Labor supply

1
Labor supply

• Its true that hard work never killed anybody,
  but I figure, why take the chance? Ronald Reagan

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Overview of the labor force
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Stylized facts about labor supply
Source Borjas, pp. 24-25
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Stylized facts about labor supply (source
Borjas, 2007)
Proportion of women in the labor force
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Cross-Country Relationship Growth in Female
Labor Force and the Wage, 1960-1980

• Source Jacob Mincer, Intercountry Comparisons
  of Labor Force Trends and of Related
  Developments An Overview, Journal of Labor
  Economics 3 (January 1985, Part 2) S2, S6.

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Stylized facts about labor supply
Source Dora Costa (1998) usual length of a
working day
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Stylized facts about labor supply
Source Dora Costa (1998) total weekly hours
worked by husbands and wives
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Labor supply model

• Framework used to analyze labor supply behavior
  is the Neo-Classical Model of Labor-Leisure
  Choice
• Utility Function measure of satisfaction that
  individuals receive from consumption of goods and
  leisure (a kind of good)
• U f(C, L), where
• U is an index
• Higher U means happier person

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The utility function
C
U
0
U40,000
U25,000
L
10
The utility function cntnd.
CC2
U
LL2
U
CC1
LL1
C
L
Assumptions
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Indifference Curves
C
500
450
400
40,000 Utils
25,000 Utils
L
125
100
150
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Indifference curves cntnd.
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Indifference curves cntnd.
Steep and flat indifference curves
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The Budget Constraint

• C wh V
• Consumption equals labor earnings (wages hours)
  plus nonlabor income (V)
• Because of time constraint, rewrite as
• C w(T L) V
• Budget constraint sets boundaries on the workers
  opportunity set of all the consumption baskets
  the worker can afford

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The budget constraint cntnd.
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The Hours of Work Decision

• Individual will choose consumption and leisure to
  maximize utility
• Optimal (interior!) solution is given by the
  point where the budget line is tangent to the
  indifference curve
• At this point the Marginal Rate of Substitution
  between consumption and leisure equals the wage
  rate
• Any other bundle of consumption and leisure given
  the budget constraint would mean the individual
  has less utility

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In a diagram this looks as follows
C
Slopewhigh
C
C
Slope-wlow
Slope-
L
L
L
Interior solution
Corner solution
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Formally

• The optimization problem is

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The Effect of a Change in Nonlabor Income on
Hours of Work
Hours of Leisure
Leisure is a normal good
Leisure is an inferior good
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Ambiguous Relationship Hours Worked and Wage
Rates

• If the Substitution Effect is greater than the
  Income Effect, then hors of work increase when
  the wage rate rises
• If the Income Effect is greater than the
  Substitution Effect, then hours of work decreases
  when the wage rate rises.

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The effect of change in the wage rate on hours of
work

• When the Income Effect dominates

Consumption ()
G
U1
R
D
Q
U0
D
F
P
V
E
110
Hours of Leisure
85
75
0
70
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The effect of change in the wage rate on hours
worked

• When the Substitution Effect dominates

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Labor Supply Curve

• Example of backward bending labor supply

Hours of Work
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APPLICATIONS

• The impact of welfare on labor supply
• Retirement/disability/early exit from the labor
  force
• The household allocation of resources and
  fertility
• (Techniques difference-in-differences,
  endogeneity correction/instrumental variables)

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Effect of a Cash Grant on Work Incentives

• A take-it-or-leave-it cash grant of 500 per week
  moves the worker from point P to point G, and
  encourages the worker to leave the labor force.

P
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Effect of a Welfare Program on Hours of Work
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The Earned Income Tax Credit, EITC
2 child family
3888
Slope0.40
1 child family
Slope-0.2106
2353
Slope0.34
Slope-0.1598
Subsidy
Earnings
6920
9720
12690
27413
31152
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The Impact of EITC on labor supply
consumption
consumption
leisure
leisure
consumption
leisure
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Evidence
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Labor supply Response of the Earned Income Tax
Credit

• Eissa and Leibman, QJE, 1996

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Eissa and Leibman (1996) estimates

• The difference-in-difference approach
• Without regression

Treatment effect (TA - TB ) - ( CA - CB )
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Eissa and Leibman (1996) estimates

• Eissa and Leibman (1996) evidence

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Eissa and Leibman (1996) estimates

• The difference-in-difference approach
• With regression
• yi ß0 ß1 treati ß2 afteri ß3
  treatiafteri other variables ei
• where treat 1 if in treatment group, 0 if in
  control group
• after 1 if after treatment, 0 if before
  treatment
• The coefficient on the interaction term (ß3 )
  gives us the
• difference-in-differences estimate of the
  treatment effect

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Eissa and Leibman (1996) estimates
To see this, plug zeros and ones into the
regression equation yi ß0 ß1 treati
ß2 afteri ß3 treatiafteri others
ei Treatment Control
Group Group Difference
Before ß0 ß1 ß0 ß1
After ß0 ß1 ß2 ß3 ß0 ß2
ß1 ß3 Difference ß2 ß3
ß2 ß3
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Eissa and Leibman (1996) estimates

• In the Eissa and Leibman (1996) case
• Estimates 1.9-2.8

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What can explain the decreasing labor force
participation among older men?

• The decision to retire
• Social security benefits
• Disability benefits

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The retirement decision
Consumption ()
Point E gives a workers leisure-consumption
bundle if he retires at age 60. Point F gives the
leisure-consumption bundle if the worker never
retires. A utility-maximizing worker chooses
point P, and retires for 10 years.
F
V80
P
U1
U0
V60
E
20
10
0
Retirement
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Effect of an increase in the wage on the
retirement decision
An increase in the wage rotates the budget line
around point E, and generates both income effects
and substitution effects as the worker moves from
point P to point R. The figure assumes that
substitution effects dominate and the worker
delays his retirement.
Consumption ()
G
R
U1
F
P
U0
E
10
20
5
Years of Retirement
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Effect of an increase in pension benefits on
retirement decision
An increase in pension benefits rotates the
budget line around point F. It too generates
income and substitution effects, but both effects
encourage the worker to retire earlier.
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Example of retirement incentives
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The disability benefit incentive

• Alternative explanation disability benefits,
  e.g. Gruber (2000)

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Household allocation of labor
Market Work
Household Work
Personal Care
Passive Leisure
Other
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Jack and Jill unmarried opportunity sets
(b) Jills Budget Line
(a) Jacks Budget Line
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Budget Lines and Opportunity Frontier of Married
Couple
At point E, Jack and Jill allocate all their time
to the household sector. If they wish to buy
market goods, Jack gets a job because he is
relatively more productive in the labor market,
generating segment FE of the opportunity
frontier. After he uses up all his time in the
labor market, Jill then gets a job, generating
segment GF of the frontier.
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Who Works Where?
(a) (b) (c)
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Comparative statics
Result of an increase in Jacks wage
Result of an increase in Jills MPL
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Non-wage determinants of husbands and wifes
labor supply

• e.g. Angrist and Evans, AER (1996) Children and
  their parents labor supply

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Motivation

• The link between fertility and labor supply may
  at least partly explain the postwar increase in
  womens labor force participation rates if having
  fewer children causes an increase in labor
  force attachment
• Problem It is difficult to say what causes what

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The omitted variables problem

• Suppose that the true model is
• But we run
• Then
• And the OLS estimator will be biased

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Solution the instrumental variable approach
(e.g. Angrist and Evans, 1998)
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Angrist and Evans (1998) results