Download Real Business Cycles

FIN 30220: Macroeconomic
Analysis
Real Business Cycles
A Complete Business Cycle consists of an expansion and a contraction
recession
Peak
2.00
1.50
1.00
0.50
0.00
-0.50
2000-I
2002-I
2004-I
-1.00
-1.50
-2.00
Expansion
Trough
Here, we are plotting percentage deviation of GDP from a HP trend
5
4
3
2
1
0
Jan-57
-1
Jan-67
Jan-77
-2
-3
-4
-5
-6
The recessions are pretty easy to spot!
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%.
Unemployment Rate
12
10
8
6
4
2
0
Jan-57
-2
Jan-67
-4
-6
Shaded areas indicate recessions
Jan-77
Jan-87
Jan-97
Jan-07
Lets look at the behavior of inflation around the business cycle…notice that
inflation tends to decline during recessions and increase during expansions.
How about interest rates? Here is the return on a 90 Day T-Bill. Interest rates
tend to decline during recessions.
Shaded areas indicate recessions
All business cycles are “alike” in that there are regular relationships between
various macroeconomic statistics
2.5
Correlation = .81
2
1.5
1
0.5
0
1990-I
-0.5
1992-I
1994-I
1996-I
1998-I
2000-I
2002-I
2004-I
-1
-1.5
-2
-2.5
GDP
Consumption
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
8
Correlation = -.51
2
7
1.5
6
1
5
0.5
0
1990-I
-0.5
4
1992-I
1994-I
1996-I
1998-I
2000-I
2002-I
2004-I
3
-1
2
-1.5
1
-2
-2.5
0
GDP
Unemployment Rate
Unemployment is one of few counter-cyclical variables (negative correlation)
All business cycles are “alike” in that there are regular relationships between
various macroeconomic statistics
2.5
2
1000
Correlation = .003
800
1.5
600
1
0.5
400
0
1990-I
-0.5
1992-I
1994-I
1996-I
1998-I
2000-I
-1
2002-I
2004-I
200
0
-1.5
-200
-2
-2.5
-400
GDP
Deficit
The deficit is an example of an acyclical variable (zero correlation)
All business cycles are “alike” in that there are regular relationships between
various macroeconomic statistics
6
5
4
4
3
2
2
1
0
1980
1988
1996
-2
0
-1
-2
-4
-3
-6
-4
-8
-5
GDP
Productivity
Productivity is pro-cyclical and leads the cycle
All business cycles are “alike” in that there are regular relationships between
various macroeconomic statistics
6
16
4
14
12
2
10
0
1980
1988
1996
8
-2
6
-4
4
-6
2
-8
0
GDP
Inflation
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
w
p
 w
 
 p
Labor markets determine
employment and the real
wage
l s (NLI )
r
Capital markets determine
Savings, Investment, and
the real interest rate
S W , Y 
*
r*
I  A' , L'
l d ( A, K )
L*
Y
Employment determines
output and income
L
F ( A, K , L)
Y*
L*
L
S, I
S, I
Real business cycle theory
suggest that the business cycle
is caused my random
fluctuations in productivity
We have three possibilities for productivity shocks that hit the economy.
At 1   At   t
Persistence parameter
At
Productivity shock
At
   1
At  0    1
At    0
L
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)
w
p
 w
 
 p
r
l s (NLI )
S W , Y 
*
r*
I  A' , L'
l d ( A, K )
L*
Y
L
S, I
Drop in
productivity
F ( A, K , L)
Y*
For a given level of employment and
capital, production drops
L*
L
S, I
At the pre-recession real wage, the demand for labor
drops due to the productivity decline
w
p
 w
 
 p
l s (NLI )
r
S W , Y 
*
Drop in
productivity
r*
I  A' , L'
l d ( A, K )
L*
Y
L
S, I
S, I
F ( A, K , L)
Y*
The first market to respond
is the labor market
L*
L
The drop in labor demand creates excess supply of labor – real wages fall
and employment decreases
w
p
 w
 
 p
l s (NLI )
r
S W , Y 
*
r*
I  A' , L'
l d ( A, K )
L*
Y
L
Drop in
employment
S, I
S, I
F ( A, K , L)
Y*
The drop in employment
creates an additional drop in
production
L*
L
The capital market reacts next
w
p
 w
 
 p
The drop in income
relative to wealth causes
a decline in savings
r
l s (NLI )
Non-Labor
income is
(relatively)
unaffected
*
Wealth is
(relatively)
unaffected
r
S W , Y 
Expected
Future
productivity
is unaffected
*
I  A' , L'
l d ( A, K )
L*
Y
L
F ( A, K , L)
Drop in
Income
S, I
S, I
Expected
Future
employment
is unaffected
Y*
The interest rate will need to
adjust to equate the new level of
savings
L*
L
The drop in savings creates excess demand for loanable
funds
w
p
 w
 
 p
r
l s (NLI )
Non-Labor
income is
unaffected
*
Wealth is
unaffected
r
S W , Y 
Expected
Future
productivity
is unaffected
*
I  A' , L'
l d ( A, K )
L*
Y
L
F ( A, K , L)
Y*
Drop in
Income
S, I
S, I
Expected
Future
employment
is unaffected
The real interest rate rises and
levels of savings and investment
fall
L*
L
Let’s take stock …
Correlations With GDP
Real Wage
Employment
Savings
Consumption
Investment
Real Interest
Rate
Productivity
Predicted
+
+
+
+
+
-
+
Actual
+
+
+
+
+
+
+
We are not generating the correct correlation with
interest rates…what if the shock was permanent…
A permanent shock creates a larger drop in NLI which causes an increase in
labor supply
w
p
 w
 
 p
l s (NLI )
r
S W , Y 
*
r*
I  A' , L'
l d ( A, K )
L*
Y
L
Drop in
employment
S, I
F ( A, K , L)
Y*
L*
L
We get a bigger drop in the
real wage and the effect on
employment becomes
ambiguous
S, I
Next, the permanent drop in income has no effect on savings, but the
permanent decline in productivity lowers investment
w
p
 w
 
 p
l s (NLI )
r
S W , Y 
*
r*
I  A' , L'
l d ( A, K )
L*
Y
L
Drop in
employment
S, I
S, I
F ( A, K , L)
Y*
Now we have interest rates
moving in the right direction
L*
L
Let’s take stock …
Correlations With GDP – Temporary Shock
Real Wage
Employment
Savings
Consumption
Investment
Real Interest
Rate
Productivity
Predicted
+
+
+
+
+
-
+
Actual
+
+
+
+
+
+
+
Real Interest
Rate
Productivity
Correlations With GDP – Permanent Shock
Real Wage
Employment
Savings
Consumption
Investment
Predicted
+
??
+
+
+
+
+
Actual
+
+
+
+
+
+
+
What we need is a shock that is permanent enough to lower investment,
but not enough to raise labor supply
A shock with a little persistence (but not too much persistence) is what we
need.
At 1   At   t
Persistence parameter
At
Productivity shock
Not enough movement in
employment
Just right!
Countercyclical interest
rate
L
Recall that today’s investment determines
tomorrow’s capital stock.
Depreciation Rate
K '  (1   ) K  I
Tomorrow’s
capital stock
Remaining
portion of current
capital stock
Purchases of New
Capital
If investment falls enough, the capital stock
shrinks – this is what gives the recession
“legs”
The drop in the capital stock worsens the recession – labor demand declines
further
w
p
 w
 
 p
r
l s (NLI )
Capital stock
declines
*
S W , Y 
r*
I  A' , L'
l d ( A, K )
L*
Y
L
S, I
Drop in
capital
F ( A, K , L)
Y*
The drop in the capital stock creates an
additional drop in production
L*
L
S, I
What about investment?
Y
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
MPK
K'
K
K
What about savings?
Savings depends on expectation of the future..
Y
During the downturn, next years
income is always lower than this
years…savings increases
Time
The drop in the capital stock worsens the recession – labor
demand declines further
w
p
 w
 
 p
r
l s (NLI )
Capital stock
declines
*
S W , Y 
r*
I  A' , L'
l d ( A, K )
L*
Y
L
S, I
Drop in
capital
F ( A, K , L)
Y*
L*
L
With lower
investment, the
capital stock
continues to fall
S, I
What about investment?
Eventually, the marginal product of capital starts to rise
again.
Y
MPK
MPK
K'
K
K
What about savings?
Savings depends on expectation of the future..
Y
During the recovery, next years
income is always higher than this
years…savings decreases
Time
The rise in MPK raises investment, while expected increases in
income lower savings
w
p
 w
 
 p
r
l s (NLI )
S W , Y 
*
r*
I  A' , L'
l d ( A, K )
L*
Y
L
S, I
Drop in
capital
F ( A, K , L)
Y*
Now, the upturn
begins!
L*
L
S, I
The capital stock begins to rise, which raises labor demand…
w
p
 w
 
 p
l s (NLI )
Capital stock
declines
*
r
S W , Y 
r*
I  A' , L'
l d ( A, K )
L*
Y
L
S, I
Increase in
capital
F ( A, K , L)
Y*
Employment starts
to increase!
L*
L
S, I
The Recession of 1981 is officially dated from July 1981 to November 1982
4
6
3
4
2
2
1
0
0
-1
1981
1982
-2
1983
-4
-2
-6
-3
-4
-8
-5
-10
-6
-12
Productivity
Employment
GDP
Investment
The Recession of 1991 is officially dated from July 1990 to March 1991
6
8
6
4
4
2
2
0
0
1990
1991
1992
1993
1994
-2
-2
-4
-4
-6
-6
-8
Productivity
Employment
GDP
Investment
The most recent recession is officially dated from March 2001 to November
2001
8
6
6
4
4
2
2
0
0
-2
2001
2002
2003
2004
2005
-2
-4
-4
-6
-6
-8
-8
-10
Productivity
Employment
GDP
Investment
As was mentioned earlier, the 2001 recession was different in that it
was almost entirely driven by capital investment rather than
productivity





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
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?