Topics in Labor Supply
Chapter 3
Extensions of Static Model
Labor supply over the lifecycle
Fertility
Household production
Retirement
Policy: Decline in work attachment among older
workers
2
Labor Supply over the Lifecycle
Workers can “save” earnings
when H* is high and enjoy
more C and L later in life
Age-earnings profile
OC of leisure _____ when
young and old
 OC of leisure _____ during
“prime” working years
 “Inverse U”

Note: Workers anticipate evolution of wages, so high
wages during prime years do not increase lifetime
income
3
Labor Supply over the Lifecycle
Given age-earnings profile,
younger and older workers
enjoy leisure more than prime
age workers

H* and w
In the lifecycle model, an
increase in w is expected
(evolutionary ∆wOC of
leisure), but does not increase
lifetime income (lifetime
opportunity set)
4
Labor Supply over the Lifecycle
Recall: In the lifecycle model, an increase in w is expected
and only induces a substitution effect for a particular worker
Comparing the level of two wage profiles generates an
income effect


Jeff ’s hours profile = Jeff if substitution effect dominates
Jeff ’s hours profile = Jeff if income effect dominates
5
LFPR over the Lifecycle
w,
Reservation wage: in years when w > ~
people will work

less likely for younger and older workers, so it is
as young and old ages that LFPR tends to be
lower (than at prime-age years)
~
w changes over the lifecycle (# children, etc),
so LFP varies over the lifecycle
6
Empirical Evidence
Should show ↑ LFPR and ↑ H* when wages are high

Intertemporal Substitution hypothesis:
LFP



Males: participation peaks between ages 20 and 50
Females: participation peaks during early 40s
Substantial decline after age 50 – retirement, health, disability
insurance programs, etc.
Hours worked


Males: increase to age 30, decline after age 50 (2100 annual
during prime years)
Females: peak during 40s (many PT before)
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Fertility
Evidence: as per capital
income rose, fertility rates
have declined
Model:





N = number of children (will
depend upon income and prices)
X = quantity of goods and
services
pN = price of another child
(~100K including foregone
earnings)
pX = price of consumption
goods
I = income
At tangency,
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Comparative Statics
Suppose I↑, ceteris
paribus

If children are a normal
good, N*
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Comparative Statics
Suppose pN↑, ceteris
paribus



Income Effect: _ to _
Substitution Effect: _ to _
Income and substitution
effects ____________
10
Empirical Evidence
Theory suggests the demand for children will
__crease with wages [corr(income , N*) _ 0] or
with a __crease in the cost of raising children
[corr(pN , N*) _ 0]
Strong negative correlation between mother’s wage
and the number of children (10% in wages decreases
N* by 3%)
 Weak negative correlation between N* and income
(10% increase in wages decreases N* by 0.4%)
 Why?:

11
Household Production
Model


Leisure = childrearing, cooking, cleaning, etc.
Household production yields commodities consumed in the
household such as meals  household production is an input to
these commodities
Evidence




Labor market activity – Married men: 40 hours; Single men: 33
hours
Women allocate fewer hours than men to the labor market.
Married women allocate fewer hours than single women to the
labor market.
Household production – Married women: 35 hours; Married
men: 14 hours
12
Household Production, cont.
Goal: Determine how households allocate time to
the labor market and to household production

Determined by comparative advantage:

Spouse with lower wage rate or greater household
productivity specializes in __________

Production Possibilities frontier
13
Household Production, cont.
OC of $1 of HH goods =
OC of $1 of HH goods =
slope =
= $ of
slope =
= $ of
market good production
market good production
Tim has a comparative advantage in
__________________, and Jane has a comparative
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advantage in _____________________
Household Production, cont.
Joint PPF

Case 1: Jane and Tim both
work in the labor market
Jane: $210
Total: $
Tim: $252

Case 2: Jane and Tim both
work at home
Jane: $225
Tim: $360

Total: $
Case 3: Specialize
Jane: $210 in labor mkt
Tim: $360 in HH prod.
15
Household Production Decision
Who does what?

Depends where joint PPF
and indifference curves are
tangent

A: flat indifference curve
(households enjoy market
goods, so must work outside
home) 

B: households enjoy both
goods 

C: steep indifference curve
(households enjoy goods
produced at home) 
16
Comparative Statics
Suppose Jane’s wage
increases


Her contribution to the PPF
becomes __________.
Tim’s productivity at home
remains the same ($360,
and slope does not change)
Jane will work ______ in
the market and may
eventually only work in
the labor market
17
Comparative Statics
Suppose Tim’s home
productivity increases


His contribution to the
PPF ________________.
Jane continues to earn a
maximum of $210 in the
labor market.
Tim will spend _______
time on household
production and may
eventually only work at
home.
18
HH Production Empirical Evidence
Gender differentials


Wage gap is shrinking
Improvements in household technology decrease the household
productivity differential
10% increase in wages (OC of HH production)  HH
hours decrease by 2%


When wage↑, HH production is less valuable and OC of
leisure↑  LFP ↑
Technological advances reduce HH productivity relative to labor
market productivity, so HH hours ↓ (H*↑), primarily for women
19
Retirement
Model
Assume H = 0 after retirement (no PT work)
 After retirement, individuals spend previous savings
and employer-provided and/or government-provided
pension benefits
 More can be consumed by those who work longer
since incomes usually exceed pensions



Tradeoff between leisure (longer retirement) and
consumption  budget constraint downward sloping
Determinants of retirement age:
Wage
 Pension benefits

20
Retirement Decision
Assume someone who
lives to age 80 decides to
retire sometime between
age 60 and age 80
Vt =
21
Comparative Statics
Suppose w↑, benefits constant

If worker retires when wage
increase goes into effect, the
increase

If retirement is delayed until
after wage increase,

Here, _____________ effect
dominates
22
Comparative Statics
Suppose benefits↑, wage
constant

If years of retirement = 0,

Income effect:

Substitution effect:

 Years of retirement __crease
23
Retirement Empirical Evidence
LFPR of older men (ages 55-64) decreased
between 13 and 35 percentage points between
1960 and 1996
Theory:

10% increase in wages reduces prob(retire before 65)
by 6 percentage points  ______________ effect
dominates
Higher benefits _________ retirement

10% increase in benefits reduces retirement age by 1
24
month
Shortcomings of Model
Model does not


In US, changed from age 65 to 70 in 1978
Abolished in 1986
Model does not


SS: 9% per year increase if individual retires between 62
and 65, additional 4% per year after age 65
2/3 of men retire between 62 and 65
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Policy Application: Labor Supply
Response to Child Care Subsidies
Examples: school lunches, day care subsidies, tax
credits
40% of American families utilize day care totaling,
on average, 7% of income
Example 1: Reduce hourly cost of day care (assume
no fixed cost component)

H* will
increase if _________effect dominates
decrease if _________effect dominates
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Policy Application: Labor Supply
Response to Child Care Subsidies
Example 2: Reduce fixed
costs (assume no variable
cost)

Equivalent to an increase in
non-labor income (V)
Non-workers
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Policy Application: Labor Supply
Response to Child Care Subsidies
Example 2, cont.: Reduce fixed
costs (assume no variable cost)

Equivalent to an increase in nonlabor income (V)
Workers
Summary: Subsidies should
__crease LFPR and __________
_____________effect on H*

Empirical evidence supports LFP
prediction, especially among low
income workers
28
Policy Application: Decline in Work
Attachment Among Older Workers
Why has LFPR among older workers (men) ↓?


________: Life expectancy at age 50 of white men rose from
22 to 26.7 years
___________________________: 26% covered in 1950, 66%
in 1990



Prob(men aged 58-63 with private penions work) ↓ by 18 percentage
points
______________________: rose in 1970s and remained
constant (when real wages ↓) in 1980s, but at most 15% of LFP
↓ attributable to SS
______________________: disabled worker receives SS
benefits as if he/she retired at age 65, regardless of when
disability occurred


Recipients (age 55-64) of DI increased from 3.5% to 10.5% between
1960 and 1985
Mixed evidence regarding effect of DI in LFPR
29
Policy Application: Decline in Work
Attachment Among Older Workers
Social Security Earnings
Test

Provision of SS system
which discourages
recipients (aged 65-69)
from working



Workers can earn up to
$17K without affecting
benefits
Earnings beyond $17K
taxed $1 for every $3 earned
(33% tax rate)
Workers over age 70
unaffected
30
Policy Application: Decline in Work
Attachment Among Older Workers
How does the SS
Earnings Test affect H*?

Worker A:

Worker B:

Worker C:
31
Policy Application: Decline in Work
Attachment Among Older Workers
Empirical Evidence on the effect of the
elimination of the SS Earnings Test on H*
Only individuals working a moderate number of
hours would increase the number of hours worked
(because of the substitution effect)
 20% of retirees work, and 60% of those workers
are affected by the SS earnings test
 Estimate: removing the Earnings Test would
increase H* by approximately 1 hour per week
(from 3.2 to 4.4 hours)

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