real business cycles fin 30220: macroeconomic analysis
TRANSCRIPT
Real Business Cycles
FIN 30220: Macroeconomic Analysis
-2.00
-1.50
-1.00
-0.50
0.00
0.50
1.00
1.50
2.00
2000-I 2002-I 2004-I
recession
Expansion
Peak
Trough
A Complete Business Cycle consists of an expansion and a contraction
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
Jan-57 Jan-67 Jan-77 Jan-87 Jan-97 Jan-07
Here, we are plotting percentage deviation of GDP from a HP trend
The recessions are pretty easy to spot!
-6
-4
-2
0
2
4
6
8
10
12
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
emp
loym
ent
Rat
e
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
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
1990-I 1992-I 1994-I 1996-I 1998-I 2000-I 2002-I 2004-I
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
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
1990-I 1992-I 1994-I 1996-I 1998-I 2000-I 2002-I 2004-I
0
1
2
3
4
5
6
7
8
GDP Unemployment Rate
Correlation = -.51
Unemployment is one of few counter-cyclical variables (negative correlation)
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
1990-I 1992-I 1994-I 1996-I 1998-I 2000-I 2002-I 2004-I
-400
-200
0
200
400
600
800
1000
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)
-8
-6
-4
-2
0
2
4
6
1980 1988 1996
-5
-4
-3
-2
-1
0
1
2
3
4
5
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
-8
-6
-4
-2
0
2
4
6
1980 1988 1996
0
2
4
6
8
10
12
14
16
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
L
p
w
)(NLIl s
*
p
w
*L
),( KAl dIS ,
r YWS ,
*r
IS ,
',' LAI
Y
L
),,( LKAF
*L
*Y
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
L
tA
We have three possibilities for productivity shocks that hit the economy.
1t t tA A Productivity shock
Persistence parameter
0tA
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)
L
p
w
)(NLIl s
*
p
w
*L
),( KAl dIS ,
r YWS ,
*r
IS ,
',' LAI
Y
L
),,( LKAF
*L
*Y
Drop in productivity
For a given level of employment and capital, production drops
L
p
w
)(NLIl s
*
p
w
*L
),( KAl dIS ,
r YWS ,
*r
IS ,
',' LAI
Y
L
),,( LKAF
*L
*Y
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
L
p
w
)(NLIl s
*
p
w
*L
),( KAl dIS ,
r YWS ,
*r
IS ,
',' LAI
Y
L
),,( LKAF
*L
*YThe drop in employment creates an additional drop in production
The drop in labor demand creates excess supply of labor – real wages fall and employment decreases
Drop in employment
L
p
w
)(NLIl s
*
p
w
*L
),( KAl dIS ,
r YWS ,
*r
IS ,
',' LAI
Y
L
),,( LKAF
*L
*Y
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
L
p
w
)(NLIl s
*
p
w
*L
),( KAl dIS ,
r YWS ,
*r
IS ,
',' LAI
Y
L
),,( LKAF
*L
*Y
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…
L
p
w
)(NLIl s
*
p
w
*L
),( KAl dIS ,
r YWS ,
*r
IS ,
',' LAI
Y
L
),,( LKAF
*L
*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
L
p
w
)(NLIl s
*
p
w
*L
),( KAl dIS ,
r YWS ,
*r
IS ,
',' LAI
Y
L
),,( LKAF
*L
*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
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”
L
p
w
)(NLIl s
*
p
w
*L
),( KAl dIS ,
r YWS ,
*r
IS ,
',' LAI
Y
L
),,( LKAF
*L
*Y
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?
Y
KK
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?
Y
Time
Savings depends on expectation of the future..
During the downturn, next years income is always lower than this years…savings increases
L
p
w
)(NLIl s
*
p
w
*L
),( KAl dIS ,
r YWS ,
*r
IS ,
',' LAI
Y
L
),,( LKAF
*L
*Y
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?
Y
KK
MPK
'K
Eventually, the marginal product of capital starts to rise again.
MPK
What about savings?
Y
Time
Savings depends on expectation of the future..
During the recovery, next years income is always higher than this years…savings decreases
L
p
w
)(NLIl s
*
p
w
*L
),( KAl dIS ,
r YWS ,
*r
IS ,
',' LAI
Y
L
),,( LKAF
*L
*Y
Drop in capital
The rise in MPK raises investment, while expected increases in income lower savings
Now, the upturn begins!
L
p
w
)(NLIl s
*
p
w
*L
),( KAl dIS ,
r YWS ,
*r
IS ,
',' LAI
Y
L
),,( LKAF
*L
*Y
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
-6
-5
-4
-3
-2
-1
0
1
2
3
4
1981 1982 1983
-12
-10
-8
-6
-4
-2
0
2
4
6
Productivity Employment GDP Investment
-6
-4
-2
0
2
4
6
1990 1991 1992 1993 1994
-8
-6
-4
-2
0
2
4
6
8
Productivity Employment GDP Investment
The Recession of 1991 is officially dated from July 1990 to March 1991
-8
-6
-4
-2
0
2
4
6
8
2001 2002 2003 2004 2005
-10
-8
-6
-4
-2
0
2
4
6
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
-8
-6
-4
-2
0
2
4
6
0 4 8 12 16
2001 1991 1981
Are jobless recoveries the new norm?
Look at the change in employment following the last three recessions!
Employment (% Deviation from trend)
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?