fin 30220: macroeconomic analysis

Real Business Cycles

FIN 30220: Macroeconomic Analysis

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recession

Expansion

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Trough

A Complete Business Cycle consists of an expansion and a contraction

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Here, we are plotting percentage deviation of GDP from a HP trend

The recessions are pretty easy to spot!

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Jan-57 Jan-67 Jan-77 Jan-87 Jan-97 Jan-07

While the average unemployment rate (excluding recessions) has been around 5% since 1957, the average unemployment rate during recessionary periods averages around 7%.

Shaded areas indicate recessions

Un

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Lets look at the behavior of inflation around the business cycle…notice that inflation tends to decline during recessions and increase during expansions.

Shaded areas indicate recessions

How about interest rates? Here is the return on a 90 Day T-Bill. Interest rates tend to decline during recessions.

All business cycles are “alike” in that there are regular relationships between various macroeconomic statistics

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GDP Consumption

Correlation = .81

Consumption is one of many pro-cyclical variables (positive correlation)

All business cycles are “alike” in that there are regular relationships between various macroeconomic statistics

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GDP Unemployment Rate

Correlation = -.51

Unemployment is one of few counter-cyclical variables (negative correlation)

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GDP Deficit

Correlation = .003

All business cycles are “alike” in that there are regular relationships between various macroeconomic statistics

The deficit is an example of an acyclical variable (zero correlation)

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1980 1988 1996

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GDP Productivity

All business cycles are “alike” in that there are regular relationships between various macroeconomic statistics

Productivity is pro-cyclical and leads the cycle

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1980 1988 1996

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GDP Inflation

All business cycles are “alike” in that there are regular relationships between various macroeconomic statistics

Inflation is pro-cyclical and lags the cycle

Business Cycles: Stylized Facts

Variable Correlation Leading/Lagging

Consumption Pro-cyclical Coincident

Unemployment Countercyclical Coincident

Real Wages Pro-cyclical Coincident

Interest Rates Pro-cyclical Coincident

Productivity Pro-cyclical Leading

Inflation Pro-cyclical Lagging

The goal of any business cycle model is to explain as many facts as possible

We have a simple economic model consisting of two markets

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Labor markets determine employment and the real wage

Capital markets determine Savings, Investment, and the real interest rate

Employment determines output and income

Real business cycle theory suggest that the business cycle is caused my random fluctuations in productivity

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We have three possibilities for productivity shocks that hit the economy.

1t t tA A Productivity shock

Persistence parameter

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1tA

0 1tA

We have developed a model with a labor market and a capital market. Suppose that a random, temporary, negative productivity shock hits the economy. (Assume no government deficit)

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Drop in productivity

For a given level of employment and capital, production drops

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Drop in productivity

The first market to respond is the labor market

At the pre-recession real wage, the demand for labor drops due to the productivity decline

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The drop in labor demand creates excess supply of labor – real wages fall and employment decreases

Drop in employment

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Expected Future productivity is unaffected

Expected Future employment is unaffected

Drop in Income

Wealth is (relatively) unaffected

Non-Labor income is (relatively) unaffected

The interest rate will need to adjust to equate the new level of savings

The capital market reacts next The drop in income relative to wealth causes a decline in savings

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Expected Future productivity is unaffected

Expected Future employment is unaffected

Drop in Income

Wealth is unaffected

Non-Labor income is unaffected

The real interest rate rises and levels of savings and investment fall

The drop in savings creates excess demand for loanable funds

Let’s take stock …

Real Wage Employment Savings Consumption Investment Real Interest Rate

Productivity

Predicted + + + + + - +Actual + + + + + + +

Correlations With GDP

We are not generating the correct correlation with interest rates…what if the shock was permanent…

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*YWe get a bigger drop in the real wage and the effect on employment becomes ambiguous

A permanent shock creates a larger drop in NLI which causes an increase in labor supply

Drop in employment

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*YNow we have interest rates moving in the right direction

Next, the permanent drop in income has no effect on savings, but the permanent decline in productivity lowers investment

Drop in employment

Let’s take stock …

Real Wage Employment Savings Consumption Investment Real Interest Rate

Productivity

Predicted + + + + + - +Actual + + + + + + +

Correlations With GDP – Temporary Shock

Real Wage Employment Savings Consumption Investment Real Interest Rate

Productivity

Predicted + ?? + + + + +Actual + + + + + + +

Correlations With GDP – Permanent Shock

What we need is a shock that is permanent enough to lower investment, but not enough to raise labor supply

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A shock with a little persistence (but not too much persistence) is what we need.

1t t tA A Productivity shock

Persistence parameter

Countercyclical interest rate

Not enough movement in employment

Just right!

Recall that today’s investment determines tomorrow’s capital stock.

IKK )1('

Tomorrow’s capital stock

Remaining portion of current capital stock

Depreciation Rate

Purchases of New Capital

If investment falls enough, the capital stock shrinks – this is what gives the recession “legs”

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Drop in capital

The drop in the capital stock creates an additional drop in production

The drop in the capital stock worsens the recession – labor demand declines further

Capital stock declines

What about investment?

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MPK

'K

Falling employment lowers the productivity of capital (labor and capital are compliments while a falling capital stock raises the productivity of capital (diminishing MPK). During the downturn, the marginal product of capital falls which continues to lower investment.

MPK

What about savings?

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Time

Savings depends on expectation of the future..

During the downturn, next years income is always lower than this years…savings increases

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Drop in capital

The drop in the capital stock worsens the recession – labor demand declines further

Capital stock declines

With lower investment, the capital stock continues to fall

What about investment?

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MPK

'K

Eventually, the marginal product of capital starts to rise again.

MPK

What about savings?

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Savings depends on expectation of the future..

During the recovery, next years income is always higher than this years…savings decreases

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Drop in capital

The rise in MPK raises investment, while expected increases in income lower savings

Now, the upturn begins!

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Increase in capital

The capital stock begins to rise, which raises labor demand…

Capital stock declines

Employment starts to increase!

The Recession of 1981 is officially dated from July 1981 to November 1982

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Productivity Employment GDP Investment

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Productivity Employment GDP Investment

The Recession of 1991 is officially dated from July 1990 to March 1991

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2001 2002 2003 2004 2005

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Productivity Employment GDP Investment

The most recent recession is officially dated from March 2001 to November 2001

Collapse of the stock market The Dow dropped 30% from its Jan 14, 2000 high of $11,722 The Nasdaq dropped 75% from its March 10, 2000 high of

$5,132 The S&P 500 dropped 45% from its July 17, 2000 high of

$1,517 Y2K/Capital Overhang A sharp rise in oil prices (oil prices doubled in late 1999) Enron/Accounting scandals Terrorism/SARS

As was mentioned earlier, the 2001 recession was different in that it was almost entirely driven by capital investment rather than productivity

Are recessions caused by high oil prices?

Recession Dates

It seems as if random fluctuations to productivity are a good explanation for business cycles. However, there are a couple problems…

If productivity is the root cause of business cycles, we would expect a correlation between productivity and employment/output to be very close to 1. The actual correlation is around .65

Where do these productivity fluctuations come from?

Haven’t we left something out?