Macroeconomic AnalysisEcon 6022

Level II

Lecture 4 and 5

Fall, 2011

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Overview

• What is a Business Cycle?• Business Cycle Facts• A framework for analysis of business cycles

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Cycles and Growth in the U.S.

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Stylized Business Cycles

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Trend vs. Cycles

• We want to study fluctuations

• We imagine that real output has two parts:real GDP = trend real GDP + cyclical part of real GDP

• Estimating the trend: a reasonably smooth curve fit into thedata on real GDP

• Cyclical part: Proportionate Deviation from the trend

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Features of Business Cycles?

• Burns and Mitchell (Measuring Business Cycles, 1946)makes five main points about business cycles:

1. Business cycles are fluctuations of aggregate economicactivity, not a specific variable

2. There are expansions and contractions3. Economic variables show comovement–they have regular

and predictable patterns over the course of the businesscycle

4. The business cycle is recurrent, but not periodic5. The business cycle is persistent

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What Is a Business Cycle?

• Expansions and contractions- After a trough, activity increases in an expansion or boom

until it reaches a peak- A particularly severe recession is called a depression- The sequence from one peak to the next, or from one

trough to the next, is a business cycle- Peaks and troughs are turning points- Turning points are officially designated by the NBER

Business Cycle Dating Committee

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What Is a Business Cycle?

• The business cycle is recurrent, but not periodic- Recurrent means the pattern of

contraction-trough-expansion-peak occurs again and again- Not being periodic means that it doesn’t occur at regular,

predictable intervals

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What Is a Business Cycle?

• The business cycle is persistent- Declines are followed by further declines; growth is followed

by more growth- Because of persistence, forecasting turning points is quite

important

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Business Cycles: Facts

• What direction does a variable move relative to aggregateeconomic activity?

- Procyclical: in the same direction- Countercyclical: in the opposite direction- Acyclical: with no clear pattern

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Business Cycles: Facts

• What is the timing of a variable’s movements relative toaggregate economic activity?

- Leading: in advance- Coincident: at the same time- Lagging: after

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Housing Expenditure as percentage of GDP

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RBC View of Fluctuations

• Fluctuations reflect shocks to the economy.• Shocks: change in technology level, A• Exogenous shocks (increase and decrease in A) drive

business cycles• What are the shocks?

• Change in A can be positive (e.g. new technologydiscoveries)

• Change in A can be negative (e.g. bad weather, shift inlegal system)

• We refer to A as the “technology level”

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Questions that We Are Interested In:

• At the time of shock: How does the economy responds toan one-time increase in A (TFP)?

• Propagation mechanism: Does the shock propagate forseveral periods into the economy? Why are businesscycles persistent?

• Key fact 1: Consumption (investment) respond less(more) than output. Why?

• Key fact 2: Consumption and output move in the samedirection as output (i.e., pro-cyclical). Why?

• Key fact 3: Wage and interest rates move in the samedirection as output (i.e., pro-cyclical). Why?

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Environment

• Labor market: supply and demand• Rental market: supply and demand• Households:

• Income: labor income and rental income• Expenditure: consumption and saving (investment)

• Firms• Decision on labor input• Decision on capital services

• Competitive markets• Price takers• Equilibrium prices

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Firm’s Problem and Aggregation

• Firms are all competitive.• Profit maximizing,

π = Akαi L1−α

i − w · Li − (r + δ) · ki

• Demand for labor input,

A · kαi (1 − α)L−α

i = w .

• Demand for capital services,

A · α · kαi L1−α

i = r + δ.

• Aggregation: L =∫

Lidi and K =∫

kidi

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A Temporary Increase in A

• A increases at period t from A to A · (1 + γ) and returnsback to A at period t + 1

– At−1 = A– At = A · (1 + γ)– At+1 = A

• Assumption: labor supply is exogenous and constantLs

t = L• Capital before Period t ,

Kt = K• Investment before Period t ,

It−1 = δ · K• Output before Period t ,

Y = A · Kα · L

1−α

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A Temporary Increase in A

• Capital does not respond to the shock immediately(pre-determined)

Kt = K• By assumption,

Lt = L

• Wage and rental rate are pro-cyclical

w∗t = At · (1 − α) · K

α · L−α

r∗t = At · α · Kα−1 · L

1−α

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A Temporary Increase in A

• An increase in A leads to a rise in Yt in current period.• It is similar to a temporary increase in income.• Consumption is pro-cyclical

– consuming only a small part of the positive shock– Why? Permanent income theory tells us ...– people smooth consumption– people save a larger fraction of the positive shock

• Investment is pro-cyclical– increasing investment/savings– so the capital Kt+1 > K

• The effect of one time increase in A propagates over time.– Yt > Y and Yt+1 > Y– Productivity boom and investment boom– The boom lasts longer than one period: persistence

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Volatility

• Permanent, temporary and persistent shocks• Utility function and inter-temporal substitution effect• Income and inter-temporal substitution effects• Consumption is less volatile than income

• Investment is more volatile than income– Increase in interest rate discourages the current

consumption– ... encourages savings/investment– Recall the definition of investment

I = Y − C

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The model and Data

• Consumption is less volatile than output• Investment is more volatile than output• Consumption is pro-cyclical• Investment is pro-cyclical• Wage is pro-cyclical• Interest rate is pro-cyclical• Unemployment and labor input?

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Labor Supply and Bussiness Cycles

• We have assumed that labor input is fixed over time.• We have to relax this assumption to study labor input

during fluctuations.• An additional assumption on Utility function:

u = u(C, l)• People like leisure time, l or dislike working,

Ls + l = L• The utility function can be written as,

u = u(C,1 − Ls)

• Wage rate, the price of leisure:• enjoy one more unit of leisure• supply one less unit of labor• earn less by w · 1

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Intra-temporal v.s. Inter-temporal

• Intra-temporal: within period• trade-off: consume more and enjoy less leisure time

• Inter-temporal: across periods• trade-off: enjoy more leisure today and enjoy less leisure

time in the future

• During booms, you work harder; during recessions, youtake vacations

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Intra-temporal effects

• The substitution effect for leisure and consumption:– higher wage implies higher price for leisure, and relatively

cheaper consumption– enjoy less leisure and supply more labor (and consume

more)– Alternatively: gets more consumption for each hour worked

• Income effect on labor supply:– For a given quantity of labor supply, Ls, higher wage implies

higher income.– higher income implies consume more and enjoy more

leisure– labor supply should decrease

• Overall effect: ambiguous– In the case of temporary increase in wage– Income effect is small– overall effect: higher wage induces more labor supply

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Inter-temporal effects

• Inter-temporal substitution effect through wage rate:– higher wage rate in current period means that wage rate

will be relatively lower in the future– the price of leisure time is high in current period and low in

the future– enjoy less leisure time now and more in the future– it means labor supply in current period increases

• Inter-temporal substitution effect through interest rate:

– when we look at the wage today and tomorrow, we will haveto discounted the future wage with interest rate 1 + rt

– during booms, interest rate is higher– the present value of wage in the future will be lower– the price for leisure time in the future is lower– current consumption and leisure time are more expensive– less leisure time and more labor supply in current period

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Equilibrium Labor Input

• So far, we have shown the labor supply increases incurrent wage rate, Ls(Wt)

• Labor demand decreases in wage, which is relativelyeasy to show,

wt = At · (1 − α) · Kα · L−α

d

• Ld(wt ,At) decrease in wt and increases in At

• Employment (and hours worked) and fluctuation• During boom: At increases from A to A · (1 + γ)

• Both wage rate and equilibrium labor input increase

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Equilibrium Labor Input

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