Chapter 3

Topics in Labor Supply

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Extensions of Static Model

Labor supply over the lifecycleFertilityHousehold productionRetirementPolicy: Decline in work attachment among older workers

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Labor Supply over the Lifecycle

Workers can “save” earnings when H* is high and enjoy more C and L later in lifeAge-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

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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 ∆wOC of leisure), but does not increase lifetime income (lifetime opportunity set)

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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 workerComparing 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

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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

w~

w~

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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 declinedModel: 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 = incomeAt 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 ____________

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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?:

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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

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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

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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 _____________________

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Household Production, cont.

Jane: $210Total: $

Tim: $252

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: $225Total: $

Tim: $360

Jane: $210 in labor mkt

Tim: $360 in HH prod.

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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)

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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

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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.

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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

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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

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Retirement Decision

Assume someone who lives to age 80 decides to retire sometime between age 60 and age 80Vt =

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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

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Comparative Statics

Suppose benefits↑, wage constant If years of retirement = 0,

Income effect:

Substitution effect:

Years of retirement __crease

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Retirement Empirical Evidence

LFPR of older men (ages 55-64) decreased between 13 and 35 percentage points between 1960 and 1996Theory: 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

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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 credits40% of American families utilize day care totaling, on average, 7% of incomeExample 1: Reduce hourly cost of day care (assume no fixed cost component)

H* will

dominateseffect _________ ifdecrease

dominateseffect _________ ifincrease

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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

non-labor income (V)

Workers

Summary: Subsidies should __crease LFPR and __________ _____________effect on H*

Empirical evidence supports LFP prediction, especially among low income workers

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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

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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

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Policy Application: Decline in Work Attachment Among Older Workers

How does the SS Earnings Test affect H*? Worker A:

Worker B:

Worker C:

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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)