FIN 30220: Macroeconomic
Analysis
Labor Markets
Of the 317 million people that make up the US population, approximately
246 million are considered by the Bureau of Labor Statistics to be
“eligible” to work.
Eligible Civilian
Population
249 Million
Under 16
On Active Military
US Population
320 Million
Duty
Non-Eligible
Population
71 Million
Inmates in Penal or
Mental Institutions
The US labor market is a very dynamic market. The 249 million
Americans currently counted as part of the US eligible population are in
a constant state of motion between three possible states
Unemployment = 9M = 5.7%
157M
Rate (UR)
Employed
148 Million
Not In Labor
Force
92 Million
Unemployed
9 Million
Participation
Rate (PR)
=
157M
= 63%
249M
Employment
Rate (ER)
=
148M
= 59%
249M
UR = 1 -
ER
PR
Source: Household Survey
The Natural Rate, or NAIRU (Non Accelerating Inflation Rate of Unemployment)
refers to what’s “normal” in the labor market.
9
8
Cyclical
Unemployment
7
6
5
4
3
2
“Natural Rate”
1
0
1990
1993
1996
2000
2003
If unemployment is at the “natural rate”, then the inflation rate should be
stable.
Note that the “Natural Rate” of unemployment is not zero! A healthy labor
market should have some turnover as workers look for better jobs.
5%
Frictional Unemployment: Workers in the
process of finding a job
1.5%
0%
Structural Unemployment: Workers whose
skills are no longer needed due to industry
evolution. These people generally require
retraining
A better measure of the labor market is simply the total number of people
working
1200
140000
1000
800
120000
600
Total
100000
400
80000
200
60000
0
40000
-200
20000
-400
0
1980
-600
1984
Recession
1988
1992
Recession
1996
2000
2004
Recession
Change From Previous Month
160000
What’s a “good” employment number?
Labor Market
US Population
300 Million
Our population
growth rate
averages
around 1% per
year
250,000 per
month
100,000 per
month
Every month,
people retire,
go back to
school, etc.
To maintain a constant unemployment rate, we need to create
approximately 150,000 jobs per month!!
The employment figures generally coincide with the unemployment rate, but
not always
Unemployment Rate
600
7
6
400
5
300
200
4
100
3
0
2000
-100
2001
2002
2003
2004
2005
2
-200
1
-300
-400
0
Unemployment Rate
Change in Employment
500
Consider two economies. Both have a labor force equal to 100. In economy A,
10 people lose their jobs every month (but find a job the following month). In
Economy B, 10 people get laid off every 3 months, but take three months to find
work.
A
10
January
B
10
February
10
March
10
10
April
10
May
10
June
July
10
At any point in time, both economies have
identical unemployment rates of 10%
Duration measures the average length of an unemployment spell. Economy A
has a duration of 1 month. Economy B has a duration of 3 months.
Suppose that we have the following data.
Labor Force = 200M
January
February
March
April
3 Million
3.5 Million
May
June
24 Weeks
12 Weeks
2.5 Million 8 Weeks
3.5 Million
2.5 Million 8 Weeks
9M
Unemployment Rate =
= 4.5%
200M
Average Duration =
3M
24
17.5M
3 Million
+
12 Weeks
2.5 Million 8 Weeks
7 Million
+
7.5 Million
17.5 Million
7M
7.5M
12 +
8 = 12.3 weeks
17.5M
17.5M
Length of unemployment spells in the US
However, average and median duration has been rising!
Mean = 39 weeks
Median = 22 weeks
Production Functions measure the relationship between inputs and
output
Y  F ( A, K , L)
Labor
Output
Capital (Fixed in Short Run)
Productivity (Exogenous)
Typically the production function used is Cobb-Douglas
Capital’s Share of
Income
1
3
2
3
Y  AK L
Labor’s Share of
Income
Production in the short run – capital is fixed
The Marginal Product of
Labor (MPL) measures the
change in production
associated with a small
change in employment
Y
MPL 
L
As labor increases
(given a fixed capital
stock), labor productivity
declines!!
Y
MPL=2
2
10
F ( A, K , L)
MPL=10
L
L'
1
1
L
Production in the short run – capital is fixed
F ( A' , K , L)
or
MPL=4
We also assume that
the marginal product of
labor is positively
related to increases in
either productivity and
capital
F ( A, K ' , L)
Y
F ( A, K , L)
MPL=2
MPL=14
K' K
A'  A
Y
MPL 
L
MPL=10
L
L'
L
We assume that firms are perfectly competitive. They choose labor hours to
maximize profits
Y  F ( A, K , L)
Wage
Rate
Price of
Capital
  pY Y  wL  pk K
Price of
Output
Total
Output
Labor
Costs
Capital Costs
(Fixed in Short
Run)
The best choice for labor can be found by taking looking at changes in both
revenues and costs at the margin.
pY MPL  w
A little rearranging gives us the following condition
w
MPL 
pY
Real Wage
Qualitatively, this tells us we would expect to see a strong positive
correlation between productivity and wages
Example:
F ( A, K , L)
Labor Hours
Output
MPL
1
40
2
52
12
3
62
10
4
70
8
5
76
6
6
80
4
w  $40
pY  $5
For the production function given
above, at a real wage of 8, 4 hours
of labor are hired
w $40

8
pY
$5
Labor demand records the hiring decision (# of hours) chosen by the firm at
every real wage
F ( A, K , L)
Real
Wage
w
p
 w
   8
 p
L4
Labor Hours
Output
1
40
2
52
12
3
62
10
4
70
8
5
76
6
6
80
4
w  $40
pY  $5
L
Hours of
Labor
MPL
w $40

8
pY
$5
Altering the real wage (holding production values fixed) allows us to trace out
the labor demand curve
F ( A, K , L)
Real
Wage
w
p
 w
   8
 p
 w
   6
 p
Labor Hours
Output
1
40
2
52
12
3
62
10
4
70
8
5
76
6
6
80
4
l d ( A, K )
L  4 L*  5
*
L
Hours of
Labor
w  $42
pY  $7
MPL
w $42

6
pY
$7
Altering the production values (holding the real wage fixed) allows us to shift
the labor demand curve
F ( A' , K , L)
Real
Wage
w
p
 w
   8
 p
Labor Hours
Output
1
60
2
80
20
3
96
16
4
108
12
5
116
8
6
120
4
l d ( A' , K )
L*  4
L*  5
l d ( A, K )
L
Hours of
Labor
w  $40
pY  $5
MPL
w $40

8
pY
$5
Households have utility functions that describe the relationship between
choices and happiness
U  U (C ,1  L)
Labor Hours
Utility
Time Endowment
Consumption
We only have a couple requirements for utility functions
•Utility is increasing in consumption (i.e. we like to buy things!)
•Utility is decreasing in labor (we don’t like to work)
•Utility exhibits diminishing marginal utility (the more we have of
anything, the less it is worth to us at the margin)
Indifference curves show various combinations of consumption and
leisure that provide the same level of utility
More is always better!
U (C )  U ( A)
C
C
A
U (C ,1  L)  25
B
U (C ,1  L)  20
1 L
The marginal rate of substitution (MRS) measures the amount of consumption
you are willing to give up in order to acquire a little more leisure
How much consumption do you require to
give up one hour of leisure (i.e. work an
extra hour)?
C
c
*
C
 (1  L)
1 L
*
MRS 
MU L
MU c
U (C ,1  L)  20
1 L
Given the assumption of diminishing marginal utility, MRS varies
predictably as consumption/leisure changes
If you have a lot of
consumption relative to
leisure, then leisure is
much more valuable than
consumption - MRS is
high!
c
If you have a lot of leisure
relative to consumption,
then leisure is much less
valuable than
consumption - MRS is
low!
MRS = 12
C
*
MRS = 2
U (C ,1  L)  20
C'
1  L*
1  L'
1 L
Households take wages and prices as given. Further, house possess some
non-labor income (i.e. asset income). Households maximize utility subject
to an income constraint.
max U (C ,1  L)
c 0, L 0
subject to
pC  wL  NLI
Note that the choice for labor will determine the level of consumption
possible.
max U (C ,1  L)
L 0
wL  NLI
where C 
p
Suppose that the hourly wage is $10 and that consumption goods cost
$2. Further, you have $20 of non-labor income. Assume you have 1
hour of time available.
C
L = 1: you work
as much as you
can
15
w
slope  5 
p
10
0
1
1 L
L = 0: You don’t work at all
Recall that maximizing anything requires equating costs and benefits at the
margin
C
MU C
 MU L
L
How much is
an extra unit of
consumption
worth to you?
How much
extra
consumption
will an extra
hour of work
buy you? (i.e.
the real wage)
How unhappy
does working
an extra hour
make you??
A little rearranging….
w MU L

 MRS
p MU C
At the optimum choice for labor, the slope of the indifference curve is
equal to the slope of the budget constraint.
Consumption
C
w
p
w
 MRS
p
15
Real Wage
l s ( NLI  20)
C  13
w
5
p
10
0
1  L  .4
1
1 L
L
L  .6
Hours of
Leisure
Hours of
Labor
Suppose the wage rate rises to $16 (non-labor income is still $20 and the
price level is still $2). Does labor supply increase of decrease?
c
Substitution Effect: As the real
wage increases, the price of
leisure has increased relative to
consumption – buy more
consumption, less leisure.
18
C  16.4
w
p
Income Effect: As the real wage
increases, your purchasing
power goes up. Buy more of
both goods (consumption and w
leisure)
p
C  13.2
C  13
Real Wage
Income
Effect:
Substitution
Effect:
8
w
5
p
10
0
1 L
.2
.4 .8
L  .2
Hours of
Leisure
L  .6
L
L  .8
Hours of
Labor
We typically assume that the substitution effect is dominant…a rise in the real
wage increases hours of labor supplied.
c
18
w
p
Real Wage
C  16.4
l s ( NLI  20)
w
8
p
w
5
p
C  13
10
0
1 L
.2
.4
L  .6
Hours of
Leisure
L
L  .8
Hours of
Labor
Suppose that the hourly wage is still $10 and that consumption goods cost $2.
However, Non-labor income increases to $40.
C
25
w
p
l s ( NLI  40)
Real Wage
l s ( NLI  20)
C  22
15
w
5
p
C  13
10
0
.4
.6
1 L
L  .4
Hours of
Leisure
L
L  .6
Hours of
Labor
An equilibrium in the labor market is defined as a real wage where
labor supply equals labor demand (i.e. the labor market clears)
w
p
l s (NLI )
 w
 
 p
Note: This
equilibrium assumes
fixed values for
productivity (A),
capital (K) and nonlabor income (NLI)
*
l d ( A, K )
L
L*
Note that once employment is known (capital is taken as fixed in the
short run), output can be determined
1
Labor Markets
2

l s  l d  L*
w
p
 w
 
 p
Production Function
Y  F A, K , L*

Y
l s (NLI )
F ( A, K , L)
Y*
*
l d ( A, K )
*
L
L
L*
L
We need to make assumptions about the evolution of productivity. Let’s
suppose that productivity evolves according to an autoregressive process
At 1   At   t
Persistence parameter
At
Productivity shock
At
   1
At  0    1
At    0
L
Suppose that the economy is hit by a positive productivity shock that is
perceived to be temporary
   0
For a given level of employment and
capital, production increases
y
w
p
l s (NLI )
F ( A, K , L)
Y*
Rise in
productivity
 w
 
 p
*
l d ( A, K )
*
L
L
*
L
L
Suppose that the economy is hit by a positive productivity shock that is
perceived to be temporary
   0
With a rise in productivity, at the
initial real wage, demand for labor
rises
w
p
Y
l s (NLI )
F ( A, K , L)
Y*
 w
 
 p
Non-Labor
income is
(relatively)
unaffected
*
Rise in
productivity
l d ( A, K )
*
L
L
*
L
L
Suppose that the economy is hit by a positive productivity shock that is
perceived to be temporary
   0
Non-Labor
income is
(relatively)
unaffected
w
p
Y
l s (NLI )
F ( A, K , L)
Y*
 w
 
 p
*
Rise in
productivity
l d ( A, K )
*
L
L
*
L
The rise in labor demand increases employment and real wages
L
An increase in productivity that is permanent will have a larger effect
on non-labor income, and create a decrease in labor supply
   1
Non-Labor
income
increases
w
p
Y
l s (NLI )
F ( A, K , L)
Y*
 w
 
 p
*
Rise in
productivity
l d ( A, K )
*
L
L
*
L
The drop in labor supply creates a larger increase in the real wage
and a smaller effect on output and employment
L
Labor Markets and the business cycle
Given the mechanics of the labor market,
what relationships would we expect to see
between productivity, wages, employment,
and output?
Just the facts ma’am.
Correlation
Employment
Output
+ or -
Wages
+
Productivity
+
GDP vs. Employment (% Deviation from trend)
6
Correlation = .84
4
2
0
1980
1982
1984
1986
1988
1990
1992
1994
-2
-4
-6
-8
Output
Employment
1996
1998
2000
GDP vs. Productivity (% Deviation from trend)
6
Correlation = .66
4
2
0
1980
1982
1984
1986
1988
1990
1992
-2
-4
-6
-8
Output
MFP
1994
1996
1998
2000
GDP vs. Real Wages (% Deviation from trend)
6
Correlation = .18
4
2
0
1980
1982
1984
1986
1988
1990
1992
-2
-4
-6
-8
Output
Wages
1994
1996
1998
2000
The low correlation between real wages and GDP suggests that labor supply
is very elastic
w
p
l s (NLI )
l d ( A, K )
L
Random labor productivity fluctuations cause large employment movements, but
very little change in the real wage
Example: Oil Price Shocks in the 1970’s
Dollars per Barrel
1979 Iranian
Revolution
(Temporary Shock)
1973 Arab Oil
Embargo
(Permanent Shock)
This dramatic rise in oil prices can be thought of as a negative productivity
shock. Remember, we are measuring GDP by value added. When energy
costs go up, value added goes down
w
p
Y
l s (NLI )
F ( A, K , L)
Y*
 w
 
 p
*
l d ( A, K )
*
L
L
L*
L
This temporary drop in labor productivity caused a decrease in labor demand
A temporary shock creates a small income effect and, therefore, no change in
labor supply. If the shock were more permanent, a rise in labor supply would push
the real wage even lower
Real Compensation (1972 – 1982)
w
p
Ls
w
p
LD
Ls
L
% Deviation From Trend
LD
1979 Iranian
Revolution
1973 Arab Oil
Embargo
L
Employment
(1972 – 1982)
w
p
w
p
s
L
LD
L
% Deviation From Trend
LD
1973 Arab Oil
Embargo
Ls
1979 Iranian
Revolution
L
Y
Y
L
% Deviation From Trend
L
1979 Iranian
Revolution
1973 Arab Oil
Embargo
GDP (1972 – 1982)