How Social Security and Medicare Affect Retirement Behavior In a World of Incomplete Markets

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1 How Social Security and Medicare Affect Retirement Behavior In a World of Incomplete Markets John Rust Christopher Phelan Econometrica 1997 Sargent Reading Group March 23, 2007 Sargent Reading Group: March 23, 2007 p. 1

Christopher Phelan Econometrica 1997 Sargent Reading

2 Introduction Puzzles 1. early retirement puzzle 2. age 65 retirement puzzle 3. Medicare puzzle Sargent Reading Group: March 23, 2007 p. 2

6 Introduction Policies and "incentive schemes" social security benefit rules social security benefit adjustment for early and late retirement Medicare eligibility Sargent Reading Group: March 23, 2007 p. 3

benefit adjustment for early and late retirement

7 Introduction Policies and "incentive schemes" social security benefit rules social security benefit adjustment for early and late retirement Medicare eligibility Incomplete market incomplete annuity market incomplete health insurance borrowing constraint Sargent Reading Group: March 23, 2007 p. 3

Medicare eligibility Incomplete market incomplete annuity market

8 Introduction Policies and "incentive schemes" social security benefit rules social security benefit adjustment for early and late retirement Medicare eligibility Incomplete market incomplete annuity market incomplete health insurance borrowing constraint Goal: construct a dynamic programming (DP) model that "explains" the puzzles Sargent Reading Group: March 23, 2007 p. 3

incomplete annuity market incomplete health insurance borrowing constraint Goal: construct a

9 DP model Sargent Reading Group: March 23, 2007 p. 4

10 DP model: setup V t (s) = max δ E δ T j=t β j t u j (s j,d j,θ u ) s t = s s t : state variables d t : control variables, δ = (d 0,...,d T ) θ = (β,θ u,θ p ): parameters characterizing preferences and beliefs about uncertain events α: social security system Estimate θ by MLE given the observed δ Sargent Reading Group: March 23, 2007 p. 5

..,d T ) θ = (β,θ u,θ p ): parameters characterizing preferences and beliefs about

11 DP model: setup state variables s t = (x,ǫ) x: observable ǫ: unobserved integrate out ǫ to obtain a conditional choice probability P t (d x,θ,α) assume ǫ follows a multivariate extreme value distribution and rewrite expected value function without ǫ (Rust 1987, 1988) Sargent Reading Group: March 23, 2007 p. 6

assume ǫ follows a multivariate extreme value distribution and rewrite

12 DP model: setup assume ǫ follows a multivariate extreme value distribution can express P t (d x,θ,α) with a multinomial logit representation P t (d x,θ,α) = exp{ν t (x,d,θ,α)} d D(x) exp{ν t(x,d,θ,α)} ν t (x,d,θ,α) = u t (x t,d t,θ u ) + β log[ exp{ν t+1 (x t+1,d t+1,θ,α)}]p t (dx t+1 x t,d t,θ p,α) d t+1 D(x t+1 ) V t (x,ǫ) = max d D(x) [ν t(x,d,θ,α) + ǫ(d)] Sargent Reading Group: March 23, 2007 p. 7

ν t (x,d,θ,α) = u t (x t,d t,θ u ) + β log[ exp{ν t+1 (x t+1,d t+1,θ,α)}]p t (dx t+1 x t,d t,θ p,α)

13 DP model: estimation Estimation Strategy L(θ) = L(β,θ u,θ p ) I T i = P t (d i t x i t,θ,α)p t (x i t x i t 1,d i t 1,θ p,α) i=1 t=1 estimate θ p using p t terms using the estimates θ p, solve the DP and estimate (β,θ u ) Sargent Reading Group: March 23, 2007 p. 8

t=1 estimate θ p using p t terms using the estimates θ p, solve

14 Data Retirement History Survey (RHS) biennial panel between of samples of age choose male heads exclude samples who expect to receive private pension benefits (44% of the samples) exclude samples who qualify for DI benefits (10%) Sargent Reading Group: March 23, 2007 p. 9

receive private pension benefits (44% of the samples) exclude samples

15 States and controls x t = (y t,ss t,e t,m t,h t,hi t,aw t ) total income: y = w + w sp + ss + ss sp + oi hc (net of health costs) social security state: not eligible, early retiree or normal retiree employment state: N E, P T and F T marital status health status: good, bad or dead health insurance status: eph, gph, mca or nhi social security average monthly earnings d t = (ed t,ssd t ) employment decision social security application no savings and consumption decision c = y Sargent Reading Group: March 23, 2007 p. 10

status: good, bad or dead health insurance status: eph, gph, mca or nhi social security average monthly earnings d t = (ed t,ssd t

16 Estimation: states transition p t (x x,d) = p 1 t (y y,ed,ss,ssd,m,h,aw) p 2 t (aw ed,y,aw) p 3 t(m m,h) p 4 t(h h,aw) p 5 t(h = dead h,m) assume independence of p j t health costs (that depends on health insurance) enter y. estimated with the Pareto distribution. Sargent Reading Group: March 23, 2007 p. 11

independence of p j t health costs (that depends on health insurance) enter

17 Estimation: preferences u t (y,e,ed,h,m,θ u ) = u 1 t(y,h,m,θ 1 u) + es u 1 t : utility from consumption es i=1 j=1 u 2 t(i,j,θ 2 u)i{e = i,ed = j} u 1 t(y,h,m,θ 1 u) = [ y θ 11 ] exp{θ 12 + θ 13 I{h = bad} θ 11 +θ 14 I{m = married} + θ 15 t/(1 + t)} Sargent Reading Group: March 23, 2007 p. 12

u 1 t(y,h,m,θ 1 u) = [ y θ 11 ] exp{θ 12 + θ 13 I{h = bad} θ 11 +θ 14 I{m

18 Estimation: preferences u t (y,e,ed,h,m,θ u ) = u 1 t(y,h,m,θ 1 u) + es i=1 es j=1 u 2 t(i,j,θ 2 u)i{e = i,ed = j} u 2 t : utility of possible labor/leisure/search decisions (recall e,ed {NE,PT,FT}), for example could, but not include age, health status and marriage status u 2 t(ne FT): potential disutility of search costs of unemployed returning to full-time job u 2 t(ne NE): utility of leisure by remaining unemployed Sargent Reading Group: March 23, 2007 p. 12

include age, health status and marriage status u 2 t(ne FT): potential disutility of search costs of unemployed

19 Estimation: preferences u t (y,e,ed,h,m,θ u ) = u 1 t(y,h,m,θ 1 u) + es i=1 es j=1 u 2 t(i,j,θ 2 u)i{e = i,ed = j} dummies for disutility by negative income disutility of working while receiving social security utility of continuing to work among the high-income people Sargent Reading Group: March 23, 2007 p. 12

disutility of working while receiving social security utility of continuing to

20 Estimation: preferences parameter estimate t-stat θ 11 (risk aversion) θ 13 (bad health) θ 14 (married) θ 15 (age) u 2 (FT FT) u 2 (FT PT) u 2 (FT NE) u 2 (PT FT) u 2 (PT PT) u 2 (PT NE) u 2 (NE FT) u 2 (NE PT) u 2 (NE NE) Sargent Reading Group: March 23, 2007 p. 13

6 u 2 (FT NE) -47.24-2.3 u 2 (PT FT) -60.77-3.0 u 2 (PT PT) -56.00-2.8 u 2 (PT NE) -51.99-2.

21 Retirement behavior Sargent Reading Group: March 23, 2007 p. 14

22 Retirement behavior Recall... Choice probabilities ed: employment decision {F T, P T, N E} ssd: social security application {DB,AB} Sargent Reading Group: March 23, 2007 p. 15

23 Retirement behavior: age FT=705, PT=58, NE=3 e=ft, N=705 FT PT NE data model e=ft, hi=eph, N=563 data model e=ft, hi=others, N=142 data model Sargent Reading Group: March 23, 2007 p. 16

24 Retirement behavior: age e=ft, N=1214 FT,DB PT,DB NE,DB FT,AB PT,AB NE,AB data model e=ft, hi=eph, N=990 data model e=ft, hi=others, N=224 data model e=ft, h=bad, N=255 data model Sargent Reading Group: March 23, 2007 p. 17

25 Retirement behavior: age Not already receiving social security e=ft, N=1221 FT,DB PT,DB NE,DB FT,AB PT,AB NE,AB data model e=ft, hi=eph, N=1065 data model e=ft, hi=others, N=156 data model Sargent Reading Group: March 23, 2007 p. 18

26 Work incentive FT PT NE e=all, t 65, ss=applied, N=3345 data model e=all, t 65,ss=not applied, N=334 data model Sargent Reading Group: March 23, 2007 p. 19

27 Remarks...it is a simple matter to perform counterfactual predictions of the impact of alternative Social Security policies" Limitation to conduct a policy analysis because: sample selection y = c no GE effects prices fiscal consequences effects on the behavior of young generations Sargent Reading Group: March 23, 2007 p. 20

28 Remarks...it is a simple matter to perform counterfactual predictions of the impact of alternative Social Security policies" Limitation to conduct a policy analysis because: sample selection y = c no GE effects prices fiscal consequences effects on the behavior of young generations Work (to be) in progress... take it to a GE model with endogenous retirement decision private pensions? Sargent Reading Group: March 23, 2007 p. 20

The PDD Model of Retirement

The PDD Model of Retirement How Social Security and Medicare affect retirement behavior in a world of incomplete markets John Rust Yale University jrust@econ.yale.edu Christopher Phelan Northwestern University cphelan@nwu.edu Revised,