Labor Supply (Static) Chapter 2

Labor Supply Why has the LFPR of men declined? Why has the LFPR of women increased? Why has the length of the workweek decreased? How will changes in the welfare system affect job mobility and/or unemployment spells? Does a change in family structure affect LFP decisions?

Measuring the Labor Force Bureau of Labor Statistics (BLS) Conducts the Current Population Survey (CPS) which surveys 60,000 households monthly Workers are considered: Employed: Unemployed: Out of the Labor Force:

Labor Force Statistics Labor Force Participation Rate = Employment-Population Ratio = Unemployment Rate (UR) =

“Hidden Unemployed” Note that “employment” is not different for full- and part-time workers, so part time workers who want full-time employment are not differentiated. People who give up searching are considered out of the labor force. Using the employment-population ratio would have flaws as well, since unemployed and out of the labor force would be grouped together. May under-state UR

Labor Supply Trends (up to 1990s) Male LFPR declined Decline in labor market attachment after age 65 10% decline between ages 45 and 64 Decline in LFPR from 46% to 17% men over 65 Decline in LFRP from 97% to 93% for ages 25-44 Female LFPR increased, particularly among married women Hours per week declined Men (4%) less likely than women (16%) to be employed PT Positive correlation between educational attainment and LFP Racial Differences White men have higher LFPR than black men. White men work more hours than black men.

Worker Preferences Workers choose: Goal: U = f (C , L)

Indifference Curves Do not intersect Unique All points along an indifference curve represent the same utility level Higher indifference curves represent higher levels of utility

Indifference Curves, cont. Downward-sloping Convex to the origin -

Indifference Curves, cont. Slope = Move from (L1,C1) to (L2,C2) Gain + Loss = 0 to maintain Utility = U

Differences in Tastes Large slope = Large MRS MUL large relative to MUC Individual enjoys _______ (willing to sacrifice a large amount of consumption for leisure) Small slope = Small MRS MUL small relative to MUC Individual enjoys _______ (willing to sacrifice a large amount of leisure for consumption)

Budget Constraint Assumptions: No saving → where V = non-labor income (endowment) w = wage H = hours worked Constant wages (no overtime)

Budget Constraint, cont. Solve for slope of BC: C = V + wH = where T = total time available for work and leisure → slope = Interpretation:

Budget Constraint, cont. Properties: Consumption bundles below the budget line are Consumption bundles outside the budget line are Consumption bundles along the budget line

Hours of Work Decision Choose C* and L* such that utility is maximized, subject to BC U(C) _ U(A) and U(C) _ U(B), and U3 _______________ Interior solution (H* > 0)

Hours of Work Decision, cont. Tangency (between IC and BL) conditions: Slope of indifference curve = Slope of budget line =

Comparative Statics Comparative Statics: How does individual behavior change when a parameter of the model changes? Suppose V increases, holding w constant Suppose w increases, holding V constant

Comparative Statics, cont. Suppose V increases, ceteris paribus Individuals have more money to spend on C (C*↑) Income effect: If leisure is a normal good, the demand for leisure will __crease (L* ) and the number of hours worked will __crease (H* )

Comparative Statics, cont. Suppose w increases, ceteris paribus Substitution effect: Since the wage rate is the OC of leisure, an increase in w increases the OC of leisure, and workers substitute ______ for __________ (L* & H* ) Income effect: An increase in w is an increase in wealth, which will _________ the demand for leisure (L* & H* )

Income and Substitution Effects Suppose V increases  Budget line _______ up Case 1: Both C* and L* __crease, so leisure must be a ________ good

Income and Substitution Effects Suppose V increases  Budget line _______ up Case 2: C* __creases and L* __creases, so leisure must be an _________ good

Income and Substitution Effects Case 1: L* __creases, so the ____________ effect dominates Suppose w increases  Budget line ________ up

Income and Substitution Effects Case 2: L* __creases, so the __________ effect dominates Suppose w increases  Budget line _______ up

Isolating the Income and Substitution Effects Suppose w increases  Budget line rotates up To isolate the income effect, draw a hypothetical budget line with same slope as old budget line and tangent to new indifference curve Income Effect: _ to _ Substitution Effect: _ to _ _________ Effect dominates H*↑ when w↑

Isolating the Income and Substitution Effects Suppose w increases  Budget line rotates up To isolate the income effect, draw a hypothetical budget line with same slope as old budget line and tangent to new indifference curve Income Effect: _ to _ Substitution Effect: _ to _ ________ Effect dominates H* when w

Decision to Work (H*>0 or H*=0) Can obtain U0 if H*=0 Trade leisure for consumption by entering labor market? If w = wlow, U* _ U0 (cannot reach a higher IC)  H* _ 0 If w = whigh, UH _ U0 (higher IC)  H* _ 0

Reservation Wage Individuals with high wage offers choose to work (H*>0); individuals with low wage offers do not work (H*=0) There exists a wage at which the individual is indifferent between H*=0 and H*>0, the reservation wage

Reservation Wage Characteristics When w < , do not work When w > , work High  less likely to enter labor market depends upon tastes for work (slope of the indifference curve) ↑ as V↑ (when V↑, L*↑, so the wage required to induce labor market participation increases) For a given , a high wage offer increases the probability of working (↑ LFPR when w↑) There is a positive relationship between wages and the probability of working (the higher the wage, the more likely it is to exceed the reservation wage) – no income effect for non-workers, so there are not competing income and substitution effects when considering how many hours to work

Individual Labor Supply Curve Recall: Work if reservation wage < wage offer; otherwise H*=0 Work more when wage ↑ if substitution effect dominates Substitution effect always dominates (income effect DNE) for non-workers  LFPR ↑ when wage ↑ Work less when wage ↓ if income effect dominates (only true for workers)

Market Labor Supply Curve Workers have unique preferences, reservation wages, indifference curves, and thus optimal hours of work decisions Market supply curve =

Elasticity of Labor Supply How responsive is labor supply to changes in wages? Interpretation: Elastic (______ responsive) when |σ|_ 1 Inelastic (______ responsive) when |σ|_ 1

Elasticity of Labor Supply: Example H1 = 2000 W1 = $15 H2 = 2200 W2 = $17.50 Suppose: Interpretation: ___________ labor supply Note: Since hours worked increased with wages, the ____________ effect dominates

Elasticity of Labor Supply Estimates Prime-Age Men: α ≈ -0.1  (1% increase due to substitution effect, and 2% decrease due to income effect) May explain decline in the length of the workweek (men now earn more in real terms, so more leisure is demanded) Elasticity estimate not significantly different from zero (most prime-age men work full-time, full-week jobs) Different estimate for younger and older men, as well as women Much variation in empirical estimates

Elasticity of Labor Supply Estimates Problems with estimates Hours of work Per year? Per month? Per week? (α ≈ -0.1calculated using hours of work per year) Hours of work likely more inelastic for shorter time periods Measurement error, especially for salaried workers Wages For salaried workers, wage definition likely measured with error Wages should measure price of leisure as the marginal wage for an additional hour of work, which is not likely average wage (may include overtime, etc.)

Elasticity of Labor Supply Estimates Problems with estimates, cont. Wages, cont. Nonworkers? Wage ≠ 0, but no reported wage (only know wage offer < reservation wage); these workers have low wage offers or high reservation wages, and are not a “random sample” of the population Non-labor income Workers with much non-labor income probably earned a lot in the past and saved earnings (which are now wealth)  If these workers continue to work a lot now, there will be a positive relationship between V and H (suggests leisure is inferior). When tastes for work are accounted for, evidence of a negative income effect is found.

Female Labor Supply Different LFPRs across countries (for ages 25-54) Italy: 50%; US: 75%; Sweden: 90% Elasticity of Labor Supply α ≈ 0.2 after correcting for the decision to work (substitution effect dominates) Women more responsive (in terms of LFP) to changes in wages than men, less responsive in terms of H* Responsiveness to husband’s wages LFP elasticity with respect to whusband = 0.53 H* elasticity with respect to whusband = 0.17

Female Labor Force Participation LFPR↑ considerably since 1960 As a cohort ages, LFPR↑ As time has passed, LFPR↑ Why? Theory: The increase in real wages over time (between 2.1% per year and 6.2% per year) has ___________ the probability of working (wages more likely to exceed reservation wage)  The increase in LFPR may be due to _________________________ _____________________________________ (Because of ↓ fertility? Or has the number of children ↓ because women now work more?)

Policy Application: Welfare AFDC, TANF, etc. Personal Responsibility and Work Opportunity Reconciliation Act Take-it-or-leave-it offer Assume V = 0 w/o benefits Lump sum benefits = 0 if individual works L1 _ L2 _ T – leave labor force with benefits Why?:

Policy Application: Welfare Cash Grants Assume V = 0 w/o benefits Full benefits if individual does not work  endowment ↑ For workers, cash grant is reduced for each dollar earned working  BL flatter Net wage < actual wage  OC of leisure ↓ so L*_ Note:

Policy Application Summary: Welfare Welfare programs __crease LFPR (an increase in non-labor income increases a worker’s reservation wage) and __crease the demand for leisure (a decrease in net wages is a decrease in the OC of leisure) Empirical evidence Negative income tax experiment: Cash grants were 95% or 140% of the poverty line, and the tax rate on labor earnings was 50% or 70%) Prob(work)↓ by 3% for husbands and 7% for wives H*↓ by 5% for men, 21% for women

Policy Application: Earned Income Tax Credit (EITC) Began in 1975 By 1990s, $25 billion distributed to low income families Dependent upon income, number and ages of children Program Up to Max Y ($8890), credit = 40% of earnings (net wage = 1.4w, up to $3556 Between $8890 and $11,160, receive max credit ($3556) For earnings in excess of $11,160, benefits are reduced by 21.06¢ per dollar earned

Policy Application: Earned Income Tax Credit (EITC) Effects of EITC on labor supply Case 1: Income < $8890 Steep indifference curve  strong preference for ______ Choose H* _ 0 w/o benefits EITC induces Recall: income effect does not exist for non-workers, so LFPR must _ when w_

Policy Application: Earned Income Tax Credit (EITC) Effects of EITC on labor supply Case 2: $8890 < Income < $11,160 Choose H* _ 0 w/o benefits EITC induces

Policy Application: Earned Income Tax Credit (EITC) Effects of EITC on labor supply Case 3: Income > $11,160 Choose H* _ 0 (many hours) w/o benefits EITC induces _________ effect likely dominant for those who work many hours

Policy Application Summary EITC __creases LFPR for non-workers (only a substitution effect exists) and __creases hours worked (either because of a pure income effect or because the individual is already working many hours) Evidence: 2.4% increase in LFPR Cash grants _______ work incentives (LFPR ), but EITC subsidizes work and __creases work incentives (LFPR )