: Implications for the Estimation of the Labor Supply Elasticity Maria Casanova UCLA UCL - PhD Alumni Conference 07/05/2012
FigureWage 1b. andexperience earnings Earning Profiles at Older Ages profiles, 1970 19 Motivation Figure: From Heckman, Lochner and Todd (2006)
Introduction Correctly specifying the shape of the age-wage profile is important in a variety of contexts: Estimation of labor supply elasticities. Measurement of income uncertainty. Understanding of drivers of retirement decisions. Assessment of different theories of wage determination.
Introduction In this paper I show that: 1 The age-wage path is flat for older workers who remain employed full-time and drops discretely at the point of transition from full-time into part-time work. 2 The smoothly-declining profile often found in the literature is a result of aggregation over workers who transit into partial retirement at different ages. 3 Transitions out of full-time jobs are not driven by self-selection on unobservables. 4 Transitions out of full-time jobs are voluntary for a majority of workers. 5 Modeling labor supply at older ages as a response to an exogenously declining wage process leads to severely biased estimates of preference parameters.
Data Health and Retirement Study Sample: Panel dataset of adults over 50 year of age and their spouses. Data collected every 2 years. Self-reported information on wages and hours. Extensive information on demographics, health and pensions. Use 9 waves from 1992 to 2008. Individuals born between 1931 and 1941. Males who are working full-time and not self-employed in the first sample year.
Partial Retirement Wage declines at older ages may be partly explained by transitions into partial retirement: Gustman and Steinmeier (1985), Johnson and Neumark (1996), Aaronson and French (2004), Rupert and Zanella (2009). Transitional period is characterized by: Part-time, bridge jobs Change of industry/occupation Low attachment to the labor force. Approximately 30% of workers partially retire before fully withdrawing from the labor force.
Partial Retirement Figure: Total/FT/PT participation rates by age. 1990 Census. 1 0.9 0.8 0.7 0.6 05 0.5 0.4 0.3 0.2 0.1 0 25 30 35 40 45 50 55 60 65 70 75 80 total FT PT
Partial Retirement Figure: Total/FT/PT participation rates by age. HRS. 1 0.8 0.6 0.4 0.2 0 50 52 54 56 58 60 62 64 66 68 70 FT baseline PT baseline R baseline
Partial Retirement Definition of partial retirement Full time work is defined as working more than 35 hours per week. An individual becomes partially retired when: he is first observed working part-time; or he first becomes self-employed Partial-retirement is an absorbing state. Alternative definitions: ignore self-employed workers change the cutoff to define part-time work use tenure changes
Parameters of Interest Log-wage profile: w it = θ w I {PR = 1} + W (Age it ) + X it β w + u it Log-hours profile: h it = θ h I {PR = 1} + H(Age it ) + X it β h + v it
Hourly Wage Profile Table: Dependent variable: log real hourly wages PR=1 (1) age 59-0.034* (0.016) age 60 0.007 (0.016) age 61-0.006 (0.016) age 62-0.037* (0.018) age 63-0.033 (0.022) age 64-0.037 (0.023) individual-year obs. 9,537 # of individuals 2,253 Tests of Joint Significance (p-value): Age 52-Age 57 0.425 Age 58-Age 69 0.000
Results: Wage Profile 2.7 Figure: Average Wage Profile, FE 2.6 2.5 2.4 23 2.3 2.2 2.1 50 52 54 56 58 60 62 64 66 68 70 FE
Hourly Wage Profile Table: Dependent variable: log real hourly wages (1) (2) PR=1-0.321** (0.021) age 59-0.034* -0.024 (0.016) (0.015) age 60 0.007 0.012 (0.016) (0.015) age 61-0.006 0.012 (0.016) (0.016) age 62-0.037* -0.005 (0.018) (0.017) age 63-0.033-0.014 (0.022) (0.020) age 64-0.037-0.014 (0.023) (0.022) individual-year obs. 9,537 9,537 # of individuals 2,253 2,253 Tests of Joint Significance (p-value): Age 52-Age 57 0.425 0.048 Age 58-Age 69 0.000 0.302
Hourly Wage Profile Table: Dependent variable: log real hourly wages (1) (2) PR=1-0.321** (0.021) age 59-0.034* -0.024 (0.016) (0.015) age 60 0.007 0.012 (0.016) (0.015) age 61-0.006 0.012 (0.016) (0.016) age 62-0.037* -0.005 (0.018) (0.017) age 63-0.033-0.014 (0.022) (0.020) age 64-0.037-0.014 (0.023) (0.022) individual-year obs. 9,537 9,537 # of individuals 2,253 2,253 Tests of Joint Significance (p-value): Age 52-Age 57 0.425 0.048 Age 58-Age 69 0.000 0.302
Hourly Wage Profile Table: Dependent variable: log real hourly wages (1) (2) PR=1-0.321** (0.021) age 59-0.034* -0.024 (0.016) (0.015) age 60 0.007 0.012 (0.016) (0.015) age 61-0.006 0.012 (0.016) (0.016) age 62-0.037* -0.005 (0.018) (0.017) age 63-0.033-0.014 (0.022) (0.020) age 64-0.037-0.014 (0.023) (0.022) individual-year obs. 9,537 9,537 # of individuals 2,253 2,253 Tests of Joint Significance (p-value): Age 52-Age 57 0.425 0.048 Age 58-Age 69 0.000 0.302
Results: Wage Profile Figure: Average Wage Profile, FE, with and without controls for PR status 2.7 2.6 2.5 2.4 23 2.3 2.2 2.1 50 52 54 56 58 60 62 64 66 68 70 FE FE (with PR indicator)
Results: Wage Profile Figure: Predicted wage profile for an individual who enters PR at age 62 14 12 10 8 6 4 2 0 50 52 54 56 58 60 62 64 66 68 70
Results: Hours Profile Figure: Average Hours Profile, FE, with and without controls for PR status 50 40 30 20 10 0 50 52 54 56 58 60 62 64 66 68 70 FE FE (with PR indicator)
Results: Hours Profile Figure: Predicted hours profile for an individual who enters PR at age 62 50 40 30 20 10 0 50 52 54 56 58 60 62 64 66 68 70
Results: Earnings Profile Figure: Predicted earnings profile for an individual who enters PR at age 62 700 600 500 400 300 200 100 0 50 52 54 56 58 60 62 64 66 68 70
Results: Discussion Wages may reflect a stochastic, downward-trending productivity process. If only workers who receive positive productivity shocks choose to remain in their full-time job, observed wage path understates decline in wages with age. Follow procedure described in Wooldridge (1995) to test for selection in panel data. Instrument transitions into partial and full retirement using wealth changes and Social Security ages. Find no evidence of self-selection. Results suggest that either productivity does not decline with age or wages do not reflect productivity.
Results: Discussion To what extent is partial retirement a choice? Ex-post responses to questions regarding reasons for full/partial retirement indicate those are voluntary in 70-80% of cases. Comparison of subjective retirement expectations with realizations leads to similar conclusions: Bernheim (1990) finds the up to two thirds of men in the RHS sample retire within one year of their expected date. Haider and Stephens (2007) confirm accuracy of subjective expectations in the HRS. They show that they are very strong predictors of retirement dates even after controlling for age. This evidence indicates than in a majority of cases the wage drop following transitions into partial retirement is endogenous.
Model Follows Chang, Kim, Kwon and Rogerson (AER, 2010). Utility function: U t = c1 ρ 1 ρ + B t where γ is parameter of interest. (1 h t ) 1 1/γ, 1 1/γ Objective is to fit evolution of PT/FT participation probabilities with age. I allow B to depend linearly on age, and add a cost of work that depends linearly on age and the number of hours worked. In total, 6 parameters are calibrated.
Baseline fit Figure: Baseline model fit for γ = 0.25 1 0.75 0.5 0.25 0 50 52 54 56 58 60 62 64 66 68 70 FT data PT data R data FT baseline PT baseline R baseline
Results II Table: Simulation results γ = 0.25 γ = 0.50 γ = 0.75 γ = 0.95 I. Baseline θ w ( w it upon PR) -0.343-0.341-0.340-0.340 θ h ( H it upon PR) -0.563-0.559-0.556-0.555 II. Declining age-wage profile, discrete labor supply θ w ( w it upon PR) -0.005-0.003-0.004-0.004 θ h ( H it upon PR) -0.579-0.576-0.579-0.578 ˆγ 0.321 1.00 1.551 2.203 III. Declining age-wage profile, continuous labor supply θ w ( w it upon PR) -0.007-0.007-0.007-0.007 θ h ( H it upon PR) -0.042-0.041-0.041-0.024 ˆγ (Frisch elasticity) 0.359 0.357 0.357 0.358
Conclusions The age-wage and hours profiles of older individuals are best represented as a step function. Wage and hours declines upon partial retirement are endogenously determined for most individuals. Assuming that hours choices are a response to an exogenously and smoothly declining wage profile leads to severely biased estimates of preference parameters.