1. Understanding Earnings, Labor Supply and Retirement Decisions
Xiaodong Fan, Ananth Seshadri, and Christopher Taber
UNSW and University of Wisconsin
July 31, 2017

2. Basic Goal
Modeling retirement behavior is fundamental to understanding effects of policy changes on retiree well-being
The goal of this work is to estimate a human capital investment model with labor supply to jointly explain
Lifecycle profiles of wages
Lifecycle profile of labor supply
Main Goal: Retirement arises endogenously as a labor supply decision in which individuals optimally bunch leisure late in life

3. The Challenge Build a model that can reconcile
The large increase in wages and small increase in labor supply at the beginning of the lifecycle
The small decrease in wages and large decrease in labor supply at the end of the lifecycle
Try to explain this without allowing preferences or technologies to depend explicitly on age.

4. Why do we care?
Human Capital literature: endogenizes lifecycle wages taking the retirement date as exogenous. Retirement date is crucial
Retirement literature: endogenizes retirement taking the wage pattern as exogenous. Wage pattern is crucial
Our goal is to endogenize both within the same model
Matters for social security policy questions: if changes in social security system induces people to retire later, human capital investments will change

5. Data We use SIPP Large panel data set
We condition on white males with exactly 12 years of education
We have data on essentially “worked last week” and “wage last week”
Consider the mean profiles by age (estimation focuses on )

6. Some Considerations
Shape of the wage profile near retirement is crucial
However, there is a major “selection problem” in that we only observe wages for non-retirees
A simple solution is to use fixed effects.
Here we run a regression of log wages on age dummies and individual specific fixed effects
We plot the estimated age dummies along with mean log wages

7. Log Wages

8. The Baseline Model Extensive margin of labor supply
Individuals maximize utility from consumption and leisure
Human capital investment makes earnings endogenous
Time used for work, human capital accumulation or leisure
We account for social security rules and taxes
Since Heckman (1975,1976) very little work combining Human Capital theory with Labor supply

9. Model Features
In the data we see almost flat wages but a large decline in labor supply for middle age/older workers
Difficult to explain this without a very large labor supply elasticity
Why are people working so little when they are old even though their wages appear high?
Two features of our model will help explain this
Other than social security, precautionary savings, and selection on wages

10. 1. Depreciation There is a shadow cost to not working
Human capital depreciates
Even middle age workers need to invest in human capital or their wages will decline
In the simplest labor supply model if wages were the same at age 50 and 70 there is no reason why labor supply should be lower at 70 than at 50.
Individuals don’t "retire” during their middle ages because of depreciation, when they return at 60 their wages would be very low

11. 2. Wages and human capital are different
Measured wages are
(1 − It) Ht
Measured wages can remain flat when Ht is falling if It is falling as well.
Since lifecycle It declines as people age, human capital has to fall faster than wages
Can reconcile a relatively small decline in wages with a relatively big decline in labor supply
Without resorting to a very large labor supply elasticity

12. Moments
We estimate using Indirect Inference with six sets of moment conditions from SIPP to represent the life-cycle profiles.
The labor force participation rate 22-65;
The first moments of the logarithm of wages 22-65;
The first moments of the logarithm of wages after controlling for individual fixed effects 22-65;
The second moments of the logarithm of wages 22-65; The first moments of consumption 27-65;
The overall transition rates: E to U and U to E.
Total Sample Size: 230,657 observations from 80,519 individuals

13. Parameter Estimates Baseline Model
Parameters
Estimates
Standard Errors
Leisure: Standard Deviation of Shock aε
0.433
(0.012)
Human Capital Depreciation δ
0.101
(0.007)
Human Capital Production Function: I factor αI
0.076
(0.019)
Human Capital Production Function: H factor αH
0.151
(0.021)
Standard Deviation of Human Capital Innovation σξ
0.405
(0.082)
Bequest Weight b1
424, 070
(90, 735)
Parameter heterogeneityb
Leisure: Mean of Intercept
µa0
−6.525
(0.050)
Leisure: Standard Deviation of Intercept
σa0
0.874
(0.053)
Human Capital Productivity, Mean µπ
1.758
(0.069)
Human Capital Productivity, Standard Deviation σπ
0.583
(0.026)
Correlation between a0 and π ρ
−0.893
(0.064)
Initial Human Capital Level at Age 18
Intercept γ0
1.625
(0.099)
Coefficient on a0
γa0
0.052
Coefficient on π γπ
0.531
(0.060)
Standard Deviation of Error Term
σH0
0.239
(0.036)

14. Fit of Labor Force Participation

15. Fit of Log Wages with Fixed Effects

16. Fit of Log Wages without Fixed Effects

17. Fit of Standard Deviations of Log Wages

18. Fit of Consumption

19. Here is what happens in the model

20. Simulation of Main Variables

21. Human Capital and “Wages”

22. Labor Supply Elasticity

23. Health
One potentially important element of the model is health-we include it to see it’s quantitative significance
Health status is a new state variable
Affects tastes for leisure, and interact this with age
We estimate transition from PSID
We fit age pattern of interaction between health and Age (from CPS)
It appears to be relatively unimportant

24. Sensitivity of Labor Force Participation to Health Status

25. Log Wages

26. Policy Counterfactuals
We conduct several counterfactual policy experiments
Increase Tax Rate by 50%
Remove the Social Security earnings test,
Delay Normal Retirement Age (NRA) two years
Remove the Social Security system completely
Remove the Social Security system-taxes only
Remove the Social Security system-benefit only
Decrease the Social Security benefit by 20%

27. Baseline Level
Increase Tax 50%
% change
No Earnings Test
NRA = 67
Panel A: Baseline Model
LFPR
40.356
3.096
0.959
1.012
Effective Labor
37.997
3.125
0.957
1.006
Pre-tax Income
4.521
0.916
1.330
Average lnw
2.613
0.468
0.322
0.268
Human Capital
2.823
0.705
0.836
Investment
2.359
2.631
0.988
1.122
Panel B: Exogenous Model
40.412
3.771
0.208
0.835
3.945
0.274
0.799
2.625
0.248
0.015
0.024

28. Baseline Level
Reduce SSB 20%
No SS
Taxes
NO SS
Benefit
NO SS
Panel A: Baseline Model
LFPR
40.356
1.570
-4.826
12.934
6.560
Effective Labor
37.997
1.563
-4.790
12.926
6.585
Pre-tax Income
2.165
-7.143
15.280
5.826
Average lnw
2.613
0.569
-0.777
1.903
0.792
Human Capital
1.326
-4.354
8.946
3.681
Investment
2.359
1.684
-5.395
13.059
6.147
Panel B: Exogenous Model
40.412
1.311
-5.475
8.552
2.245
1.264
-5.118
7.705
2.030
2.625
0.076
-0.103
-0.009
-0.069

29. Conclusion Model is able to fit wage and labor supply profiles well
Model produces retirement endogenously
Depreciation of human capital is really key to understanding retirement decisions
And Health shocks play a much less important role
Policy responses to changes in SS benefits are meaningfully different from model with exogenous wage processes