r2, since

z′FK((1− d)K + I1)− d = r1

then investment increases I1 ↑ I2(marginal benefit goes down)

Slide 16 of 18

183 of 260


• If z′ tomorrow increases or if K decreases, investment curve shiftsto the right (marginal benefit increases since MP ′K increases)

Slide 17 of 18

The Firm and Investment Decision: Formal

Suppose that the production function is Cobb-Douglas:

zF (K,N) = zKαN1−α

Then optimality implies

z′α(K ′

N ′

)α−1= r + d

substituting K ′ = (1− d)K + I we get

I =

[z′αr + d

] 11−α

N ′ − (1− d)K

Note that I is increasing in z′ and decreasing in r and K.

Slide 18 of 18

184 of 260

9.6 Equilibrium

185 of 260


1 Equilibrium in the complete two period model

• The output supply curve

• The output demand curve

2 Experiments/ Policy

1 Change in government expenditures

2 Production shocks:

• Change in productivity

• Change in capital stock

Slide 3 of 52

Equilibrium in the complete two period model

Slide 4 of 52

Competitive Equilibrium: Dynamic

• Definition of equilibrium expands what we have done in Lecture 5.

Definition (Competitie Equilibrium)

For a set of exogenous variables (K,G,G′, z, z′) A competitiveequilibrium is a set of endogenous variables (C,N s, S, I,Nd, B, T, Y, r, w)for both today (without prime) and tomorrow (with prime), so that:

1 The consumer chooses consumption, savings and labor supplyoptimally, taking as given wages, interest rate, taxes and dividends.

2 The firm chooses labor demand and investment to maximize profits,taking as given wages, interest rate and current/futureproductivity.

+ Turn to next page...

186 of 260

Competitive Equilibrium: Dynamic

Definition (Competitive Equilibrium (continued))

[...] continued:

3 Government balances the budget (B is borrowing):

G = T + B; G′ + (1 + r)B = T ′

4 Labor market clears: Nd = N s; N′d = N

′s

5 Goods market clears: Y = C + I + G Y ′ = C ′ + I ′ + G′

6 Financial market clears: B = S

Equilibrium: 2 Markets

• Analytical or graphical characterization of equilibrium is hard.

• We focus on the equilibrium of two markets:

1 Today’s labor market (relating wages and employment)

2 Today’s goods market (relating interest rate and output)

Which markets are we NOT focusing on?

Slide 7 of 52

Equilibrium in the Labor Market

We equate demand for labor (firm) and supply of labor (household):

• We determine employment level: N∗

• We determine wage rate: w∗

• !! supply of labor depends on r∗

Slide 8 of 52

187 of 260

Equilibrium in the Goods Market

We equate demand of goods (Y d) and supply of goods (Y s), where:

Y s = zF (K,N s)

Y d = C(we, r) + I(r) + G

+ Goal: determine the relationship between Y s, Y d and r

Slide 9 of 52

The Output Supply Curve

• Y s as a function of r is called output supply curve.

• How does Y s vary with respect to r? Recall that N s(we, r, w)

dY s

dr=

d

drzF (K,N s) = zFN (K,N s)

dN s

dr︸︷︷︸>0

> 0

Ü Y s is an increasing (and concave) function of r

Slide 10 of 52

The Output Demand Curve

• Y d as a function of r is called output demand curve.

Y d(r) = C(we, r) + I(r) + G

• Changing r:

dY d

dr=

dC(we, r)

dr︸︷︷︸<0

+dI(r)

dr︸︷︷︸<0

< 0

Ü Y s is a decreasing (and concave) function of r

Slide 11 of 52

188 of 260

Output Supply Output Demand

Graphing together demand and supply:

• We determine output level: Y ∗

• We determine interest rate: r∗

Slide 12 of 52

Graphical Equilibrium

• Combining with the labor market equilibrium graph:

Slide 13 of 52

2 Questions

1 On March 11, 2011, Japan was hit by a massiveearthquake.

What do you forecast will happen to GDP, wages, employment,investment, interest rates?

2 On February 17, 2009 the US passed theAmerican Recovery and Reinvestment Act.

What do you forecast will happen to GDP, wages, employment,investment, interest rates?

Slide 14 of 52

189 of 260

Online Survey!

Q: Suppose the government increases spending (G) by adollar by how much does GDP (Y) change?


1 Between 0 and $0.5

2 Between $0.5 and $1

3 Between $1 and $2

4 More than $2

Slide 15 of 52

Shifting Output Curves

Slide 16 of 52

Shifting the Output Supply Curve

Questions:

• How does output supply change following a change in G?

1 If G ↑ then T ↑ so we ↓2 If we ↓ then Ns ↑3 So zF (K,Ns) ↑, Supply curve shifts to the right!

• How does output supply change following a change in z?

1 If z ↑ then zF (K,N) ↑2 If zF (K,N) ↑ then Nd ↑3 Supply curve shifts to the right!

• Note: these are exogenous changes,not changes due to r or w

Slide 17 of 52

190 of 260

Shifting the Output Supply Curve: Graphically

• Suppose TFP increases z1 ↑ z2

Slide 18 of 52

Shifting the Demand Curve

• A change in output demand is due to a change in one of it’scomponents:

∆Y d ∝ ∆C + ∆I + ∆G

• G is exogenous but C and I are endogenous

• We need to look closer at what exogenous change impacts C and I

Slide 19 of 52

Shifting the Output Demand Curve

Impacting C and I:

1 decrease in present value of taxes: Ü C ↑

2 increase in future income: Ü C ↑

3 increase in future TFP : Ü I ↑

4 decrease in the capital stock: Ü I ↑

Each of these either affects C, or I. Also:

these are exogenous changes, not changes due to r or w

Slide 20 of 52

191 of 260

Shifting the Demand Curve: Quantitative

• Quantitatively, how much does Y d change due to a change inenvironment?

• Key difficulty changes in Y affect income which affects the wealthof the worker.

• So what happens if the household become wealthier?(for example with higher labor income)

more demand for C Ü more demand for output Ü

Ü more labor income Ü even more demand for C . . .

Slide 21 of 52


• MPC (Marginal Propensity to Consume) defined as:

The rate at which consumption increases when (disposable) incomeis increased by a small amount

• Formally:dC

dwe= MPC ·∆we

Note that in general 0 < MPC < 1

Slide 22 of 52

Average Propensity to Consume

• Average propensity to Consume is AMPC = consumptiondisposable income

It can be shown that AMPC > MPC

!"#$

!"#%$

!"#&$

!"#'$

!"##$

!"($

!"(%$

!"(&$

!"('$

)(&#$ )(*#$ )('#$ )(+#$ )(##$ )((#$ %!!#$

!"#$%&#'($)*#+,-./'.)'0)+,12#'

Taken from: Hoover (2011)

Slide 23 of 52

192 of 260


• The additional “wealth” effect of an increase in Y is:

dC

dwe= MPC · ∆Y d

︸︷︷︸change in wealth

• Introduce the indirect increase in C following a increase in Y

∆Y d =

Wealth effect︷︸︸︷MPC ·∆Y d +

Additional change︷︸︸︷∆C︸︷︷︸

Total consumption change

+∆I + ∆G =

=1

1−MPC︸︷︷︸The Multiplier

(∆C + ∆I + ∆G)

• The multiplier since “multiplies” changes in demand, captures theoverall income effect. Note that the multiplier is greater than 1.

Experiments

Slide 25 of 52

Experiments

We next go over the following examples studying equilibrium changes:

1 Temporary Increase in G

2 Increase in TFP today

3 Decrease In Capital Stock

4 Increase in TFP tomorrow

5 Permanent Increase In G

Slide 26 of 52

193 of 260

Algorithm

To solve these exercises follow these steps:

1) Identify effect of change on consumer, government, firm(these are exogenous changes, not changes due to r or w)

2) Identify first tentative equilibrium in labor market

3) Identify effect on output supply curve

4) Identify effect on output demand curve

5) Determine changes in Y and r in the goods market.

6) Using result in 2) and change in r determine change in N and w

7) In 5) and 6), specify which result are determinate andwhich are indeterminate

Slide 27 of 52

Government Expenditure in Equilibrium

Suppose government increases expenditures ∆G > 0:

1) ∆N s > 0, why?

2) Output supply shifts to the right

3) Output demand (start from key formula):

∆Y d =1

1−MPC(∆C + ∆G + ∆I)

∆G > 0, ∆I = 0 also ∆C =dC

dwe︸︷︷︸Effect of taxes

= MPC · (−∆G)

4) So that:

∆Y d =(−MPC ·∆G + ∆G)

1−MPC= ∆G > 0

Slide 28 of 52

Increase in G: graphical summary

• Note that if Y s shift “a little” Ü r increases

Note that if Y s shifts less than Y d

Slide 29 of 52

194 of 260

Increase in G: summary

The effect of a stimulus:

• C goes down (government is crowding out private consumption)

• N and Y go up

• w goes down

• r goes up

• Important: ∆Y < ∆G

(Government multiplier < 1,for every dollar spent GDP goes up by less than a dollar)

Slide 30 of 52

Government Spending and GDP

• Question: what is the relation between G and Y in the data?

• Answer: no consensus among economist

• Our theory predicts a government multiplier < 1

• Keynesian analysis is based on a government multiplier > 1

+ For a quick summary look at this discussion between Boldrin -DeLong starting at 42:20

http://tinyurl.com/BoldrinDelong

Slide 31 of 52


• Question: what is the relation between G and Y in the data?

TABLE 2

PRESENT VALUE MULTIPLIERS OF THE POLICY SHOCKS

1 qrt 4qrts 8 qrts 12 qrts 20 qrts Maximum

DEFICIT FINANCED TAX CUT 0.20 0.53 2.08 6.19 3.80 9.59 (qrt 14)

DEFICIT SPENDING 0.44 0.31 0.37 0.29 0.33 0.44 (qrt 1)

This table shows the present value multipliers for a deficit financed tax cut policy shock and for a deficit

spending fiscal policy shock. The multipliers given are the median multipliers in both cases.

4.3 A Deficit Financed Tax Cut Fiscal Policy Shock

The impulse responses for a deficit financed tax cut fiscal policy shock are shown in

Figure 8. The shock is designed so that tax revenues fall by 1% and government spending

remains unchanged for four quarters following the shock. The responses look very similar

to a mirror image of the responses to the basic government revenue shock in Figure 3.

Thus the tax cut stimulates output, consumption and investment significantly with the

effect peaking after about three years. The effect on prices is initially negative but

subsequently positive following the rise in output.

4.4 The Balanced Budget Spending Shock

The balanced budget spending shock is identified by requiring both government revenues

and expenditures to increase in such a way that the increase in revenues and expenditure

are equal for each period in the four-quarter window following the shock. For ease of

comparison we choose a rise in government spending of 1% and a rise in government

revenues of 1.28%. Government revenue rises by more than government spending since

over the sample government revenue’s share of GDP is 0.162 while that of government

spending is 0.208 thus we require government revenues to rise by (0.208/0.162)%. The

results are shown in Figure 9. These show that on impact there is a small expansionary

effect on GDP but thereafter the depressing effects of the tax increases dominate the

spending effects and GDP, consumption and investment falls.

4.5 Measures of the Effects of Policy Shocks

To compare the effects of one fiscal shock with another it is useful to define summary

measures of the effects of each fiscal shock. One measure used in the literature is the

14

Taken from: Mountford and Uhlig (2005)

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• When does government spending have an effect?

TABLE 5

MAXIMUM AND MINIMUM IMPACT MULTIPLIERS OF FISCAL POLICY SHOCKS

Fiscal Shock Maximum Multiplier Minimum Multiplier

Median Confidence Interval Median Confidence Interval

Multiplier 16th,84th Quantiles Multiplier 16th,84th Quantiles

Deficit Spending 1.36 0.75, 1.59 -0.73 -2.73, -0.22

lag 9 lag 1, lag 24 at lag 24 lag 24, lag 5

Balanced Budget 0.45 0.18, 1.59 -3.64 -6.39, -2.26


Tax Cut 3.45 3.11, 4.65 -0.11 -0.40, 0.28


Deficit Spending 0.71 0.56, 0.89 0.03 -0.25, 0.17

In first year lag 4 lag 4, lag 4 at lag 3 lag 4, lag 1

Balanced Budget 0.31 0.05, 0.71 -0.83 -1.39, -0.60

In first year at lag 1 lag 4, lag 1 at lag 1 lag 4, lag 2

These statistics relate to the distribution of the maximum and minimum impact multiplier ef-

fects of each fiscal shock. For each draw the maximum and minimum fiscal multiplier is cal-

culated and the 16th, 50th and 84th percentiles of these results are displayed. The multiplier

statistic is calculated in terms of the initial, lag 0, fiscal shock as follows: multiplier for GDP

=GDP response

Fiscal shock at Lag 0/(Average Fiscal variable share of GDP).

and minimum multipliers of the two spending shocks in the first year after the shock.

In this case we now get the result that the deficit spending shock’s minimum multiplier

is insignificantly different from zero but that for the balanced budget spending shock is

still significantly negative.

4.8 Policy Conclusions

An important lesson one can draw from the results is that while a deficit-financed ex-

penditure stimulus is possible, the eventual costs are likely to be much higher than the

immediate benefits. For suppose that government spending is increased by two percent,

financed by increasing the deficit: this results, using the median values from Table 5,

19

Taken from: Mountford and Uhlig (2005)

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Shocks to the Production Function

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Change in Productivity

Suppose TFP today increases: ∆z > 0

1) ∆Nd > 0, why? marginal product of labor increases

2) Output supply shifts to the right (higher z and N)

3) Output demand: ∆C = 0, ∆I = 0, ∆G = 0. So that

∆Y d =1

1−MPC(∆C + ∆G + ∆I) = 0

No shift!

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• Don’t forget affect of r2 on labor supply

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Summarizing:

• Output supply shift to the right → lowers r

• This causes labor supply to shift to the left

In equilibrium:

• Effect on N ambiguous (most likely increasing); w increases

• Y increases and r decreases

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RBC Model and the US

• Changes in z can be used to model US economy Cycles

Taken from: Kydland and Prescott (1982)

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Change in Capital Stock: Japan 2011

Suppose capital stock today decreases: K ↓

1) Labor demand shifts to the left (why?)

2) Output supply shifts to the left

3) Output demand: ∆I > 0. Output demand shift to the right.(Firm increases investment since K decreased)

Slide 39 of 52

Change in Capital Stock

4) Increase in r makes labor supply shift to the right

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Change in Capital Stock

Summarizing in equilibrium:

• I increases

• Y ambiguous, r goes up

• w decreases; N ambiguous (most likely down)

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Japan: Data

Slide 42 of 52

Changing Future Income

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Changing Future Income

• The peculiarity of the next two examples is that GDP tomorrowwill change.

• In solving for equilibrium it will be important to understand howthe household will anticipate future income changes.

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Increase in Future TFP

• Suppose that z′ goes up

• No change (for now) in current labor market or labor supply

• Recall:

∆Y d =1

1−MPC(∆C + ∆G + ∆I)

∆I > 0 firm anticipate higher return to capital tomorrow∆C = MPC ·∆Y ′ > 0

• Interest rate go up

• Labor supply shifts to the right

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Slide 46 of 52


Punchline:

• C might go up if income effects due to future income increasedominate substitution effect due to higher r

• I goes up

• N and Y go up

• r goes up

• w goes down

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Permanent Increase in G

• We model permanent changes as changes to G and G′

(suppose both go up by ∆G)

• When G and G′ increase it implies T or T ′ prime go up.Change in NPV of taxes

∆(taxes) = ∆G +∆G

1 + r

⇒ Labor Supply and Output Supply shift to the right

Slide 48 of 52


• Recall:

∆Y d =1

1−MPC(∆C + ∆G + ∆I)

and ∆C = MPC ·∆(income)

• The tricky shift is on the output demand curve;two effects on income

1) increase in NPV taxes: ∆G + ∆G1+r

2) changes in income: ∆Y ′/(1 + r)

Slide 49 of 52


∆Y d =MPC

[∆Y ′1+r −∆G− ∆G

1+r

]+ ∆G + ∆I

1−MPC

• Permanent changes imply same changes today and tomorrow⇒ no changes in saving of the household

• If r does not change ⇒ no changes in investment, so that:∆I = 0 and ∆Y ′ = ∆G

∆Y d = ∆G

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• Q: Does r change?

• A: NOSlide 51 of 52


Punchline:

• C unchanged

• I unchanged

• N and Y go up

• r unchanged

• w goes down

• Important: ∆Y = ∆G

(Government multiplier = 1)

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Chapter 10

Credit Imperfections

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Online Survey!

Q: In your opinion what is the biggest shortcoming in ourmodeling of credit markets?


1 Lack of collateral for loans

2 Lack of default and bankruptcy

3 Lack of financial panics

4 Lack of bid/ask spreads

5 Lack of bank failures

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Plan for This lecture

1 Financial Imperfections: Asymmetric information

• Effect on Spreads

• Effect on Ricardian Equivalence

2 Financial Imperfections: Limited Commitment

• Collateral

3 Panics and Bank Runs

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Credit Market Imperfections

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Credit Market Imperfections

How do real credit markets compare to what we have studied?

• Borrowing and lending at different rates

Ü Different rates for different borrowers

• Limits on the quantity borrowed

Ü Collateral requirements for loans

Definition

Credit Imperfection: Any type of obstacle, either technological orinstitutional that prevents an optimal level of trade in the credit market.

We will look into two types of credit market imperfections:

• Asymmetric information

• Limited commitment

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Asymmetric Information

• We have asymmetric information when some market participantsknow more about own characteristics than other participants.

• In the credit market: a borrower knows more about his or her owncredit worthiness than do potential borrowers.

• Why does it matter?

Ü A lender cannot differentiate between good and bad borrowers.

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Asymmetric Information: Implications

• If lender cannot distinguish between good and bad borrowers:

Ü Lending is more risky (some borrowers will default)

Ü Different rates at which consumers can borrow and lend

• Suppose that: good borrowers, repay; bad, do not.

• 0 < a < 1: fraction of good borrowers

• 1 − a: fraction of bad borrowers

• Suppose that a measure 1 of savers saves (deposits) amount L

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Banks, Lenders, Borrowers

Banks:

• Issues loans at interest rate rL

• Pays interest rD on deposit

• Diversify by lending to a large number of borrowers

Ü a fraction of borrowers a will not default, 1 − a will default

Good borrowers:

• Choose the same loan quantity L

Bad borrowers:

• Mimic good borrowers and choose loan quantity L

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Banks: Default Premium

Profit of banks:

π = aL(1 + rL) + (1 − a)L× 0 − L(1 + rD)

In equilibrium each bank makes 0 profits Ü π = 0. So that

aL(1 + rL) = L(1 + rD)

Equilibrium interest rate on a loan:

rL =1 + rDa

− 1

Each borrower pays a default premium on a loan

• Premium is equal to the difference rL − rD

• It grows as the fraction of bad borrowers increasesSlide 10 of 38

Interest rate spreads during the Financial crisis

• A credit spread is the difference in interest rate betweentwo different loans.

• Source: St. Louis Fedhttp://research.stlouisfed.org/fred2/categories/119

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Asymmetric Information and Ricardian Equivalence

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Asymmetric Information and Ricardian Equivalence

• To prove Ricardian Equivalence we require perfect credit markets.

Ü Ricardian equivalence fails in the presence ofasymmetric information

• Use our basic inter-temporal model• consumer has income y and y′ in periods 0 and 1• consumption of c and c′ in periods 0 and 1• saving denoted by s = y − c

• Consumer lends at the interest rate r1 and borrows at rate r2, with

r1 < r2

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The Inter-temporal Budget Constraint

Budget constraint: AEF .

Households that picks to the right of E are “credit constrained”:they would like to borrow more if rate was r1.

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Credit Market Imperfections and Ricardian Equivalence

Suppose that:

• Key assumption:

Ü the interest rate on government debt is the lending rate r1

• There is a tax cut in the current period ∆t < 0

• A tax increase in the second period −∆t(1 + r1)

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Credit Market Imperfections and Ricardian Equivalence

• Change in timing of taxesshifts the endowment point

• In the figure consumes newendowment point E2

• Consumption today increase bythe amount of the tax cut

Ü Ricardian equivalence fails!

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Credit markets and Limited Commitment

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Credit markets and Limited Commitment

• A loan is a promise to pay in the future.

• In the future, the borrower may decide to not keep his promise.

• Whenever a borrower cannot commit to repay we have a creditimperfection: Limited Commitment.

• With limited commitment, lender needs to set up contracts suchthat borrower has the incentive to pay.

• One possible incentive device: require collateral

Definition

Collateral: An asset owned by the borrower that the lender has aright to seize if the borrower defaults on the loan.

Housing as collateral

• Suppose household owns a house of value H:

• Value of the house is p ·H. Where p is the housing price level

• House are illiquid assets. Cannot be sold quickly to finance currentconsumption

• Consumer’s lifetime wealth:

we = y − t+y′ − t′ + p ·H

1 + r

• Note: wealth depends on p

• Suppose household uses H as a collateral

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Banks and Housing

• Let: c+ s = y − t

• Using H as collateral, banks offer loan s so that: the amountborrowed s by the consumer must satisfy:

s(1 + r)︸︷︷︸Repayment

≥ −p ·H︸︷︷︸Value of collateral

this inequality is called the “collateral constraint”

• Since c = y − t− s, we have

c ≤ y − t+p ·H1 + r

consumption depends on value of collateral!

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Consumption and Collateral Constraints

• The budget constraint with a collateral constraint:

• Consumption today and tomorrow is impacted by p

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Consumption and Collateral Constraints

What happened to the valued of housing from 2007 onwards?

Source:http://research.stlouisfed.org/fred2/series/SPCS20RSA?rid=199Slide 22 of 38

Financial Intemidiation

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Intermediation and Growth

Definition

Share of Private Credit: Value of credit by financialintermediations to the private sector devided by GDP.

Fig. 3. Partial scatter plot of growth vs. private credit.

!"Speci"cally, when we remove South Africa and Switzerland the coe$cient on Private Creditrises to 4.72 and the t-statistics equals 3.65 while the GMM estimate satis"es the litany of diagnostictests. Similarly, when the seven additional countries are removed, the Private Credit enters witha value of 4.53 and a t-statistic of 3.91, while passing the diagnostic tests.

!#For the COMMERCIAL-CENTRAL BANK regressions, Haiti's level of "nancial develop-ment is much less than predicted by its country characteristics. Nonetheless, removing Haitiincreases the estimated coe$cient on COMMERCIAL-CENTRAL BANK to 13.4 (with a t-statisticof 3.35). Moreover, when removing other potential outliers such as Korea, Niger, and Peru, theresults are unchanged (coe$cient estimate of 9.6 on Commercial-Central Bank and a t-statistic of2.44). When examining the GMM residuals, Niger, Honduras, Jamaica, Korea, Mauritius, Pakistan,Senegal, and Taiwan are more than two-standard deviations from zero. Removing these countriesproduces an estimated coe$cient of 7.71 on COMMERCIAL-CENTRAL BANK, with a t-statisticof 2.92, and the regression passes the battery of diagnostic tests discussed in the text. In terms ofLIQUID LIABILITIES, the robustness checks produce similar results. The partial scatter plotspoint to Niger and Korea as potential outliers. Removing these countries does not a!ect the results(The estimated coe$cient becomes 2.24 with a t-statistic of 2.71). Similarly, when using the GMMresidual criteria, Korea, Jamaica, Switzerland, Taiwan, and Zaire fall more than two-standarddeviations away from zero. Removing these countries produces a coe$cient estimate of 2.63 onLIQUID LIABILITIES, with a t-statistic of 4.24, and a regression that passes the various diagnostictests used in this paper.

seven additional countries with residuals more than two-standard deviationsaway from zero (Belgium, El Salvador, Guyana, Jamaica, Mauritius, Niger,and Senegal.) This did not change the conclusions either.!" We followed thesame procedures in checking for the e!ect of outliers for COMMERCIAL-CENTRAL BANK and LIQUID LIABILITIES. In no case did removingoutliers alter the results.!# The strong positive connection between the

48 R. Levine et al. / Journal of Monetary Economics 46 (2000) 31}77

Source: Levine, Loayza, Beck (2000)

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What is Happening?

• September 2007:

Slide 25 of 38

What is Happening?

• March 2014:

Source:http://www.reuters.com/article/slideshow/idUSBREA2P02H20140326#a=2Slide 26 of 38

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Financial Intermediation

• Up to this point in the course we have abstracted fromfinancial intermediation.

• The previous models of private information and limitedcommitment introduce the concept of an intermediary: a bank.

• There is substantial evidence linking growth to the “maturity” ofthe financial sector.

+ Given this let’s have a close look at the benefits and costs of bankas financial intermediary.

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Banks as Intermediaries

• What do Bank-like intermediaries do:

1 They borrow from one group of agents and lend to anothergroup of agents.

2 The borrowing and lending groups are large, suggestingdiversification on each side of the balance sheet.

3 The structure of the bank loans does not mirror the banksobligations in the form of deposits.

Source: Gorton, Wintonhttp://fic.wharton.upenn.edu/fic/papers/02/0228.pdf

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Banks as Intermediaries

• Why do banks exists?

1 They are delegated monitors:

Banks monitor borrowers; given comparative advantage is naturalto have one agent specializing in it.

2 They generate information:

By searching and allocating loans banks provide signals to otherinvestors.

3 They provide insurance to consumers:

Providing loans helps consumer smooth consumption over time.

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Intermediation: Diamond - Dybvig

• Model of banking studied by Diamond and Dybvig

• Written to explain bank runs(could also be applied to financial panics)

• Basic idea: depositors/investors play a coordination game:

1 With good coordination no problem for the bank;

2 With bad coordination bank fails.

• Note: failure can occur without fundamental problemswith the bank.

Slide 30 of 38


The model

• Bank offer deposits:• Short term Ü return Rs

• Long term Ü return Rl (Rl > Rs)

• Investors/Depositors have need for liquidity either:

• In the short term (1/2 of the population)

• In the long term (1/2 of the population)

• Bank is aware of the need for liquidity and invests accordingly:

Ü Bank has half it’s asset in short securities half in long securities


The problem:

• Depositors can withdraw at any time(even if they do not need liquidity)

• Banks has half of it’s asset in short securities.If every agent withdraws at the same time the bank FAILS!

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• Decision to withdraw for long term investors dependson their beliefs of what others do:

• If they believe other investors are not withdrawing the best decisionis to wait for the long run and cash higher return Rl

• If they believe other investors are withdrawing the is best torun to the bank and withdraw now!

• Why run? they believe (and are correct) that the bank will fail.

Slide 33 of 38


• Model as a 2 person game between myself and others:

Table : Payoffs from a Diamond Dybvig game

Me - Others Run Don’t Run

Run 12Rs Rs

Don’t Run 0 Rl

• The game has two Nash equilibria:

1 No panic: Don’t run / Don’t run

2 Panic: Run/ Run

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Suspension of Convertibility

• The foundamental issue is that:

1 Liquidity needs are non-observable/non-contractable.

2 Consumers reach the bank 1 by 1: a sequential service constraint.

3 A solution to the problem of runs can be simple: the bank cansimply close. This is usually referred to suspending convertibility.

4 Suspending convertibility is costly for consumers who need liquidity.

• Is there a better solution? YES

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The FDIC

• Federal Deposit Insurance Corporation signed into law in theBanking Act of 1933.

• Simply: It provided a Federal guarantee to bank deposits.

• Nine banks failed in 1934, compared to more than 9,000 in thepreceding four years.

• Today: FDIC insurance covers all deposit accounts, includingchecking and savings accounts, money market deposit accounts andcertificates of deposit. The standard insurance amount is $250,000per depositor, per insured bank, for each account.

Source http://www.fdic.gov/bank/historical/brief/brhist.pdf

Slide 36 of 38


• How does the FDIC work in the DD framework?

Table : Payoffs from a DD game with FDIC

Me - Others Run Don’t Run

Run Rs Rs

Don’t Run Rl Rl

• Q: In the model described, how much does the FDIC pay out?

Slide 37 of 38

Deposit Insurance Across Countries

Source: Kunt, Karacaovali, Laeven (2005).Slide 38 of 38

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Chapter 11

Money

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Outline

1 Money

• Money aggregates

• Real and nominal interest rates

2 Monetary model

• The consumers, firms and government using money

• Money Demand, effects of money

3 The Federal Reserve

• History and Structure

• Changing money supply

4 Simple monetary policy

• Inflation Targeting

• Interest Rate Targeting

Slide 3 of 47

Money

Slide 4 of 47

Money

Three questions:

1 What is money?

• A medium of exchange

• A store of value

• A unit of account

2 Why does money matter?

3 Why do people hold money?

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Measuring the money supply

Federal Reserve issues 3 measure of monetary aggregates:

M0: Liabilities of the Federal Reserve: currency

M1: M0 + travelers checks + demand deposits

M2: M1 + savings deposits + money market mutual funds

Table : Billions of Dollars. Data April 7, 2014

M1 2,754.2

Currency 1,196.9Travelers’ checks 3.3Demand deposits 1,079.3

Other checkable deposits 474.6

M2 11,194.0

Savings deposits 7,269.9Time deposits 528.6

Money market mutual funds 641.3

Source: http://www.federalreserve.gov/releases/h6/Current/h6.pdfSlide 6 of 47

Who Holds The Cash?

• In 2012, U.S. currency averaged about $2800 per person

• Surveys show U.S. HH only hold about $100

• Some is held by businesses and the underground economy(another $200/300)

• The rest is held abroad!

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Changes in Money Supply

• Federal Reserve controls the money supply

Source: http://research.stlouisfed.org/fred2/categories/29Slide 8 of 47

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Changes in Money Supply

• What does it effect?

• Strong relation between Money Supply and Prices.

• This Introduces a relation between Money Supply andreturn on a bond.

Slide 9 of 47

The Return on a Bond

We focus on risk-less bonds:

• A nominal Bond is an asset that sells for one unit of dollars todayand returns 1 + R dollars tomorrow.

• The nominal return is R, what is the real return?

• Recall the inflation rate i = P ′−PP

(P is the price level today, P ′ tomorrow)

• The real return r is given by the Fisher equation:

1 + r =1 + R

1 + i

• For small inflation rates, approximate to r ≈ R− i

Slide 10 of 47

Appendix: Deriving The Fisher Equation

• Real cost today: 1P

• Real return tomorrow: 1+RP ′

• Real return:

1 + r =1+RP ′1P

=1 + R

P ′P

=1 + R

1 + i

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Nominal Returns and Inflation

Comparing the nominal returns on a 1 Year T-bill and inflation:

Slide 12 of 47

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11.1 Monetary model

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A Monetary Model

• We want to build a model where Household and Firms use money.

• Let’s look at real return on money (rm):

1 + rm =1 + 0

1 + i=

1

1 + i

so rm < r, money always has lower real returns thanother safe assets.

• A Puzzle: Why do households use money?

Slide 14 of 47

Models of Money

There are several way to introduce money in a model:

1 Money in the utility function(people hold money because they like too)

2 Money search(people need money to ease transactions)

3 Cash in advance model(people need money to finance consumption and investment)

Slide 15 of 47

A Monetary Model : Cash in Advance

Some new ingredients for our model:

1 Nominal prices of goods today (price level): P

2 Household:

• needs cash to buy goods

• uses bonds to save

3 Firms: need cash to pay for Investments

4 Government controls the quantity of money: M

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The Government

• In the model Government is in charge of the Federal Reserve.

• Changes the money supply:

∆M = M ′ −M

• Budget constraint is:

P ·G + (1 + R) ·B︸︷︷︸Old debts

= P · T + B′ + M ′ −M︸︷︷︸Change in money supply

Question:Is there a problem if the government controlsboth B and M?

Slide 17 of 47

Changing The Money Supply

Slide 18 of 47

Changing The Money Supply: Model/ Real Life

• In the Model Ü from the government budget constraint:

M ′ −M︸︷︷︸Change in money supply

= P ·G− P · T + (1 + R)B −B′

Can change money supply with:1 Changes in T : rebates2 Changes in B′: open market operations

(exchange of cash for debt)

• In the US and most economies Ü money supply is controlled bya central bank (the Federal Reserve System in the US)

Changes in the money supply are achieved with:

1 Reserve Requirements (rare)2 Open Market operations3 Discount loans

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The Federal Reserve System - History I

1775-1791: US Currency in the Beginning

• Continental Congress prints paper money (“Continentals”) tofinance the American Revolution.

• Over printing lead to high inflation and loss of faith in notes.

1791-1811: First Attempt at Central Banking

• Treasury Secretary Alexander Hamilton pushes Congress toestablish the First Central Bank of the United States,headquartered in Philadelphia, in 1791.

• 1811 when the bank’s 20-year charter expired, Congress refused,by one vote, to renew it.

Slide 20 of 47

The Federal Reserve System - History II

1836-1865: The Free Banking Era

• State-chartered banks and unchartered “free banks” took holdduring this period, issuing their own notes, redeemable in gold.

• Beginning of modern banking: demand deposits, checktransactions, clearinghouses...

1863: National Banking Act

• Nationally chartered banks, whose circulating notes had to bebacked by US government securities.

• Amendment required taxation on state bank notes but not nationalbank notes, creating a uniform currency for the nation.

Slide 21 of 47

The Federal Reserve System - History III

1873-1907: Financial Panics Prevail

• Regular bank runs and financial panics.

• 1893 a banking panic triggered the worst depression the UnitedStates had ever seen.

1913: The Federal Reserve System is Born

• Federal Reserve Act signed into law by PresidentWilson on December 23, 1913.

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The Structure of the Federal Reserve System

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11.2 The Fed and Monetary Policy

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Board of Governors:

• Seven members appointed by the President and confirmed by theSenate to 14-year terms of office.

• President designates, and the Congress confirms, two members ofthe Board to be Chairman and Vice Chairman for 4-year terms.

• The President by law selects a fair representation of the financial,agricultural, industrial, and commercial interests and geographicaldivisions of the country.

Slide 24 of 47


Federal Open Market Committee (FOMC):

• 12 members–the seven members of the Board of Governors of theFederal Reserve System; the president of the Federal Reserve Bankof New York; and four of the remaining eleven Reserve Bankpresidents, who serve one-year terms on a rotating basis.

• Holds eight meetings per year. At these meetings, the Committeereviews economic and financial conditions, determines theappropriate stance of monetary policy, and assesses the risks to itslong-run goals of price stability and sustainable economic growth.

http://www.federalreserve.gov/monetarypolicy/fomccalendars.htm

Slide 25 of 47

FED and Banks Balance Sheet

• The Banks:

Balance sheet of the Banking SystemAssets Liabilities

US securities Checkable DepositsReserves Discount loans

Loans and Mortgages

• Definition:

Reserves = Required Reserves + Excess Reserves

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FED and Banks Balance Sheet

• The Fed:

Balance sheet of the FEDAssets Liabilities

US securities Currency in CirculationDiscount loans to banks Reserves

• Definition:

Monetary Base = Currency in Circulation + Reserves

Slide 27 of 47

FED Balance Sheet

Taken from: http://www.clevelandfed.org/research/

Slide 28 of 47

Open Market Operations

• For example the Fed buys 1$ in US securities from banks:


US securities +1$ Currency in CirculationDiscount loans to banks Reserves +1$


US securities −1$ Checkable DepositsReserves +1$ Discount loans

• Monetary base increase by 1$

• Question: what if the T-bill is purchased fromthe Household?

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Discount Loans

• For example: the Fed loans 1$ to banking system:http://tiny.cc/8RDgD


US securities Currency in CirculationDiscount loans to banks +1$ Reserves +1$


US securities Checkable DepositsReserves +1$ Discount loans +1$

• Monetary base increase by 1$

Slide 30 of 47

Money Demand and Equilibrium

Slide 31 of 47

Equilibrium in the Monetary Model

Four markets must be in equilibrium:

1 Goods Market: Y = C + I + G

2 Labor Market: Ns = Nd

3 Credit Market: B = S

4 NEW! Money Market:

Md︸︷︷︸

Money Demand

= M s︸︷︷︸

Money Supply

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The Money Demand Equation

• Money Supply is set by the Government/FED

• We need a money demand equation

• How is it derived?

Lot’s of algebra...for this course let’s take it as given

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Equilibrium in the Money Market

• Since government supplies M s inelastically:

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Targeting Rules

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Targeting rules

• Central Banks use one of the following “rules” for monetary policy:

1 Inflation Targeting:Set i = i∗

2 Nominal Interest Rate Targeting:

Set R = R∗; Where R = r + i

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Inflation Targeting: Data

• Recent FED behavior seems to target i∗ = 2% or 3%

• Other central banks:

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Interest Rate Targeting: Data

Taken from: http://www.newyorkfed.org/charts/ff/

Slide 39 of 47

Targeting rules: Example

• Recall Md = P · L(Y, r)

• Function L is increasing in Y

• Function L is decreasing in r

• Suppose Y increases and r decreases.

• This implies that money demand shifts outwards.

• How should policy respond?

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Targeting rules: Example

• Suppose the central bank targets i∗ = 0, so that P1 = P2.

• Money supply must shift outward

• Interest rate targeting is similar in spirit but morecomplicated since both r and i are changing.

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The effects of inflation

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Changes in M and Real Variables

• Question: what is the long run effect on C, Y,N of changes inmoney supply?

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Changes in M and Real Variables: Long Run

• To answer this let’s (for example) look at the budget constraint:

P · C + (1 + R) ·B + M ′ = P · Y + B′ + M

Ü Given long run focus i = 0 so that R = r

Ü Changes in level of M and M ′ are ofset by changes in P

• The answer: is none!

• This result is called long run money neutrality.

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Changes in M and Real Variables: Short Run

• Question: what is the effect on Y and N of changes in moneysupply in the short run?

• The answer depends on weather inflation is expected or not:

If inflation is expected Ü output decreases

If inflation is unexpected Ü output increases

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Expected Inflation

• Suppose workers get paid today and can use wages only for nextperiod consumption.

• From optimality of the household:

MRSl,C′ =P · wP ′

=w

i− 1

Intuition:• Higher wages Ü higher incentive to work• Higher inflation Ü lower purchasing power next period =

less incentive to work!

• Note: this case assumes the agent expects inflation (i).

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Unexpected Inflation

• What if inflation is unexpected? Ü Friedman-Lucas model

• Suppose wage is payed next period, so that nominal wage is P ′ ·w.

• Suppse also that P ′ · w (nominal wages) increases.

• Summary:

1 Workers do not expect inflation.

2 Nominal changes in wage are perceived as real changes in wage(P = P ′ and w ↑)

3 Wages goes up so workers work more Ü output increases.

• Question: how many times will workers be “surprised” by inflation?

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11.3 What Economists Do

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What Economists Do

Robert E. Lucas, Jr.

December 9, 1988

Economists have an image of practicality and worldliness not shared by physicistsand poets. Some economists have earned this image. Others–myself and many Of mycolleagues here at Chicago–have not. I’m not sure whether you will take this as a con-fession or a boast, but we are basically story-tellers, creators of make-believe economicsystems. Rather than try to explain what this story-telling activity is about and why Ithink it is a useful–even an essential–activity, I thought I would just tell you a story andlet you make of it what you like.

My story has a point: I want to understand the connection between changes in themoney supply and economic depressions. One way to demonstrate that I understandthis connection–I think the only really convincing way–would be for me to engineer adepression in the United States by manipulating the U.S. money supply. I think I knowhow to do this, though I’m not absolutely sure, but a real virtue of the democratic systemis that we do not look kindly on people who want to use our lives as a laboratory. So Iwill try to make my depression somewhere else.

The location I have in mind is an old-fashioned amusement park–roller coasters, funhouse, hot dogs, the works. I am thinking of Kennywood Park in Pittsburgh, where Ilived when my children were at the optimal age as amusement park companions - abeautiful, turn-of-the-century place on a bluff overlooking the Monongahela River. Ifyou have not seen this particular park, substitute one with which you are familiar, as Iwant you to try to visualize how the experiment I am going to describe would actuallywork in practice.

Kennywood Park is a useful location for my purposes because it is an entirely in-dependent monetary system. One cannot spend U.S. dollars inside the park. At thegate, visitors use U.S. dollars to purchase tickets and than enter the park and spend thetickets. Rides inside are priced at so many tickets per ride. Ride operators collect thesetickets, and at the end of each day they are cashed in for dollars, like chips in a casino.

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For obvious reasons, business in park fluctuates: Sundays are big days, July 4 iseven bigger. On most concessions–I imagine each ride in the park to be independentlyoperated–there is soma flexibility: an extra person can be called in to help take ticketsor to speed people getting on and off the ride, on short-notice if the day is unexpectedlybig or with advanced notice if it is predictable. If business is disappointingly slow, anoperator will let some of his help leave early. So “GNP” in the park (total tickets spent)and employment (the number of man hours worked) will fluctuate from one day to thenext due to fluctuations in demand. Do we want to call a slow day–a Monday or aTuesday, say–a depression? Surely not. By an economic depression we mean somethingthat ought not to happen, something pathological, not normal seasonal or daily ups anddowns.

This, I imagine, is how the park works. (I say “imagine” because I as just makingmost of this up as I go along.) Technically, Kennywood Park is a fixed exchange ratesystem, since its central bank–the cashier’s office at the gate–stands ready to exchangelocal currency–tickets–for foreign currency–US dollars–at a fixed rate.

In this economy, there is an obvious sense in which the number of tickets in circu-lation is economically irrelevant. No-one–customer or concessioner –really cares aboutthe number of tickets per ride except insofar as these prices reflect U.S. dollars per ride.If the number of tickets per U.S. dollar were doubled from 10 to 20, and if the pricesof all rides were doubled in terms of tickets–6 tickets per roller coaster ride instead of3–and if everyone understood that these changes had occurred, it just would not makeany important difference. Such a doubling of the money supply and of prices wouldamount to a 100 percent inflation in terms of local currency, but so what?

Yet I want to show you that changes in the quantity of money–in the number oftickets in circulation–have the capacity to induce depressions or booms in this economy(just as I think they do in reality). To do so, I want to imagine subjecting KennywoodPark to an entirely operational experiment. Think of renting the park from its ownersfor one Sunday, for suitable compensation, and taking over the functions of the cashier’soffice. Neither the operators of concessions nor the customers are to be informed of this.Then, with no advance warning to anyone inside the park, and no communication tothem as to what is going on, the cashiers are instructed for this one day to give 8 ticketsper dollar instead of 10. What will happen?

We can imagine a variety of reactions. Some customers, discouraged or angry, willturn around and go home. Others, coming to the park with a dollar budget fixed byMom, will just buy 80 percent of the tickets they would have bought otherwise. Stillothers will shell out 20 percent more dollars and behave as they would have in the

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absence of this change in “exchange rates”. I would have to know much more than Ido about Kennywood Park patrons to judge how many would fall into each of thesecategories, but it is pretty clear that no-one will be induced to take more tickets than ifthe experiment had not taken place, many will buy fewer, and thus that the total numberof tickets in circulation–the “money supply” of this amusement park economy–will takea drop below what it otherwise would have been on this Sunday.

Now hear does all of this look from the point of view of the operator of a rideor the guy selling hot dogs? Again, there will be a variety of reactions. In general,most operators will notice that the park seems kind of empty, for a Sunday, and thatcustomers don’t seam to be spending like they usually do. More time is being spenton “freebies”, the river view or a walk through the gardens. Many operators take thispersonally. Those who were worried that their ride was becoming passe’ get additionalconfirmation. Those who thought they were just starting to become popular, and hadhad thoughts of adding some capacity, begin to wonder if they had perhaps become over-optimistic. On many concessions, the extra employees hired to deal with the expectedSunday crowd are sent home early. A gloomy, “depressed” mood settles in.

What I have done, in short, is to engineer a depression in the park. The reductionin the quantity of money has led to a reduction in real output and employment. Andthis depression is indeed a kind of pathology. Customers are arriving at the park, eagerto spend and enjoy themselves, Concessioners are ready and waiting to serve them. Byintroducing a glitch into the park’s monetary system, we have prevented (not physically,but just as effectively) buyers and sellers from getting together to consummate mutuallyadvantageous trades.

That is the end of my story. Rather than offer you some of my opinions about thenature and causes of depressions in the United States, I simply made a depression andlet you watch it unfold. I hope you found it convincing on its own terms–that what I saidwould happen in the park as the result of my manipulations would in fact happen. If so,then you will agree that by increasing the number of tickets per dollar we could as easilyhave engineered a boom in the park. But we could not, clearly, engineer a boom Sundayafter Sunday by this method. Our experiment worked only because our manipulationscaught everyone by surprise. We could have avoided the depression by leaving thingsalone, but we could not use monetary manipulation to engineer a permanently higherlevel of prosperity in the park. The clarity with which these affects can be seen is thekey advantage of operating in simplified, fictional worlds.

The disadvantage, it must be conceded, is that we are not really interested in un-derstanding and preventing depressions in hypothetical amusement parks. We are in-

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terested in our own, vastly more complicated society. To apply the knowledge we havegained about depressions in Kennywood Park, we must be willing to argue by analogyfrom what we know about one situation to what we would like to know about another,quite different situation. And, as we all know, the analogy that one person finds persua-sive, his neighbor may well, find ridiculous.

Well, that is why honest people can disagree. I don’t know what one can do aboutit, except keep trying to tell better and better stories, to provide the raw material forbetter and more instructive analogies. How else can we free ourselves from the limitsof historical experience so as to discover ways in which our society can operate betterthan it has in the past? In any case, that is what economists do. We are storytellers,operating much of the time in worlds of make believe. We do not find that the realmof imagination and ideas is an alternative to, or a retreat from, practical reality. On thecontrary, it is the only way we have found to think seriously about reality.

In a way, there is nothing more to this method than maintaining the conviction (whichI know you have after four years at Chicago) that imagination and ideas matter. I hopeyou can do this in the years that follow. It is fun and interesting and, really, there is nopractical alternative.

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Chapter 12

The End: 7 lessons from this course

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Tools you have learned

Four “fronts”:

1 Theory: You know how to build equilibrium macro models:

• Micro-foundations

2 Empirics: You know where to look for any type of Macro data:

• Proficient in using aggregate datasets

• Graphical analysis and basic statistics

• Filtering: linear and Hodrick-Prescott

3 Forecasting: Do you know what unemployment will be on Friday?

4 Quantitative: You know how to map models to data:

• Calibration: factor shares, TFP, disutility from labor, capital stock

• Effect of taxes on hours; Optimal Taxation

7 Lessons to remember

Slide 6 of 8


1 In data households and firms display dynamicand forward looking behaviour.

2 Government expenditures reduce wealth and henceconsumption. Government multiplier is less than 1.

3 Taxes discourage work, optimal taxes should take theresponse of workers into account.

4 Without credit frictions the timing of taxesand stimuli are irrelevant.

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5 Without capital accumulation technology cannot leadto sustained growth of standard of living.

6 Borrowing short and lending long makes the bankingsystem prone to panics. Policy can prevent panics atno cost.

7 Money creation has no long run real effect.Unexpected inflation can have short term real effects.

Slide 8 of 8

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Part III

Problem Sets

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73-240 – Spring 2014

73-240 – Problem set 1

Due Friday Feb. 7th

From the Syllabus:

1. Homework must be turned in on the day it is due. Late homework will NOT beaccepted unless you are sick and have a doctor’s note.

2. You may work in groups of up to 4. BUT: You MUST put names of other groupmembers on your homework. You MUST write up your own set of answers.

3. TYPE your work. Long equations may be hand written. Buy a stapler!

4. Write your first and last name on the title of each graph. Graphs may be hand drawn.

5. Carefully explain your work.

Problem 1 (20 points)

Consider the following data:

Quantities/Time 2013 2014

Red Widgets 32 15Blue Widgets 32 9

PricesRed Widgets $1.75 $1.6Blue Widgets $2 $2.2

1. Compute the Laspeyres and Paasche indices for each year taking as base year 2013.

2. Compute Nominal GDP and its growth rate.

3. Compute Real GDP using both the Laspeyres and Paasche indices. Compute growthrates of real GDP using both indices.

4. Compute inflation in 2014 using both the Laspeyres and Paasche indices.


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Problem 2 (15 points) A first glance at NIPA

1. Write the formula for GDP following the expenditure approach.

2. Refer to table 1.1.6 (Real Gross Domestic Product) of the NIPA tables. You canfind them here http://www.bea.gov/iTable/index nipa.cfm, click on “Begin Using theData” then click on Section 1. Map each of they item in the formula of GDP in termsof expenditure approach to one of the line of table 1.1.6.

3. For each item in the formula of GDP compute the fraction of total GDP. You can pickthe last quarter of 2012.

Problem 3 (15 points)

Problem 3 of Chapter 2 (page 65) In Williamson 5th edition.(The wheat and bread economy.)

Problem 4 (30 points) Working with data: Forecasting

This question will introduce you to some data work, also refer to Lecture 3 for details.

Using data from http://research.stlouisfed.org/fred2/:

1. Use series (UNRATE): Civilian unemployment rate.(Hint: type UNRATE in the search box)

2. Compute the average (in percent) unemployment rate from 1950 to 2008.

3. Using a linear forecast (careful in deciding the data to use) predict when unemploymentwill hit the average unemployment rate from 1950 to 2008. Make sure to carefullyexplain all the steps you do.

Problem 5 (20 points) Working with data: Filtering

This question will introduce you to some data work, also refer to Lecture 3 for details.

Using data from http://research.stlouisfed.org/fred2/:


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1. Use series (GDPCA): Real gross domestic product. Take data from 1980 to 2012included. Compute the Hodrick-Prescot filter of the time series. This will be the trendof GDP.

2. Plot the trend over time.

3. Compute the deviation from trend of GDP. This will be the cyclical components.

4. Plot the cyclical component of GDP.


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Due Monday Feb. 24th

From the Syllabus:






Problem 1 (30 points): The U.S. firm

Consider the Cobb-Douglas production function:

Y = zKαN1−α (1)

where α is the share of capital in the production function

1. Write down the problem of the firm and determine the labor demand function.

2. Suppose wages (w) change by 1%, by how much does labor demand change?

3. Using the optimality condition of the firm, write down a formula to compute α fromthe data.

4. Using data on Compensation of employees (BEA, NIPA Table 2.1 line 2) and GDP,compute α. Use yearly data from 1970 onwards and report the average value of alphafor this time period.

5. In a graph plot the time of α changes by year. On the same graph plot the HP filteredversion of the time series (see also Hw 1).

This version: February 19, 2014 1 Prof. Laurence Ales

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Problem 2 (30 points): The U.S. household

In this problem you will study the representative household. Suppose that the utility functionis given by

U(C, l) = log(C) +1

δlog(l)

Where C is consumption, l is leisure, and 1/δ is a parameter that determines how muchthe representative household values consumption versus leisure. Let h be the total timeendowment, w the wage and π the dividend payments.

1. Write the problem of the household making sure to include the budget constraint (don’tforget taxes and dividends in the budget constraint)

2. Solve the household problem. This implies deriving two equations one providing avalue of C and one for the value of l. These two equation must only depend on h, δ,w and π − T .

3. Suppose π−T = 0. Derive the optimality condition for the household using first orderconditions. Using the optimality condition write a formula for leisure. How does leisurechange when wages change? Explain in terms of income and substitution effect.

4. Let’s calibrate the model to the US household. Keep π−T = 0. In US data we observethat households enjoy 2/3 of their time endowment in leisure. Given this fact derive arealistic value for the parameter δ.

5. Let’s simulate a recession. Suppose the wages decrease by 10% how do hours workedchange? What happens to consumption? Explain in terms of income and substitutioneffect. For this question set w = 1 (initially) also set h = 1, π − T = 0.1 and use thevalue of δ calculated in the previous step.

• Hint: Be careful not to mix leisure with hours worked.Also π − T is now different than zero!

Problem 3 (40 points): Health and the Macroeconomy

In this question you are asked to analyze the behavior of U.S. health spending at an aggregatelevel. The aggregate behavior of health spending in the U.S. is potentially worrying; in thenext question you are asked to show that it might not be the case.

1. Use Information reported by the BEA in NIPA table 1.5.5. Compute the share of GDPdue to health spending from 1970. Plot this time series. Explain which data series youwill use.


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2. Using the above data, compute a linear trend from 1970. Use this trend to forecast theshare of health spending up to 2030. Plot the overall time series from 1970 to 2030.

3. A model for health care. Suppose a household has income equal to Y . Supposeincome can be spent on either consumption C or health goods H. Suppose thatconsumption and health goods have prices equal to 1. Write the budget constraint forthe household

• Hint: note that there is not leisure decision, income is fixed and equal to Y .

4. Suppose that health goods increase the enjoyment of consumption goods (think aboutbeing healthy and enjoying more consumption). Formally let the utility from H andC be given by

U(C,H) = Hγ(b+ log(C))

where b is a parameter that describes the “value of being alive” and γ is a givenparameter. Write the problem of the household.

5. Using Excel solve the problem of the household. Set b = 15, γ = 0.2 and considerthree distinct income levels Y = 10, 15, 35. Plot the share of income devoted to healthcare for this household. How does it change as income increases?

• This is a hard step. In recitation the TA will help you with this step!

6. Look for a definition of luxury good. Using this definition and the results in theprior question, comment on the behavior of health care in the US. Provide a possibleexplanation for it’s behavior.


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Due Friday Mar. 28th

From the Syllabus:






Problem 1 (25 points): Optimal Taxation

Refer to Lecture 8. Write a formula for the optimal top tax rate (τ) that contains theelasticity of reported income with respect to tax rate (e).

1. Plot the optimal top tax rate over a range of e going from 0.1 to 5. Assume thata = 1.5.

2. Find the top labor income tax rate in the US today (make sure to correctly cite yoursource). Call this value τUS. For what value of e roughly we have τ = τUS?

Problem 2 (25 points): Solow

Consider the Solow growth model. Derive an equation that determines the steady state levelof capital per capita. Analyze the long-run effects on the steady state of the followingchanges to the environment:

1. Tax rates on savings are decreased, hence saving rates increase.

2. A fraction of the country capital stock gets destroyed. For this last case also explainin detail what happens in the short run (i.e. the transition to the new steady state)

This version: March 21, 2014 1 Prof. Laurence Ales

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Problem 3 (25 points): Malthus

Consider the Malthusian model of growth. Analyze the long-run effects on the steady stateof the following changes to the environment:

1. Increase in the hygiene in medical practice increases the survival rates of newborns.

2. Following a war, the country looses land.

Note that you are required to support your argument with either graphs or equations!

Problem 4 (25 points): Solow and the US

In this question you will calculate the capital stock in the US. Your starting point will bethe following equation (refer to lecture 10):

Kt+1 = Kt(1 − d) + It, (1)

where Kt+1 is the capital stock in year t + 1, Kt in year t, It investment in year t. Set thedepreciation rate d = 0.05. Use data from table 1.1.6 of the NIPA accounts. For GDP (line1) and Investment (line 7). Use annual data from 1960 to 2013.

1. Calculate the level of capital in 1960 assuming that the capital output ratio for thatyear is equal to 2: K1960/Y1960 = 2.

2. Using equation (1) and the value of K1960, calculate Kt+1 for all years 1961 to 2013.

3. Plot the capital output ratio between 1960 to 2013.

This version: March 21, 2014 2 Prof. Laurence Ales

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73-240 – Spring 2014


Due Wednesday April 9th

From the Syllabus:

1. Homework must be turned in on the day it is due.

2. You may work in groups of up to 4. But: You must put names of other group memberson your homework. You must write up your own set of answers.

3. Type your work. Long equations may be hand written. Buy a stapler!



Problem 1 (30 points): Taxes and Household Behavior

Consider the household in the two period model studied in Lecture 12. Study the impacton consumption today (c) and consumption tomorrow (c′) of the following changes in taxes(assume taxes are lump sum):

1. It is announced that this year every household in the US will receive a 10% reductionin this years taxes.

2. For this year you receive (and only you) a larger than expected tax refund.

Problem 2 (40 points): The Dynamic Household

Consider the problem of the household studied in Lecture 13 (with endogenous labor supply).Describe every symbol you use. Suppose the utility function in every period is U(c, l).

1. Write down the problem of the household. Make sure to write the objective functionand all of the constraints. (Hint use the lifetime budget constraint)

2. Write down the four first order conditions for consumption today (c) consumptiontomorrow (c′), labor today (l′) and labor tomorrow (l′).


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3. Show that two first order conditions can be combined so that MRSc,c′ = 1 + r.

4. Consider a graph plotting c versus c′ show how a change in r might affect the optimalchoice of c and c′.

Problem 4 (30 points): The Dynamic Firm

Consider the problem of the firm studied in Lecture 13.

1. Write the two period problem of the firm labeling every symbol.

2. Compute the first order condition for investment (I).

3. Show how changes in the interest rate (r) impact I.

4. Show how changes in tomorrow (z′) impact I.


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Due Wednesday April 30th

From the Syllabus:

1. Homework must be turned in on the day it is due.

2. You may work in groups of up to 4. But: You must put names of other group memberson your homework. You must write up your own set of answers.

3. Type your work. Long equations may be hand written. Buy a stapler!



Problem 1 (20 points): Asymmetric Information

Williamson 5th edition: Problem 1 (page 372) of Chapter 10.

Problem 2 (30 points): The Effects of TFP Growth

For this question you will need to refer to Lecture 14. Suppose that both productivity today(z) and productivity tomorrow (z′) grow. Use the equilibrium diagrams (for current labor andgoods market) to determine the effects this will have on current aggregate output, currentemployment, the current real wage, the real interest rate, consumption and investment.Explain your results.

Problem 3 (20 points): Limited Commitment

Williamson 5th edition: Problem 2 (page 372) of Chapter 10.


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Problem 4 (20 points): Hyper-Inflations

In this question you are asked to work with data on money, prices indices and output. Thedata has been collected by Warren Weber (CMU Ph.D 69’) economist at the MinneapolisFederal Reserve Bank. I have attached the data in a separate file (hw-prices-money.xlsx)on Blackboard. In the tab “Prices” looking across countries, what is the biggest episodeof inflation you observe over time? How large was inflation during this “hyper-inflation”period? In the tab “Money” locate in line 1 the series for M0 and M2. For the country youhave identified experiencing a “hyper-inflation” episode, plot the behavior of the natural logof M0 and M2. Describe what you observe.

Problem 5 (10 points): The End

Write down one topic, result or fact you have learned from this class and would like toremember beyond the final examination.


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Due Thursday May 1st and Friday May 2nd

Rules:

1. This homework is optional.

2. The grade of this homework will be averaged with your previous 5 problem sets if itwill increase the average score. This way there is no risk in submitting the homework.

3. You may work in groups. Each group member must submit an answer independently.

Question 1

On Friday May 2nd at 8:30AM (EST) the Bureau of Labor Statistics will release the Em-ployment Situation for April 2014. In this homework you are asked to forecast some of thekey metrics in this release. In particular answer the following:

1. Forecast 1: By what amount will Total Nonfarm Payroll Employment grow by.

2. Forecast 2: The Unemployment Rate.

Here are important guidelines and tips for the homework:

1. The numerical values of the forecast must be submitted here: http://tinyurl.com/73240-hw6 by Thursday May1st at 11:59PM Pittsburgh time.

2. To homework will be graded not by the precision of the forecast but by the methodologyused. A detailed description of the methodology used must be submitted in class onFriday May 2nd.

3. Any official data including ADP data might be used to generate the forecast.

4. Any of the procedures studied in Lecture 3 or Lecture 856 will be acceptable (moreadvanced procedures are also welcomed).

5. A sample of the same release for March 2014 can be found here:http://www.bls.gov/news.release/empsit.nr0.htm


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Index

ADP, 160, 257Aggregation, 62Asymmetric Information, 203, 255

Bank Runs, 203Banks, 203Behavioral Responses, 108BLS, 160Bonds, 160Budget Constraint, 62

Caldor Facts, 129Calibration Exercise, 248Capital Shares Across Countries, 251Cash in Advance model, 221Competitive Equilibrium, 93Confidence interval, 39Consumption smoothing, 160Convergenze, 129Counter-cyclical, 48CPI, 56Credit Imperfection, 203

Data on money, prices and output, 255Default Premium, 203Deficits, 173Depression, 48Determinants of Growth, 119Deviation from trend, 39Diamond-Dybvig model, 203Discount loans, 231Distortionary Taxation, 108

Durbin Watson, 160Dynamic budget, 160Dynamic equilibrium, 185

Education across countries, 146Endogenous growth, 146Equilibrium in goods market, 185Equilibrium in labor market, 185Expenditure Approach, 25

Failures of GDP, 25FDIC, 203Feasibility, 93Fed balance sheet, 226Federal Reserve System, 226Filtering, 245Financial Panics, 203Firm investment, 180First Welfare Theorem, 104Fiscal stimulus, 185Fiscal Stimulus: static, 93Fisher Equation, 216Flow of funds, 160FOMC, 226Forecasting, 245Forecasting: definition, 39Friedman on Methodology, 14Friedman-Lucas Model, 231Full Redistribution, 108

GDP deflator, 56Government Budget Constraint, 88

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Government multiplier, 185Growth and deficits, 245Growth Miracles and Disasters, 119

Health Spending, 248Heavy Truck Sales, 160Historical Growth Data, 119History of the Fed, 226Hodrick-Prescott filter, 48Homogeneity, 62Household saving, 160Human Capital, 146Hyperinflation, 255

Income Approach, 25Income Effect, 62Indifference Curves, 62Inequality, 25Inflation, 56Inflation targeting, 231, 255Information set, 39Interest rate targeting, 231Interest rates and the consumer, 177Interest rates and the firm, 180International Interest Rates, 160

Job Openings, 160

Laffer Curve, 108Land in the Production Function, 129Laspeyres Index, 56Leading Indicators, 160Limited Commitment, 203, 255Liquidation value, 180Loan Defaults, 203log-scales, 39Lucas Critique, 160Lump Sum Taxes, 88

M0,M1,M2, 216Macroeconomics, 14

Maddison Data, 251Malthus Model, 129Malthus to Solow: Hansen-Prescott 1999,

129Malthusian Trap, 129Marginal Product, 77Marginal propensity to consume, 185Marginal Rate of Substitution, 62Marginal Taxes, 108Mean Logarithmic Deviation, 119Methodology, 14Modern Growth Data, 119Money, 216Money and Prices, 216Money demand, 221Multiplier, 185

National Income Identities, 25National saving rate, 160NIPA Tables, 25Nominal Bonds, 216

Open Market Operations, 221Open market operations, 231Optimal Saving, 160Output demand, 185Output supply, 185

Paasche Index, 56Pareto Optimum, 104Penalty function, 39Penn World Tables, 251Phillips curve, 231Popper on Methodology, 14Price Index, 56Pro-cyclical, 48Product Approach, 25Production Function, 77Production Possibility Frontier, 93Productivity shock, 185Progressive Taxes, 108

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Real and Nominal Variables, 56Recession, 48Regressive Taxes, 108Return on Money, 221Ricardian Equivalence, 253Ricardian equivalence, 173

Saving Rate, 129School efficiency, 146Scientific Method, 14Sectoral Deficit Identity, 25Share of Capital: α, 77, 248Solow Accounting, 251Solow Model, 129Sovereign Default, 160Structure of the Fed, 226Substitution Effect, 62Summary behavior, consumer, 177Summary behavior, firm, 180

Tax Elasticity of Income, 108Taxes in the Data, 88Technology shocks, 93TFP, 77Timing of taxes, 173Total Nonfarm Payroll Employment, 257Trend, linear, 39Trend, nonlinear, 48

Underground Economy, 25Utility Function, 62

Wealth Shares, 119Working with NIPA tables, 245World Inequality, 119

Yield Curve, 160

260 of 260

intermediate macro

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