labor markets fin 30220: macroeconomic analysis of the 317 million people that make up the us...
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Labor Markets
FIN 30220: Macroeconomic Analysis
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.
US Population 320
Million
Non-Eligible Population
71 Million
Eligible Civilian Population
249 Million
Under 16
On Active Military Duty
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
Not In Labor Force 92 Million
Employed 148 Million
Unemployed 9 Million
Unemployment Rate (UR)
9M157M
= 5.7%=
Participation Rate (PR)
157M249M
= 63%=
Employment Rate (ER)
148M249M
= 59%=
ERUR = 1 -
PR
Source: Household Survey
0
1
2
3
4
5
6
7
8
9
1990 1993 1996 2000 2003
“Natural Rate”
Cyclical Unemployment
The Natural Rate, or NAIRU (Non Accelerating Inflation Rate of Unemployment) refers to what’s “normal” in the labor market.
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.
0%
5%
1.5%
Structural Unemployment: Workers whose skills are no longer needed due to industry evolution. These people generally require retraining
Frictional Unemployment: Workers in the process of finding a job
A better measure of the labor market is simply the total number of people working
0
20000
40000
60000
80000
100000
120000
140000
160000
1980 1984 1988 1992 1996 2000 2004
-600
-400
-200
0
200
400
600
800
1000
1200
Recession Recession Recession
To
tal
Ch
ang
e Fro
m P
reviou
s Mo
nth
What’s a “good” employment number?
US Population 300
MillionOur population growth rate averages around 1% per year
250,000 per month
Labor Market
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
-400
-300
-200
-100
0
100
200
300
400
500
600
2000 2001 2002 2003 2004 2005
0
1
2
3
4
5
6
7
Unemployment Rate
Un
emp
loym
ent R
ateC
han
ge
in E
mp
loym
ent
January February JulyMarch April May June
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.
10 10 10 10 10 10
10 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.
A
B
Suppose that we have the following data.
January February March April May June
24 Weeks3 Million
12 Weeks
8 Weeks 2.5 Million
3.5 Million
Labor Force = 200M
12 Weeks
8 Weeks 8 Weeks
Unemployment Rate = 17.5 Million9M
200M= 4.5%
3.5 Million
2.5 Million2.5 Million 7.5 Million
7 Million
3 Million
+
Average Duration = 3M
17.5M7M
17.5M7.5M
17.5M24 12 8+ + = 12.3 weeks
Length of unemployment spells in the US
Mean = 39 weeks
Median = 22 weeks
However, average and median duration has been rising!
Production Functions measure the relationship between inputs and output
),,( LKAFY Labor
Capital (Fixed in Short Run)Output
Productivity (Exogenous)
Typically the production function used is Cobb-Douglas
3
2
3
1
LAKY
Labor’s Share of Income
Capital’s Share of Income
Y
LAs labor increases (given a fixed capital stock), labor productivity declines!!
),,( LKAFThe Marginal Product of Labor (MPL) measures the change in production associated with a small change in employment
L 'L
1 1
10
2MPL=2
MPL=10
Production in the short run – capital is fixed
L
YMPL
Y
L
We also assume that the marginal product of labor is positively related to increases in either productivity and capital
),,( LKAF
L 'L
Production in the short run – capital is fixed
MPL=14
MPL=2
MPL=10
MPL=4
),,'( LKAF
),',( LKAFor
L
YMPL
AA
KK
'
'
KpwLYp kY
We assume that firms are perfectly competitive. They choose labor hours to maximize profits
Total Output
Price of Output
Labor Costs
Capital Costs (Fixed in Short Run)
Wage Rate
Price of Capital
),,( LKAFY
wMPLpY
The best choice for labor can be found by taking looking at changes in both revenues and costs at the margin.
A little rearranging gives us the following condition
Yp
wMPL
Real Wage
Qualitatively, this tells us we would expect to see a strong positive correlation between productivity and wages
Labor Hours Output MPL
1 40
2 52 12
3 62 10
4 70 8
5 76 6
6 80 4
),,( LKAFExample:
5$
40$
Yp
w 85$
40$
Yp
w
For the production function given above, at a real wage of 8, 4 hours of labor are hired
Labor demand records the hiring decision (# of hours) chosen by the firm at every real wage
L
p
w
8
p
w
4L
Labor Hours Output MPL
1 40
2 52 12
3 62 10
4 70 8
5 76 6
6 80 4
),,( LKAF
5$
40$
Yp
w 85$
40$
Yp
w
Hours of Labor
Real Wage
Altering the real wage (holding production values fixed) allows us to trace out the labor demand curve
L
p
w
8
p
w
4* L
Labor Hours Output MPL
1 40
2 52 12
3 62 10
4 70 8
5 76 6
6 80 4
),,( LKAF
7$
42$
Yp
w 67$
42$
Yp
w
Hours of Labor
Real Wage
5* L
6
p
w
),( KAl d
Altering the production values (holding the real wage fixed) allows us to shift the labor demand curve
L
p
w
8
p
w
4* L
Labor Hours Output MPL
1 60
2 80 20
3 96 16
4 108 12
5 116 8
6 120 4
),,'( LKAF
Hours of Labor
Real Wage
),( KAl d
5$
40$
Yp
w 85$
40$
Yp
w
5* L
),'( KAl d
Households have utility functions that describe the relationship between choices and happiness
)1,( LCUU Labor Hours
Time EndowmentUtility
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)
( ,1 ) 20U C L L1
C
A
B
C
More is always better!
)()( AUCU
Indifference curves show various combinations of consumption and leisure that provide the same level of utility
( ,1 ) 25U C 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
L1
C
*c
*1 L
( ,1 ) 20U C L
How much consumption do you require to give up one hour of leisure (i.e. work an extra hour)?
C
)1( L
L
c
MUMRS
MU
L1
c
*C
*1 L
20)1,( LCU'C
'1 L
If you have a lot of leisure relative to consumption, then leisure is much less valuable than consumption - MRS is low!
Given the assumption of diminishing marginal utility, MRS varies predictably as consumption/leisure changes
MRS = 12
MRS = 2
If you have a lot of consumption relative to leisure, then leisure is much more valuable than consumption - MRS is high!
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.
)1,(max0,0
NLI wL pCtosubject
LCULc
Note that the choice for labor will determine the level of consumption possible.
)1,(max0
p
NLIwLC where
LCUL
L1
C
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.
L = 0: You don’t work at all
10
L = 1: you work as much as you can
10
15
p
wslope 5
Recall that maximizing anything requires equating costs and benefits at the margin
LC MUL
CMU
A little rearranging….
MRSMU
MU
p
w
C
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??
L1
C
At the optimum choice for labor, the slope of the indifference curve is equal to the slope of the budget constraint.
10
10
15MRS
p
w
13C
L
Consumption
Hours of Labor
Hours of Leisure
p
wReal Wage
4.1 L
5p
w
6.L
)20( NLIl s
c
10
0 4.
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?
18
LHours of Labor
p
wReal Wage
5p
w
6.LL1
Hours of Leisure
8p
w
2.
13C
8.L
4.16C
Substitution Effect: As the real wage increases, the price of leisure has increased relative to consumption – buy more consumption, less leisure.
Income Effect: As the real wage increases, your purchasing power goes up. Buy more of both goods (consumption and leisure)
2.L8.
2.13C
Income Effect:
Substitution Effect:
c
10
0 4.
We typically assume that the substitution effect is dominant…a rise in the real wage increases hours of labor supplied.
18
LHours of Labor
p
wReal Wage
5p
w
6.LL1
Hours of Leisure
8p
w
2.
13C
8.L
4.16C )20( NLIl s
C
10
0 4.
Suppose that the hourly wage is still $10 and that consumption goods cost $2. However, Non-labor income increases to $40.
15
25
LHours of Labor
p
wReal Wage
5p
w
6.LHours of Leisure
4.LL1
)20( NLIl s
)40( NLIl s
6.
13C
22C
L
p
w
)(NLIl s
*
p
w
*L
),( KAl d
An equilibrium in the labor market is defined as a real wage where labor supply equals labor demand (i.e. the labor market clears)
Note: This equilibrium assumes fixed values for productivity (A), capital (K) and non-labor income (NLI)
Y
L
),,( LKAF
*LL
p
w
)(NLIl s
*
p
w
*L
),( KAl d
*Y
Note that once employment is known (capital is taken as fixed in the short run), output can be determined
1 Labor Markets
*Lll ds
2 Production Function
*,, LKAFY
L
tA
We need to make assumptions about the evolution of productivity. Let’s suppose that productivity evolves according to an autoregressive process
1t t tA A Productivity shock
Persistence parameter
0tA
1tA
0 1tA
y
L
),,( LKAF
*L
*Y
Suppose that the economy is hit by a positive productivity shock that is perceived to be temporary
L
p
w
)(NLIl s
*
p
w
*L
),( KAl d
Rise in productivity
For a given level of employment and capital, production increases
0
Y
L
),,( LKAF
*L
*Y
Suppose that the economy is hit by a positive productivity shock that is perceived to be temporary
L
p
w
)(NLIl s
*
p
w
*L
),( KAl d
Rise in productivity
With a rise in productivity, at the initial real wage, demand for labor rises
Non-Labor income is (relatively) unaffected
0
Y
L
),,( LKAF
*L
*Y
Suppose that the economy is hit by a positive productivity shock that is perceived to be temporary
L
p
w
)(NLIl s
*
p
w
*L
),( KAl d
Rise in productivity
Non-Labor income is (relatively) unaffected
The rise in labor demand increases employment and real wages
0
An increase in productivity that is permanent will have a larger effect on non-labor income, and create a decrease in labor supply
Y
L
),,( LKAF
*L
*Y
L
p
w
)(NLIl s
*
p
w
*L
),( KAl d
Rise in productivity
Non-Labor income increases
The drop in labor supply creates a larger increase in the real wage and a smaller effect on output and employment
1
Just the facts ma’am.
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?
Correlation Output
Employment + or -
Wages +
Productivity +
-8
-6
-4
-2
0
2
4
6
1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000
Output Employment
GDP vs. Employment (% Deviation from trend)
Correlation = .84
-8
-6
-4
-2
0
2
4
6
1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000
Output MFP
GDP vs. Productivity (% Deviation from trend)
Correlation = .66
-8
-6
-4
-2
0
2
4
6
1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000
Output Wages
GDP vs. Real Wages (% Deviation from trend)
Correlation = .18
L
p
w
)(NLIl s
),( KAl d
The low correlation between real wages and GDP suggests that labor supply is very elastic
Random labor productivity fluctuations cause large employment movements, but very little change in the real wage
Example: Oil Price Shocks in the 1970’s
Dol
lars
per
Bar
rel
1973 Arab Oil Embargo(Permanent Shock)
1979 Iranian Revolution(Temporary Shock)
This temporary drop in labor productivity caused a decrease in labor demandA 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
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
Y
L
),,( LKAF
*L
*Y
L
p
w
)(NLIl s
*
p
w
*L
),( KAl d
% D
evia
tion
Fro
m T
rend
Real Compensation (1972 – 1982)
1973 Arab Oil Embargo
1979 Iranian Revolution
w
p
L
sL
DL
w
p
L
sL
DL
% D
evia
tion
Fro
m T
rend
Employment (1972 – 1982)
1973 Arab Oil Embargo
1979 Iranian Revolution
w
p
L
sL
DL
w
p
L
sL
DL
% D
evia
tion
Fro
m T
rend
GDP (1972 – 1982)
1973 Arab Oil Embargo
1979 Iranian Revolution
Y
L
Y
L
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