# Investment and Real Business Cycles by fla46398

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```									FIN 30220: Macroeconomic
Analysis

A Complete Business Cycle consists of an expansion and a contraction

recession
Peak

2.00

1.50

1.00

0.50

0.00
2000-I               2002-I          2004-I
-0.50                                                 Trough
-1.00

-1.50

-2.00

Expansion
GDP: Deviations from Trend:1947-2005

6

4

2

0
1955-II

1966-II

1977-II

1988-II

1999-II
1949-

1952-

1960-

1963-

1971-

1974-

1982-

1985-

1993-

1996-

2004-
1947-I

1958-I

1969-I

1980-I

1991-I

2002-I
-2

-4

-6

-8

Since WWII, the US has experienced 10 contractions lasting an average
of 10 months (from peak to trough) – 63 months from peak to peak
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   1992-I   1994-I   1996-I   1998-I   2000-I   2002-I   2004-I
-0.5

-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                                                                          4
1990-I   1992-I   1994-I    1996-I    1998-I   2000-I   2002-I   2004-I
-0.5
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                                                                        1000
Correlation = .003
2
800
1.5

1                                                                        600

0.5
400
0
1990-I   1992-I   1994-I   1996-I   1998-I   2000-I   2002-I   2004-I   200
-0.5

-1                                                                        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          0
-2
-1

-4                                                           -2

-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

Consumption               Pro-cyclical          Coincident
Unemployment              Countercyclical       Coincident
Real Wages                Pro-cyclical          Coincident
Interest Rates            Pro-cyclical          Coincident
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

Capital markets determine
Labor markets determine
Savings, Investment, and
w        employment and the real

p
wage
l s (NLI )
r    the real interest rate
S W , Y 

*
 w
 
 p                                                     r*
 

l d ( A, K )                                        I  A' , L'
S, I
L                        S, I
L*

Y            Employment determines
output and income
F ( A, K , L)    Real business cycle theory
Y*                                                        suggest that the business cycle
is caused my random
fluctuations in productivity

L*
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                            l s (NLI )
r                             S W , Y 

*
 w
 
 p                                                         r*
 

l d ( A, K )                                                I  A' , L'
S, I
L                                  S, I
L*
Drop in
productivity
Y
F ( A, K , L)
Y*

For a given level of employment and
capital, production drops

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

w
p                      l s (NLI )                 r                       S W , Y 

*
 w
 
 p                                               r*
                                  Drop in
productivity

l d ( A, K )                                     I  A' , L'
S, I
L                              S, I
L*

Y
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                      l s (NLI )                r                          S W , Y 

*
 w
 
 p                                              r*
 

l d ( A, K )                                         I  A' , L'
S, I
L                              S, I
L*                          Drop in
employment

Y
F ( A, K , L)
Y*
The drop in employment
production

L*
L
The capital market reacts next               The drop in income
Wealth is      Drop in
relative to wealth causes          unaffected     Income
a decline in savings
w
p                       l s (NLI )                    r                                S W , Y 

*                          Non-Labor                                                        Expected
 w
 
 p
income is
r   *                                          Future
                                unaffected                                                       productivity
is unaffected

l d ( A, K )                                                    I  A' , L'
S, I
L                                     S, I
L*
Expected
Future
Y                                                                                        employment
F ( A, K , L)                                                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                                                              Wealth is      Drop in
unaffected     Income
w
p                      l s (NLI )               r                         S W , Y 

*                         Non-Labor                                            Expected
 w
 
 p
income is
r   *                                   Future
                               unaffected                                           productivity
is unaffected

l d ( A, K )                                        I  A' , L'
S, I
L                         S, I
L*
Expected
Future
Y                                                                           employment
F ( A, K , L)                                    is unaffected

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

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

Depreciation Rate

K '  (1   ) K  I

Purchases of New
Tomorrow’s
Capital
capital stock

Remaining
portion of current       If investment falls enough, the capital stock
capital stock            shrinks – this is what gives the recession
“legs”
The drop in the capital stock worsens the recession

w
p                      l s (NLI )                     r                           S W , Y 

*
 w
 
 p                                                   r*
 

l d ( A, K )                                               I  A' , L'
S, I
L                                S, I
L*
Drop in
capital
Y
F ( A, K , L)
Y*

The drop in the capital stock creates an

L*
L
Even at the lower wage, a drop in the capital stock
further depresses labor demand

w
p                     l s (NLI )                    r                       S W , Y 

*
 w
 
 p
                                                  r*
Drop in
capital

l d ( A, K )                                           I  A' , L'
S, I
L                                  S, I
L*

Y
F ( A, K , L)
Y*
A second labor market
response further lowers real
wages and employment –
production falls further
L*
L
A drop in the capital stock creates expectations of persistent declines in
Income
employment which begin to influence investment demand
continues to
fall
w
p                                     l s (NLI )                r                        S W , Y 
Drop in
 w
*                                                                                            expected
 
 p                                                             r*                                 future
                                                                                                  employment

l d ( A, K )                                       I  A' , L'
S, I
L                                S, I
L*

Y                                                                    A second capital market
F ( A, K , L)              response further lowers
Y*                                                                    savings, and investment –
with both investment and
savings affected, the
interest rate effect is
ambiguous
L*
L
How do we know when we’ve hit rock bottom (i.e. the trough)?

Falling employment lowers the productivity of capital (labor
Y            and capital are compliments while a falling capital stock
raises the productivity of capital (diminishing MPK).
Eventually, these two effects offset each other.

MPK
MPK

K
K'            K
The Recession of 1981 is officially dated from July 1981 to November
1982
4                                                                6

3                                                                4
2
2
1
0
0
-2
1981                  1982             1983
-1
-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
Are recessions caused by high oil prices?
Recession Dates
Are jobless recoveries the new norm?
6

4

2

0
0          4              8           12        16
-2

-4

-6
Employment (% Deviation from trend)
-8

2001       1991   1981

Look at the change in employment following the last three recessions!
What was different about the 2001 Recession?

4

2

0
0              4               8            12        16
-2

-4

-6

Productivity (% Deviation from trend)
-8

2001       1991   1981

Productivity was actually growing during the 2001 recession!!
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
Can preference shocks cause recessions?

w
l s (NLI )
r
p                                                                S Y ,W 

*
r*
 w
 
 p
 
l d ( A, K )                                I  A, L 
S, I
l*               L                       SI

Y
F ( A, K , L)        If recessions are caused by a
Y*                                           sudden drop in labor supply,
then wages would be
countercyclical (rising during
expansions)

L*
L
Can preference shocks cause recessions?

w
l s (NLI )
r
p                                                                    S Y ,W 

*
 w
 
 p                                       r*
 

l d ( A, K )                                 I  A, L 
S, I
L*               L                       SI
Y
If households suddenly lower
F ( A, K , L)        consumption expenditures
*
Y                                              (increase savings), the drop
in interest rates should trigger
an offsetting rise in
investment spending

L*
L
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? Is it possible
to separate technology from capital?

Haven’t we left something out?

```
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