1 Labor Supply Responses to Marginal Social Security Benefits: Evidence from DiscontinuitiesJeffrey B. Liebman, Harvard Kennedy School Erzo F.P. Luttmer, Harvard Kennedy School David G. Seif, Harvard Economics Dept. June 2009

2 1. Motivation A common argument for Social Security reform:The effective Social Security tax is lower than the statutory rate because benefits (generally) increase with taxes paid Due to the complexity in Social Security benefit rules, individuals do not recognize the tax-benefit link They respond to the statutory rate rather than to the effective rate, causing excess deadweight loss from labor distortion A more transparent system (personal accounts, notional defined benefits) would eliminate this excess DWL The validity of this argument depends on the extent to which people recognize the tax-benefit link This paper: examine the perception of the tax-benefit link by estimating the labor supply response to marginal Social Security benefits

3 Contribution to the Large Literature on Labor Supply Responses to Social Security IncentivesDevelop identification strategy that relies on discontinuities in Social Security incentives E.g., individuals have a choice of claiming 100% of own benefits or 50% of their spouse’s benefits Woman whose own benefits are 49% of spouse’s benefits will claim spousal benefits  no tax-benefit link Woman whose own benefits are 51% of spouse’s benefits will claim her own benefits  tax-benefit link First to examine intensive-margin labor supply responses (hours, earnings) in addition to extensive margin labor supply (retirement) Examine retirement, hours, and earnings responses for men and women We examine incentives just from work decision (not from claim decision)

4 2. Methodology We exploit five sources of discontinuities in theSocial Security Benefits rules: The “35-year rule” Only the 35 highest years of indexed earnings count After 35 years of earnings, new years will crowd out earlier years of earnings, thus reducing their marginal effect on the AIME Spousal benefits (PIA=Primary Insurance Amount  Benefits) Claim on spousal record if PIAown<0.5 PIAspouse Claim on own record if PIAown>0.5 PIAspouse Widow/Widower benefits Claim on spousal record if PIAown< PIAspouse Claim on own record if PIAown> PIAspouse Kinks in the AIME-PIA schedule Vesting rule (generally 40 quarters of earnings)

5 Example: Effect of 35-year rule on incentivesTwo hypothetical workers: Single males Earned in each year the age- & gender-specific mean earnings Individuals differ only by length of work history: Individual 1 started working at age 25 (dashed line) Individual 2 started working at age 30 (solid line) The figure 5 plots work incentives by age: - Extensive-margin incentive = log effective Social Security net-of-tax share for working an additional year

6 Figure 5

7 Regular RD Approach Not FeasibleRegular Regression Discontinuity approach would be: Find effective tax rate: denotes all (current and future) information to calculate SSW yit denotes earnings (also included in X vector) Regress labor supply (hit) on incentives and a non-linear function of all the information needed to calculate the incentives, and other controls: The control function f() must be continuous but can be arbitrarily flexible. The labor supply response, α, identified off of the discontinuities. Problem: is not yet known (unless perfect foresight) Taking the expectation over turns some discontinuities into non-linearities “discontinuities-in-the-limit” ≡ true discontinuities and non-linearities that converge to a discontinuity as uncertainty gets resolved

8 Approach using Discontinuities-in-the-limitFeasible approach: Regress labor supply (hit) on expected incentives and a non-linear function of all current information needed to calculate the expected incentives (X), and other controls (Z): The control function f() must be continuous. However, it cannot be arbitrarily flexible because then the discontinuities-in-the-limit would be absorbed too How to determine the right amount of flexibility for f()? Needs to be flexible enough to absorb any determinants of labor supply that are correlated with general non-linearities in incentives Cannot be so flexible that the credible variation (discontinuities-in-the-limit) is absorbed too We develop a criterion that allows us to test whether f() is sufficiently flexible

9 Criterion for flexibility of control function f()Idea: The control function should absorb all non-linearities in incentives not related to the 5 features that cause the discontinuities-in-the-limit Implementation: Create a hypothetical set of Social Security rules that have been stripped of the 5 features that give rise to discontinuities-in-the-limit: Replace AIME by the sum of all indexed earning divided by 35 Give everyone a fixed fraction of own and spousal benefits (fraction matches the population average for each sex*marital status*spousal retirement cell) Replace kinked AIME-PIA schedule by best-fitting quadratic schedule Eliminate the vesting requirement (40 quarters) Calculate the “smoothed” effective tax rate, defined as the effective tax rate based on this set of hypothetical rules Make sure that f() is sufficiently flexible that a regression of labor supply on the smoothed effective tax rate and the control function does not yield significant estimates of a labor supply response.

10 3. Data Health and Retirement Study (HRS) linked toadministrative Social Security records HRS: Longitudinal survey of individuals born between 1931 and 1941 as well as their spouses (original cohort, N=12,582) Interviewed every two years starting in 1992 We use seven waves ( ) We obtained permission to link HRS data to administrative Social Security records

11 4. Results A. Effective Tax RatesMeasure incentives by log of the net-of-tax share (1-eff) Incentive on Intensive Margin (work a bit harder or not): Intensive-margin Net-of-Tax Share = INTSit = Ln(1-effective) = Ln(1 - nominal + E[SSWit]/ yit) SSW = Social Security Wealth (=PDV of SS benefits)

12 Figure 3 There a fewer minimum values with the intensive margin because there is more uncertainty (i.e. usually some possibility of a positive linkage).

13 Effective Tax Rates Incentive on Extensive Margin (work vs. retire):Extensive-margin Net-of-Tax Share = ENTSit = Ln(1-eff) = Ln(1-nom+ E[SSWit(retire in t+1)-SSWit(retire in t)]/yit) ENTS = Incentive to postpone retirement by one year Benefit claim date is held constant in this calculation

14 Figure 4

15 4B. Baseline Results Two Steps:Determine the appropriate flexibility in the control function f(Xt-1) The R2 of smoothed incentives on the control function should be very high Regressions of labor supply on smoothed incentives and the control function should yield insignificant results Regress labor supply on true incentives and the control function determined by step 1  estimates identified off of discontinuities-in-the-limit

16 Step 1: Determining the control function

17 Step 1: Determining the control function

18 Final test: No significant results with smoothed incentives

19 Specification for the control function“Baseline” (433 variables): Dummies for race (3), education (4), marital status (4), and year of observation (7); Idem for spouse Sex*age dummies for the respondent, sex*age dummies for spouse, and linear difference in age between respondent and spouse Own and spousal earnings history (log earnings (if > $1000) for each spouse in each of past 52 years; dummies for earnings > $1000) Cubic polynomials in log(SSW), log(PDV of own lifetime earnings)*sex, log(PDV of spousal lifetime earnings)*sex Cubic in total years worked (and idem for spouse), quadratic in current job tenure (and idem for spouse), spousal retirement status, and number of years spouse has been retired Log household assets Dummies for Census region of residence (10), industry (13), occupation (17), veteran status, foreign born.

20 Step 2: Regress Labor Supply on True IncentivesStep 2: Regress Labor Supply on True Incentives (using baseline control function) High explanatory power for earnings because last year’s earnings are included as control.

21 4C. Robustness 1. Effects of flexibility of control function on the estimates (433 variables)

22 4D. Which Discontinuities Matter Most?

23 5. Conclusion We developed a methodology that relies on the variation from discontinuities-in-the-limit in the Social Security tax-benefit schedule Since this variation is plausibly exogenous, we are willing to interpret our estimates causally

24 Conclusion, continued Estimates reject the notion of zero-response to incentives Reasonably robust evidence of response on the extensive margin Some evidence on response on the intensive margin Implication: Benefit from increasing the transparency of the link between Social Security taxes and benefits not as large as generally assumed How credible is it that individuals respond to incentives implicit in complex benefit rules? We just fielded a survey in which we ask people about their understanding of incentives in the Social Security rules Area for further research

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26 2. Robustness to Changes in SpecificationRecall: Baseline ENTS is topcoded at 0.5 to prevent ridiculously high incentives from the vesting rule Earnings-based definition: First year that earnings are less than $2500 real and don’t exceed this amount in future years.

27 2. Robustness to Changes in Specification, continuedNote, never significant results for the earnings regression. Recall: Baseline hours specification is conditional on working at least hours (so that we capture the intensive-margin response)

28 3B. Implementation Expected Social Security WealthPresent discounted value of the sum of expected future Social Security benefits to individual and his/her spouse Apply current Social Security rules Expectation with respect to: Individual’s age of death Spouse’s age of death Individual’s future labor supply Spouse’s future labor supply Death probabilities from gender-specific cohort life-tables adjusted for mortality difference by race and education using method of Brown et al. (2002) Future labor supply: retire with age- & gender-specific retirement hazard earnings conditional on working follow age- & gender-specific growth rates Claim benefits when retiring (but always between 62 & 70)

29 Figure 2

30 Example: Effect of rules on spouse/widow benefitsFigures 7 and 8 are based on three hypothetical workers: 63-year-old women Started working at age 30 Earned in each year the age- & gender-specific mean earnings Individuals differ only by marital status: Individual 1 is single (long dashes) Individual 2’s husband is 63 y.o., started working at age 25, retired at age 62, and earned in each year a fraction x of the age- & gender-specific mean earnings (solid line) Individual 3’s husband is like person 2’s husband, except that he died (after first retiring) at age 62 (short dashes) The figure plots work incentives by husbands’ earnings (x): - Figure 7: Extensive-margin incentives - Figure 8: Intensive-margin incentives

31 Figure 8

32 Figure 7

33 Point out: 1. The 35 years rule most strong for extensive margin incentives 2. We find that effective tax rates are progressive

34 Marital status is very important determinant of effective tax rate for women (much higher if married or widowed) Ratio of own to spousal lifetime income is a huge predictor for the effective tax rate