advanced macroeconomics module 3: empirical …amoneta/m2018_1.pdf · 2018-03-14 · advanced...

Advanced MacroeconomicsModule 3: Empirical models & methods

1. Outline — Stylized Facts — Trends and Cycles in GDP

Alessio Moneta

Institute of EconomicsScuola Superiore Sant’Anna, Pisa

[email protected]

March 2018

LM in EconomicsScuola Superiore Sant’Anna - Universita di Pisa

Macroeconomic fluctuations 1/43

Outline of the module: Empirical models & methods in macroeconomics

• Business cycles: definition and identification

• Stylized facts in macroeconomic fluctuations

• Trends and cycles in macroeconomic variables

• Empirical relationships:

Income and unemployment

Income (unemployment) and inflation (wages)

Income and money (monetary policy rules)

Income and fiscal policy

Income and consumption

• Methodological issues:

Causality (theory driven vs. data driven)

Testing theoretical models


Business cycles: definition and identification


Industrial production index in US, 1919 -2017 (monthly, seasonally adj.)


Industrial production index in US, 1919 -2017 (monthly, seasonally adj.)logarithmic scale


Production in Total Manufacturing for Italy.


A definition of macroeconomics

The central goal of macroeconomics is to provide “coherent and robustexplanations of aggregate movements of output, employment and the pricelevel, in both the short run and the long run”. (cfr. Snowdon and Vane, 2005: 304)


Business cycles

B Arthur Burns and Wesley Mitchell, Measuring the Business Cycles(1946):

“Business cycles are a type of fluctuations found in the aggregate economicactivity of nations that organise their work mainly in business enterprises.A cycle consists of expansions occurring at about the same time in manyeconomic activities, followed by similarly general recessions, contractions,and revivals which merge into the expansion phase of the next cycle: thissequence of changes is recurrent but not periodic, in duration businesscycles vary from more than one year to ten or twelve years”

Main features:

• alternation of states (ups and downs) of the economy;

• recurrence;

• rough coherence between different measures of the economy.


Real GDP per capita, US 1947-2017, quarterly, seasonally adj.


Real GDP, US 1947-2017, quarterly, seasonally adj.


Real GDP, Italy 1995-2017, quarterly, seasonally adj.


GDP in US, Japan and Italy.

95

100

105

110

115

120

125

130

2002 2004 2006 2008 2010 2012 2014

2015research.stlouisfed.org

GrossDomesticProductbyExpenditureinConstantPrices:TotalGrossDomesticProductforItaly©,2001:Q1=100RealGrossDomesticProduct,2001:Q1=100GrossDomesticProductbyExpenditureinConstantPrices:TotalGrossDomesticProductforJapan©,2001:Q1=100

(Index)


Hourly labour productivity: Italy vs. Germany

Sources: Manasse (2013), The roots of italian stagnation, http://www.voxeu.org/article/roots-italian-stagnation


Terminology

B Trend: dominant path of a macroeconomic time series indicatingeconomic activity (e.g. real GDP)

B Cycle: fluctuations around this trend alternating peaks andtroughs

B Recession (aka slump, contraction, bust): period between peakand trough


Terminology

B NBER definition of recession for US:(http://www.nber.org/cycles.html)

“significant decline in economic activity spread across the economy, lastingmore than a few months, normally visible in real GDP, real income,employment, industrial production, and wholesale-retail sales”

B CEPR definition of recession for euro area:(http://www.cepr.org/content/euro-area-business-cycle-dating-committee)

“a significant decline in the level of economic activity, spread across theeconomy of the euro area, usually visible in two or more consecutive quartersof negative growth in GDP, employment and other measures of aggregateeconomic activity for the euro area as a whole”


Terminology

B Expansion (aka boom, recovery): period between trough andpeak

B Depression: A particularly severe recession (in terms ofpercentage change and duration), e.g. US Great Depression of1929-1933; 2009-? Greek depression

B Growth recession (slowdown): period of slower than trendgrowth

B Cycle: (i) period between trough and next trough: (ii) periodbetween peak and next peak.


A stylizes macroeconomic time series

Source: Hoover K.D. (2012) Applied Intermediate Macroeconomics, Cambridge UniversityPress, Figure 5.6.


Stylized facts about macroeconomic fluctuations


Facts about economic fluctuations

1 No clear and simple regularity in the cyclical pattern

2 Symmetries and asymmetries in output movements

3 Fluctuations are distributed very unevenly over the componentsof output

4 Co-movements

5 Some regularities in recessions

Cfr. Romer D. (2012) op.cit, sec. 5.1


1. Regular cycles?

Table: Recessions in the United States since World War II

Number of months Change in real GDP HighestRecession dates from peak to through from peak to through unemployment rate*

Nov. 1948-Oct. 1949 11 -1.7% 7.9%July 1953-May 1954 10 -2.7 5.9Aug. 1957-Apr. 1958 8 -1.2 7.4Apr. 1960-Feb. 1961 10 -1.6 6.9Dec. 1969-Nov. 1970 11 -0.6 5.9Nov. 1973-Mar. 1975 16 -3.1 8.6Jan. 1980-July 1980 6 -2.2 7.8July 1981-Nov. 1982 16 -2.9 10.8July 1990-Mar. 1991 8 -1.3 6.8Mar. 2001-Nov. 2001 8 -0.5 6.0Dec. 2007 - June 2009 18 -4.3 10

*included the aftermath period of the recession

Source: NBER


2. Symmetries and asymmetries

• In US output growth is distributed roughly symmetricallyaround its mean

• In US (post-World War II) the expansion phase is longer (aboutfive times) than the recession phase


2. Symmetries and asymmetries

years

perc

ent p

er y

ear

1950 1960 1970 1980 1990 2000 2010

−10

−5

05

1015

quarterly growth rate(compound annual)

annual growth rate

mean a. growth rate

Real GDP Growth Rates, US 1948−2012


3 Heterogeneous behaviour of output components

Table: Behaviour of the components of output in recessions

Average share in fallAverage share in GDP in recessions

Components of GDP in real GDP relative to normal growth

ConsumptionDurables 8.9% 14.6%Nondurables 20.6 9.7Services 35.2 10.9

InvestmentResidential 4.7 10.5Fixed nonresidential 10.7 21.0Change in inventories 0.6 44.8

Net exports -1 -12.3

Government purchases 20.2 1.3

Source: Romer D. (2012) Advanced Macroeconomics, Mc Graw Hill, Table 5.2.


4. Co-movements

Variable Direction TimingProduction

Industrial production Procyclical Coincident

ExpenditureConsumption Procyclical CoincidentBusiness fixed investment Procyclical CoincidentResidential investment Procyclical LeadingInventory investment Procyclical LeadingGovernment purchase Procyclical -

Labour market variablesEmployment Procyclical CoincidentUnemployment Countercyclical No clear patternAverage labour productivity Procyclical LeadingReal wage Procyclical -

Money supply and inflationMoney supply Procyclical LeadingInflation Procyclical Lagging

Financial variablesStock prices Procyclical LeadingNominal interest rates Procyclical LaggingReal interest rates Acyclical -

Source: Abel, A.B. and Bernanke, B.S. (2001) Macroeconomics, Addison-Wesley, p. 288Snowdon B. and Vane, H.R. (2005) Modern Macroeconomics, Efward Elgar, p. 306


0

20

40

60

80

100

120

1920 1940 1960 1980 2000

ShadedareasindicateUSrecessions-2015research.stlouisfed.org

Source:BoardofGovernorsoftheFederalReserveSystem(US)

IndustrialProductionIndex(Index2007=100)


2

3

4

5

6

7

8

9

10

11

1950 1960 1970 1980 1990 2000 2010


Source:US.BureauofLaborStatistics

CivilianUnemploymentRate(Percent)


50,000

60,000

70,000

80,000

90,000

100,000

110,000

120,000

130,000

140,000

150,000

1950 1960 1970 1980 1990 2000 2010


Source:US.BureauofLaborStatistics

CivilianEmployment(T

hou

sandsof

Per

sons)


20

30

40

50

60

70

80

90

100

110

1950 1960 1970 1980 1990 2000 2010


NonfarmBusinessSector:RealCompensationPerHourNonfarmBusinessSector:RealOutputPerHourofAllPersons

(Index

2009=100)


400

800

1,200

1,600

2,000

4,000

6,000

8,000

12,000

1960 1970 1980 1990 2000 2010



M2MoneyStock(BillionsofDollars)


10

20

30

40

50

60

70

90

110

1960 1970 1980 1990 2000 2010


Source:US.BureauofEconomicAnalysis

PersonalConsumptionExpenditures:Chain-typePriceIndex(Index2009=100)


0.0

2.5

5.0

7.5

10.0

12.5

15.0

17.5

1940 1950 1960 1970 1980 1990 2000 2010



3-MonthTreasuryBill:SecondaryMarketRate(Percent)


5. Regularities and recessions

• In US “aggregate fluctuations do not appear dramaticallydifferent before the Great Depression than in the first fourdecades or so after World War II” (Romer 2001 op.cit.:171)

• Regularities in the behaviour of some important macroeconomicvariables during recessions

• E.g. Okun’s law describes possible relationships betweenshortfalls in GDP and rises in unemployment rate.


Trends and cycles in macroeconomic variables


Measuring economic fluctuations

B NBER methodologylocal maxima and minima

data on output, income, employment and trade (sectoral and aggregate levels)

announcement with a lag

B Methods to isolate the cyclical component of time series

• Linear time trends and its limits

• Nelson and Plosser (1982): cycles vs. random walks

• Spectral analysis

Baxter and King (1994) band-pass filter

• Hodrick and Prescott (1997) filter

B Methods to analyse co-movementscointegration

common factors

Cfr. Stock, J.H. and Watson, M.W. (1999) “Business Cycle Fluctuations in US Macroeconomic Time Series”, in Taylor, J.B. and M. Woodford(eds.), Handbook of Macroeconomics, Elsevier, vol. 1A, Ch. 1.


Cycles vs. Random Walks

0 50 100 150 200

−2

−1

01

23

1:n

y

White noise (normal)

0 50 100 150 200−

15−

10−

50

510

1:n

X

Random walk



0 50 100 150 200

−15

−10

−5

05

10

1:n

X

Random walk

0 50 100 150 2000

510

1520

2530

35

1:n

Z

Random walk with drift



B Reversible cyclical fluctuations:

Yt = gt + bYt−1 + εt − 1 < b < 1 (1)

where gt is a deterministic trend. E.g. linear trend: gt = a + ct.

B Fluctuations as stochastic trend:

Yt = d + Yt−1 + εt (2)

Yt is a random walk with drift.

B Nelson and Plosser (JME 1980): GNP follows a random walk

B trend reverting vs. permanent shocks


White noise process:

Yt = εt E[εt] = 0 E[ε2t ] = σ2 E[εtετ ] = 0 for t 6= τ

Random walk:

Yt = Yt−1 + εt εt ∼ w.n.

Y1 = Y0 + ε1

Y2 = Y0 + ε1 + ε2

· · ·Yn = Y0 + ε1 + ε2 + . . . + εn

Random walk with drift:

Yt = d + Yt−1 + εt εt ∼ w.n.

Y1 = d + Y0 + ε1

Y2 = d + d + Y0 + ε1 + ε2

· · ·Yn = nd + Y0 + ε1 + ε2 + . . . + εn


Stationary autoregressive process (AR1):

Yt = d + bYt−1 + εt εt ∼ w.n. − 1 < b < 1

Y1 = d + bY0 + ε1

Y2 = d + b(d + bY0 + ε1) + ε2

Y3 = d + b(d + b(d + bY0 + ε1) + ε2) + ε3

= d + bd + b2d + b3Y0 + b2ε1 + bε2 + ε3

· · ·Yn = d(1 + b + b2 + . . . + bn−1) + bnY0 + εn + bεn−1 + b2εn−2 + . . . + bn−1ε1

= d(

11− b

)+ bnY0 + εn + bεn−1 + b2εn−2 + . . . + bn−1ε1


Hodrick-Prescott (1997) filter:

Decomposition ot time series yt in trend τt and cycle ct:

yt = τt + ct + εt

Given the parameter λ find τ such that

minτ

(T

∑t=1

(yt − τt)2 + λ

T−1

∑t=2

[(τt+1 − τt)− (τt − τt−1)]2

)

Hodrick, Robert J., and Edward C. Prescott. ”Postwar US business cycles: an empirical

investigation.” Journal of Money, credit, and Banking (1997): 1-16.


Baxter-King (1994) filter:

Based on the Fourier decomposition of a time series (spectral representation):

Yt =∫ −π

πξ(ω)d(ω)

Filter:

Yt =∫ −π

πα(ω)ξ(ω)d(ω)

Baxter, Marianne, and Robert G. King. ”Measuring business cycles: approximate band-pass filters

for economic time series.” Review of economics and statistics 81.4 (1999): 575-593.


The concept of potential output

Potential output, as many notions in economics, is an abstract and idealizedconcept.

It answers the question: how much output (i.e. GDP) would be produced ifits inputs (i.e. Labour and Capital) were fully employed in an optimal way,given a state of technology.

Potential output may be operationally estimated by assuming a productionfunction: Yp = F(AL, K), where L is equal to the entire the labour force (LF),and K is capital at full capacity. The term A refers to technology.

At full capacity the capacity utilization rate (CU) is equal to one:

CU =index of industrial production

industrial capacity index


The concept of potential output

Given the definition of potential output we have:

Yp = F(A · LF, K)

Actual output is (taking into account capital in effective use):

Y = F(A · L, CU · K)

Scaled output:

Y =YYp

Example (Cobb-Douglas production function):

Y =ALα(CU · K)1−α

A(LF)αK1−α=

(L

LF

)α

CU1−α


In sum, there are at least three different ways to estimate potentialoutput (and output gap):

• Filtered trend (linear detrending, HP filter, band-pass filter)

• Potential output as Yp = F(A · LF, K)

• CBO’s potential output:

Ypott = Apot

t [(1−NAIRUt) LF]αK1−αt

−−−−−−−−−CBO: Congressional Budget Office

NAIRU: Nonaccelerating inflation rate of unemployment


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