Economic Growth Models, Population, and Inequality

econ c175 1

Economic DemographyDemog/Econ c175

Prof. Ryan EdwardsSpring 2020

2/11/2020

2/11/20 12:06 PM

Current events

• Media outlets reported that the death toll from the coronavirus (was “2019-nCoV” now “COVID-19”) has now exceeded the 774 dead to SARS coronavirus in 2003

• WHO reported 1,017 dead as of 5 hours ago• Among the dead last week was Li Wenliang, an

ophthalmologist at Wuhan Central Hospital who had reportedly alerted fellow doctors on December 30 to wear protective clothing. Authorities reportedly had him recant his advice

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Announcements

• We’ll start counting iClicker’s today• Syllabus updated about iClicker grade

– One click per iClicker session = full credit for that class– You can miss up to 4 classes with iClicker sessions and

still get full credit (10% of overall)

• Request by a senior writing an honors thesis for declared and intended economics majors to complete a 5-minute survey here

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Complete a survey for a colleague• My name is Ishira and I am a senior writing a thesis in economics this

semester. • To collect data for my topic, I have designed a survey intended for

declared and intended econ majors. • The survey revolves around your potential interest in pursuing a PhD

in economics. • The survey is open from Feb 4th- Feb 18th, and will not take more

than 5-6 minutes. It is also anonymous; I will not be collecting any identifiable data.

• I would really appreciate it if you could spare a few minutes to take the survey- I believe the topic that I am writing about is extremely relevant and important, and a survey is the only way for me to collect data for it. Thank you so much in advance!

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Today’s agenda

• Class demographics and fun with iClickers

• Review Solow with iClicker questions

• Piketty-Saez, growth models, and inequality

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Census 2020

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2/11/20 12:06 PM econ c175 7

The race question in the Census

• Since 2000, people can check multiple boxes• The boxes changed in 2010 and again in 2020• In 2020, more chance to write in “subcategories”• In 2010, 97.1% answered one race, 2.9%

answered two races

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iClicker demographics

• Participation in this data collection is not required. Feel free to pass if you want

• We will NOT share these individual-level data with anybody

• We will NOT report averages etc. in cells smaller than 10 students

• We will report averages and cross tabs to the class

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iq6.a. What is your sex?

A. Male

B. Female

2/11/20 12:06 PM econ c175 10

iq6.b. What age in years will you be on April 1, 2020?

A. 19 or under

B. 20

C. 21

D. 22

E. 23 or older2/11/20 12:06 PM econ c175 11

iq6.c. Are you of Hispanic, Latino, or Spanish origin?A. No, not of Hispanic, Latino, or Spanish

originB. Yes, Mexican-Am., ChicanoC. Yes, Puerto-RicanD. Yes, CubanE. Yes, another Hispanic, Latino, or Spanish

origin

2/11/20 12:06 PM econ c175 12

iq6.d. What is your race? (1 of 2)

A. WhiteB. Black or African Am.C. Chinese, Vietnamese, Native Hawaiian,

Filipino, Korean, Samoan, Japanese, Chamorro

D. Asian IndianE. Other

2/11/20 12:06 PM econ c175 13

iq6.e. What is your race? (2 of 2)

A. WhiteB. Black or African Am.C. Chinese, Vietnamese, Native Hawaiian,

Filipino, Korean, Samoan, Japanese, Chamorro

D. Asian IndianE. Other

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iq6.f. Were you born in the U.S. or were you born abroad?A. U.S. citizen by birth:

born in the U.S.born in U.S. territories (like Puerto Rico)

or born abroad to U.S. parentsB. Foreign born, U.S. citizen by naturalizationC. Foreign born, not a citizen of the U.S. (like

foreign students, green card, etc.)

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iq6.g. Were your parents born in the U.S. or were they born abroad?A. Both mother and father were born in the U.S.

B. One parent was born in the U.S. and the other was born abroad

C. Both mother and father were born abroad

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iq6.h. Is your generation (that is: you and any brothers and sisters) the first generation to attend a 4-year college in your family?

A. Yes. My parents and their siblings did not attend college.

B. No.

C. I don’t know

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iq6.i. Please indicate the importance to you personally of:Obtaining recognition from my colleagues for contributions to my special field

A. Essential

B. Very Important

C. Somewhat Important

D. Not Important

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These questions appear on the CIRP Freshman Survey

iq6.j. Please indicate the importance to you personally of:Raising a family

A. Essential

B. Very Important

C. Somewhat Important

D. Not Important

2/11/20 12:06 PM econ c175 19

These questions appear on the CIRP Freshman Survey

iq6.k. Please indicate the importance to you personally of:Being very well off financially

A. Essential

B. Very Important

C. Somewhat Important

D. Not Important

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These questions appear on the CIRP Freshman Survey

iq6.l. How many children do you want to have?

A. ZeroB. OneC. TwoD. ThreeE. Four or more

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iq6.m. How many siblings and step-siblings do you have?

A. ZeroB. OneC. TwoD. ThreeE. Four or more

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iq6.I. The California primary is Tuesday, March 3. Are you registered and planning to vote?

A. YesB. NoC. I don’t know

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iq6.II. The California primary is Tuesday, March 3. Who has your vote today?

A. Joe BidenB. Pete ButtigiegC. Bernie SandersD. Elizabeth WarrenE. Other / Not Sure/ I don’t know

2/11/20 12:06 PM econ c175 24

iq6.III. What is the most important issue facing the U.S. today

A. The cost of health insuranceB. Income or wealth inequalityC. ImmigrationD. Foreign tradeE. The environment

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Back to Solowwith some iClicker questions

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iq6.1. What happens in the short run if a one-time wave of new immigrant arrivals increases labor by 10%? Immigrants do not bring capital or technology and are otherwise identical to natives.

Outputper workerper year(y)

capital per worker, k

y = f(k)

(n+d)k

s y(k)

k*

y*

econ c175 272/11/20 12:06 PM

A. Capital and output per worker will rise

B. Capital and output per worker will fall

C. Nothing will happen

D. It’s ambiguous

iq6.2. What happens in the long run if a one-time wave of new immigrant arrivals increases labor by 10%? Immigrants do not bring capital or technology and are otherwise identical to natives.

Outputper workerper year(y)

capital per worker, k

y = f(k)

(n+d)k

s y(k)

k*

y*

econ c175 282/11/20 12:06 PM

A. Capital and output per worker will rise

B. Capital and output per worker will fall

C. Nothing will happen

D. It’s ambiguous

iq6.3. What happens in the short run if a one-time wave of new immigrant arrivals increases labor by 10%? Immigrants do not bring capital but they bring and share improved technology and are otherwise identical to natives.

Outputper workerper year(y)

capital per worker, k

y = f(k)

(n+d)k

s y(k)

k*

y*

econ c175 292/11/20 12:06 PM

A. Capital and output per worker will rise

B. Capital and output per worker will fall

C. Nothing will happen

D. It’s ambiguous

iq6.4. What happens in the long run if a one-time wave of new immigrant arrivals increases labor by 10%? Immigrants do not bring capital but they bring and share improved technology and are otherwise identical to natives.

Outputper workerper year(y)

capital per worker, k

y = f(k)

(n+d)k

s y(k)

k*

y*

econ c175 302/11/20 12:06 PM

A. Capital and output per worker will rise

B. Capital and output per worker will fall

C. Nothing will happen

D. It’s ambiguous

So what does Solow explain? (cont.)

• With tech change, neo-classical growth gives us a way for population to grow and income to grow

• Say A(t) = A0 e g t

• à Population N grows at rate n; • à Economy Y grows at rate n + g;• à per capita output y grows at rate g

econ c175 312/11/20 12:06 PM

What doesn’t Solow explain?

Exogenous factors:

• Technology (why it improves)

• Population

• (Also, savings rate s)

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Solow Conclusions• Solow approach retells the Malthusian story: a

different steady-state• Good news :

– Can accommodate constant population growth without worsening wages (not possible in Malthus)

– Technological change creates permanent improvement (not transitory like Malthus)

• Bad news :– Faster population growth implies lower income (unless

forego consumption and keep savings up)– Key to long-term per capita growth is technology, not

savings.

econ c175 332/11/20 12:06 PM

Growth and Inequality

Piketty’s argument

econ c175 342/11/20 12:06 PM

Why are we reading Piketty and Saez?

• Thomas Piketty and UC’s Emmanuel Saez (and also UC’s Gabriel Zucman) have spent a lot of time constructing new databases that show historical patterns in wealth or income inequality

• Inequality is a pretty hot topic these days, at least among Democrats and Europeans!

• Piketty and Saez (2014) present some of these data and then analyze it through the lens of the Solow Model

• Parts of the big upshots have to do with the rates of population growth and economic growth

2/11/20 12:06 PM econ c175 35

Caveat

• This is an ongoing area of vibrant research• IMHO, the relevance of this article for understanding

inequality in the U.S. is limited• Piketty and Saez would probably agree — they state as

much in the article• But this perspective is also useful for thinking about

European inequality, and maybe for inequality elsewhere too

2/11/20 12:06 PM econ c175 36

Why the caveat?

• Income inequality in the U.S. is more about big inequality in labor earnings (among the college educated!) and less about inequality in returns to wealth (p. 839, far right column, halfway down)

• You might not know this based on the usual tenor of political discourse in the U.S.

• This is somewhat also true of the UK but far less true about other European countries

• What’s the story with China and India and Brazil, etc.? I think we know far less, and I personally know very little

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New stylized fact #1: Income inequality’s fall and rise

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• Income inequality in the U.S. today is higher than what it was in Europe before WWI

• It has also risen in Europe

• In both zones, income inequality was minimized in the postwar (WWII) period

New stylized fact #2: Wealth inequality shows similar patterns

econ c175 392/11/20 12:06 PM

• Not as strong a rebound toward inequality in the U.S., more like a plateau with a blip

• More of a downward trend in wealth inequality in Europe

New stylized fact #3Wealth-to-income ratios (K/Y) definitely fell in

Europe then rebounded (U-shaped), U.S. was flatter

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• Here is where the Solow Model might help us think about the European experience

• Preview: What was different about Europe?

1. More destruction of K2. Slower population growth

New stylized fact #4Net returns to K (after taxes & depreciation), r, declined after WWI then rebounded and usually exceeded GDP growth, g

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• This is the hardest thing to think about

• If r > g usually, then especially with random processes, old wealth tends to dominate new wealth generated from income

• Maybe wealth inequality is fated to rise — unless destruction or taxes reduce its returns

Learning objectives here

• Be comfortable using the Solow Model to say some things about population growth and things that we care about

• Be aware of this perspective of Piketty and Saez and the policy implications

2/11/20 12:06 PM econ c175 42

What determines the wealth-to-income ratio?

• What is wealth?• Claims on capital, land, or other resources — in

the Solow model, there is just K

• So we’re talking about !"• In words: this is the value of the capital stock in

units of annual GDP. In the U.S., !" ≈ 4• Because % ≡ !

' and ( ≡ "', it’s also )*

2/11/20 12:06 PM econ c175 43

How can we see !" in the Solow diagram?

Outputper workerper year(y)

capital per worker, k

y = f(k)

(n+d)k

s y(k)

k*

y*

econ c175 442/11/20 12:06 PM

• k is the horizontal variable, the “run”

• y is the vertical variable given by y = f (k), the “rise”

• The slope is the rise over the run

• So !" =$

%&'()

of a line from the origin to the point (k*,y*)

What happens to !" if the population growth rate n falls?

Outputper workerper year(y)

capital per worker, k

y = f(k)

(n+d)k

s y(k)

k*

y*

econ c175 452/11/20 12:06 PM

• The (n+d)k curve pivots clockwise

• The line from the origin to the point (k*,y*) gets flatter, i.e., the slope gets smaller

• So !" must have become larger

Piketty’s capital idea

• Maybe mechanism is that lower population growth increases capital per worker k

(via Solow effect)

• Population growth in Europe is and has been lower than U.S. pop growth

• And maybe more capital per worker increases income inequality?

(How could this be?)econ c175 462/11/20 12:06 PM

Piketty’s argument

1. Slower pop. growth à more capital per person(The neo-classical result)

2. Might more capital per person increase the capital share of the economy? (technical & hard)

3. Maybe capital income is more unequally distributed than labor income (a little more obvious)

econ c175 47

Note: to explain, we'll start with 3 and then do 2.

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Piketty 3. Income from capital is much more unequal than labor income

econ c175 48

Source: Goldstein & Lee (2014)

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(Back to Piketty 2)Some accounting

• Total income is paid to labor (l) and capital (k)Y = Yl + Yk

• Assuming perfectly competitive marketsYk = MP(K) * K

and it turns outyk = MP(k) * k

• What are Yl and yl? It’s what’s left overYl = Y - Yk yl = y - yk

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Marginal product

• Answers the question: if we increase an input factor, how much does output increase

• The slope of the production function(a.k.a. the derivative)

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The marginal product of (k)apital= the slope of the production function

econ c175 51

y = f(k)

k

y To do: Sketch how MP(k) changes with k.

Does it go up, down, stay constant?

Does this remind you of anything in Malthus?

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Distribution of incomeIn competitive economy, capital

and labor each receives its marginal product:

Wage per person = mp(L)Return on capital = mp(K)Per capita output: y = f(k). Of this, return on capital =

k × mp(k) So, wages = f(k) – k × mp(k) If population growth falls,

output increases, wages increase, and return on capital falls. (cf. Piketty) capital per worker, k

y = f(k)

(n+d) k

s y(k)

k

Output going to capital:k × mp(k)

Output going to labor: wagey – [k × mp(k)]

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Does capital intensification (rising k) increase capital’s share of income?

• Maybe yes, because there’s more capital• Maybe not, because rate of return on capital

goes down• Which effect is stronger?• (Answer: it depends on how quickly MP

declines)

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Share of income from capital

Sharecapital = yk / y = MP(y) * k y

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Cobb-Douglas: capital intensification cancels out

• With Cobb-Douglas: y = ka

• We calculate MPMP(k) = dy/dk = a k a-1

• We then substitute into Sharecapital = MP(k) * k / y

= (a k a-1) * k / ka = a• So capital intensification exactly balanced by

diminishing marginal returns. Share of national income from capital is constant = a

econ c175 552/11/20 12:06 PM

2. But what if MP(k) declines more slowly?

• Can still have diminishing marginal returns• But now increase in capital won’t be fully

offset by declines in MP(k)• Result is increasing share of national

income goes to capital owners.• This is what Piketty highlights as possible.

(And he thinks might worsen because of slow declining MP of new technology like robots and automation)

econ c175 562/11/20 12:06 PM

Piketty’s argument

1. Slower pop. growth à more capital per person(The neo-classical result)

2. Might more capital per person increase the capital share of the economy? (technical & hard)

3. Maybe capital income is more unequally distributed than labor income (a little more obvious)

econ c175 572/11/20 12:06 PM

Next week

• Tues: Understanding technological change: intensification or innovation?

• Thurs: Are we doomed? (Running out of resources)

econ c175 582/11/20 12:06 PM