1. Topics in Labor Supply
Chapter 3

2. Extensions of Static Model
Labor supply over the lifecycle
Fertility
Household production
Retirement
Policy: Decline in work attachment among older workers

3. 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

4. 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)

5. 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

6. LFPR over the Lifecycle
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)
changes over the lifecycle (# children, etc), so LFP varies over the lifecycle

7. Empirical Evidence Should show ↑ LFPR and ↑ H* when wages are high LFP
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)

8. 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,

9. Comparative Statics Suppose I↑, ceteris paribus
If children are a normal good, N*

10. Comparative Statics Suppose pN↑, ceteris paribus Income Effect: _ to _
Substitution Effect: _ to _
Income and substitution effects ____________

11. 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?:

12. Household Production Model Evidence
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

13. 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

14. Household Production, cont.
OC of $1 of HH goods = slope = = $ of market good production
OC of $1 of HH goods = slope = = $ of market good production
Tim has a comparative advantage in __________________, and Jane has a comparative advantage in _____________________

15. Household Production, cont.
Joint PPF
Case 1: Jane and Tim both work in the labor market
Case 2: Jane and Tim both work at home
Case 3: Specialize
Jane: $210
Total: $
Tim: $252
Jane: $225
Total: $
Tim: $360
Jane: $210 in labor mkt
Tim: $360 in HH prod.

16. 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) 

17. 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

18. 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.

19. 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

20. 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

21. Retirement Decision
Assume someone who lives to age 80 decides to retire sometime between age 60 and age 80
Vt =

22. 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

23. Comparative Statics Suppose benefits↑, wage constant
If years of retirement = 0,
Income effect:
Substitution effect:
 Years of retirement __crease

24. 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 month

25. Shortcomings of Model Model does not
In US, changed from age 65 to 70 in 1978
Abolished in 1986
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

26. 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

27. 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

28. Policy Application: Labor Supply Response to Child Care Subsidies
Example 2, cont.: Reduce fixed costs (assume no variable cost)
Equivalent to an increase in non-labor income (V)
Workers
Summary: Subsidies should __crease LFPR and __________ _____________effect on H*
Empirical evidence supports LFP prediction, especially among low income workers

29. 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 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

30. 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

31. Policy Application: Decline in Work Attachment Among Older Workers
How does the SS Earnings Test affect H*?
Worker A:
Worker B:
Worker C:

32. 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)