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