Are Americans Saving Optimally for Retirement?

Transcription

1 Figure : Median DB Pension Wealth, Social Security Wealth, and Net Worth (excluding DB Pensions) by Lifetime Income, (99 dollars) 400,000 Are Americans Saving Optimally for Retirement? 350, ,000 50,000 Dollars 00,000 John Karl Scholz, UW-Madison Ananth Seshadri, UW-Madison Surachai Khitatrakun, ERS Group 50,000 00,000 50, Lifetime Income Pension Social Security Wealth Net Worth Source: Authors' calculations from the 99 HRS Assessing the optimality of household saving Our strategy is straightforward. We write down a specific augmented life-cycle model. Use the model to determine optimal wealth, household-by-household in the HRS. Compare the model to observed wealth in HRS. Joint test: a) Did we write down a sensible model? And b) given the model, are people saving enough? If the approach fails, it s hard to say whether a) or b) is the problem. A close match, however, is noteworthy for both the policy issue and for the life-cycle model. Later in the paper we explore whether alternative models might do better and conduct sensitivity analyses. We Build on the Large Life- Cycle Consumption Literature Features of the literature and our paper Precautionary saving (Deaton; Carroll; Aiyagari). Asset-tested transfers (Hubbard, Skinner, Zeldes, 995) Medical shocks (Palumbo, 999) We build on the fine paper of Engen, Gale, and Uccello (999), which also addresses these issues. The new features of our work include 40 years of data on actual household earnings. These allow us to develop household-specific targets solving the dynamic programming problem for each household. We model empirically household expectations about SS, DB pension benefits, and earnings trajectories We incorporate time-varying representations of the individual income tax and transfer system.

2 A simple, augmented life-cycle model D j S E β U( cj / g( Aj, K j), subject to j= S { } y = e + ra + T(), j S,..., R, j j j R yj = SS ej + DB( er) + raj + T( ), j { R,..., D}, j= S j j+ j j j j j+ j j j j ( ), {,..., } τ ( ), {,..., } c + a = y + a τ y j S R c + a + m = y + a y j R D Recursive formulation: retired households Uc ( / g(,0)) + β phj pwj V( er, ER, a, j+, m',3) dω jm( m' m) + Ve ( R, ER, ajm,,,3) = max m, ca, β phj ( pwj ) V( er, ER, a, j+, m',) dω js ( m' ) + m β pwj ( phj ) V( er, ER, a, j+, m', ) dω js ( m' ) subject to y = SS( E ) + DB( e ) + ra+ T( e, E, a, j, n), R R R R c+ a + m= y + a τ ( y), Recursive formulation: the working adult case ' ' ' V(, e E, a, j) = max U( c/ g( Aj, K j)) + β V( e, E, a, j ) d j( e e), ca, + Φ ' e subject to y= e+ ra+ T( e, a, j, n), ( ) c+ a' = y+ a τ y, and E = E + e. The Health and Retirement Study (HRS) National panel study of 7,70 households (,65 persons) in 99. Face-to-face interviews of birth cohort and their spouses (if married). Oversamples blacks, Hispanics, and Floridians. Follow-up telephone interviews every two years since 99 (up to 00). We primarily use the 99 survey. Key features: social security earnings histories, fertility history, DB pension information, wealth data, and out-of-pocket medical expenses.

3 Our HRS Sample We make three sample exclusions, dropping 379 married households where one spouse refused to participate in the 99 survey; We lack needed information on household characteristics 93 households who never worked full time; We do not have a reasonable measure of lifetime resources 908 households where the highest earner began working fulltime before 95. Our model used to impute earnings is computationally more difficult with missing initial values. Our resulting sample has 6,3 households. Imputing Missing or Top- Coded Earnings Information Two problems (not created equally).8 percent of respondents refused to release SS earnings records (95-9) Results are unchanged if we drop these hhlds (fn. 9). 6 percent between are top-coded (we have W records from 980-9). Assume individual log-earnings process, where * indicates the latent variable * ' yi,0 = xi,0β0 + εi,0 * * ' yit, = ρyit, + xit, β + εit, t {,,..., T} ε = α + u it, i it, Imputing Earnings, cont. Estimate with a dynamic panel Tobit model, with random effects assumption for the error term Parameters: Estimate separately for 4 groups: gender x some college. Estimates are in Appendix Table A. Undoing top-coded data: Once we have the parameter estimates, we use a Gibbs Sampling procedure to calculate the conditional expectation of top-coded observations. An analytic expression is not available. Model parameters γ Preferences c, if γ Uc () = γ log c, if γ = β =.96 and γ = 3 Equivalence scale g( A, K ) = ( A K ) 0.7 j j j j Taxes (dollar amounts in thousands) ( ) 0 ( a a τ y = a y y a + ), from Gouveia and Strauss (994, 999) 3

4 Model parameters, continued Transfers { [ ]} T = max 0, c e+ ( + r) a, Household Earnings Expectations i log e = α + β AGE + β AGE + u j j j j uj = ρuj + ε j, Estimate parameters for 6 groups: married (one earner), married (two earner), and single, by education statuses (college degree, yes or no). Rho is.58 to.76 (sensitivity to.9) Real return 4% (sensitivity to 5%, 7%) Model Parameters, continued Social Security Using earnings realizations and expectations, we model social security rules. DB Pensions We estimate empirical DB pension functions based on years of service in pension-covered job, unionization status, and the expectations about the final-year earnings. Out of Pocket Medical expenses (married*ed) mt = β0 + βaget + β AGEt + ut, ut = ρut + εt, εt ~ N(0, σε ), Solving the model Start at the oldest possible date (00), solve backwards for all possible individual states of the world each period. We construct discrete grids of feasible assets (00 points) and interpolate. We successively move backwards solving for the value function and the decision rule for assets. Once we have all decision rules, we take the specific earnings realizations (from SS earnings records) for each household (and other characteristics) to solve for the optimal level of wealth in the 99 HRS. Optimal Net Worth.0e e+06 Observed Net Worth 4

5 Group All Households No High School Diploma High School Diploma College Degree Post College Education Lowest Lifetime Income 4 th Income 7 th Income Highest Lifetime Income Percentage Failing to Meet Optimal Target Median Deficit (conditional on deficit) Optimal Net Worth Target Median Net Worth Median Social Security Wealth Median DB Pension Wealth 8.7% $5,000 $65,486 $0,600 $96,684 $7,37 0.7% $,637 $,84 $36,800 $7,57 $0 8.9% $5,000 $66,68 $0,885 $96,689 $,90 6.0% $,693 $3,34 $09,66 $7,78 $60,75 6.8% $,065 $63,5 $53,000 $4,06 $5, % $,875 $,054 $5,000 $5,667 $0 4.0% $4,957 $44,634 $74,70 $76,4 $8,48.0% $0,48 $84,854 $33,500 $3,730 $55,00 7.7% $8, $46,94 $388,69 $00,438 $3,9 Table X: Mean and Median Optimal Wealth Targets With and Without the Safety Net (Earlier version of the With Safety Net Without Safety Net Median Target Mean Target Median Target Mean Target All Households $69,777 $79,98 $69,785 $8,400 No High School Diploma $,54 $8,087 $5,85 $84,63 High School Diploma $70,383 $6,44 $70,387 $6,760 College Degree $37,58 $69,87 $37,533 $70,497 Post-College Education $78,94 $38,37 $78,95 $38,897 Lowest Lifetime Income $,94 $5,94 $9,56 $56,097 4th Income $48,00 $36,00 $48,09 $37,779 7th Income $89,488 $84,700 $89,495 $85,309 Highest Lifetime Income $53,63 $58,686 $53,63 $58,767 Correlates of Undersaving df/dx Standard Error nd Lifetime Income rd Lifetime Income th Lifetime Income th Lifetime Income th Lifetime Income th Lifetime Income th Lifetime Income -.06**.05 9th Lifetime Income th Lifetime Inc Retired.00.0 Has Pension Social Security Wealth -9.4e-08.88e-07 Age Male Black Hispanic Married -.7***.07 High School Degree College Degree Graduate Degree Self Employed , , ,000 50,000 00,000 50,000 00,000 50, ,000 Figure 3: Dis tributio n o f "Saving Adequacy" Obs erved Minus Simulated No n-db-p ens io n Net Wo rth (All Ho us eho lds ) Lifetime Earning s 0t h Percent ile 5th Percentile 50t h Percent ile 75t h Percent ile 90t h Percent ile 5

6 8th Lifetime Income 9th Lifetime Income 0th Lifetime Income Has Pension Social Security Wealth Married Self-Employed Number of Children Number of Grandchildren Subjective Probability of Living > 75 Subjective Probability of Living > 85 Subjective Probability of Bequest > $0k Subjective Probability of Bequest > $00k Mid-Atlantic Division East North Central Division West North Central Division SD, NE South Atlantic Division East South Central Division Median Regression of Saving Adequacy (Actual-Optimal Net Worth) Coefficient Estimates Standard Error 5,908.9*** 5,908.9*** ,34.5*** 4,34.5*** -,736.* -,736.* 0.046** 0.046** 9,84.0*** 9,84.0*** 4,466.*** 4,466.*** Sensitivity Analysis: Housing and Social Security Some believe the elderly are unwilling to use housing equity to support consumption. Not clear this is true (Hurd, 003). Even if it is, we like including housing in net worth. Still Figure 4 assumes households are unwilling to use half of housing net worth to support living standards. 57.9% of households meet or exceed their targets 5 th (0 th ) percentile conditional deficit is $0,96 ($40,37) The social security system modeled in the paper may be fiscally unsustainable. Cut expected and actual SS benefits by 5 percent (from 95) 36. percent of households fail to meet optimal targets. West South Central Division Mountain Division Pacific Division 54.*** *** Table 6: Alternative Models Naïve (save a constant fraction of Y t ) Naïve (save an income-varying fraction of Y t ) Modigliani (S t =a+by p ) Constant Alpha Reduced-Form Regression Including 4 Years of Earnings Reduced-Form Regression Including Quadratic Terms for 4 Years of Earnings Monte Carlo Draws on Earning Sequence Base Case in Paper R (in percent) Does the Model Match Other Features of the Data? Consumption tracks income. Consumption trajectories (netting out the effects of children) are hump-shaped and peak at 46 (income trajectories peak at 5). The wealth distribution is skewed. The top percent holds 7 percent of wealth (it s 4 percent in the data, which is consistent with bequests playing a role in wealth accumulation). The model can explain 8 percent of the change in wealth. A reduced-form regression model with X s, 4 years of earnings, and earnings squared, accounts for 6.6%. 6

7 Ratio to Age 5 Figure 5: Consumption and Income by Age Age Source: Authors' calculations from the baseline model and the 99 HRS Consumption Income Parameter Value Baseline: β = 0.97, γ = 3, r = 4% Sensitivity Analysis: Fundamental Parameters Percentage Failing to Meet Optimal Target Measure of fit: R (in %) Deficit Conditional on Failing to Meet Optimal Target (99$) ,000 β = ,00 β = ,35 r = 5% ,769 r = 7% ,65 γ = ,3 γ = ,568 ρ = ,596 5% chance of nursing home costs (4 years at $60k per year) ,93 Conclusions With a common formulation of the life-cycle model, we explain 86 percent of the 99 cross-sectional variation in wealth of HRS households. Moreover, we find 8 percent of households meet or exceed their optimal wealth targets. And the conditional deficits tend to be small. We interpret this as a) strongly suggestive that the lifecycle model is capable of explaining life-cycle wealth accumulation and b) that the consumption changes around retirement noted by Bernheim et al. are not driven by inadequate retirement wealth accumulation. Results are prior to the 990s stock market run-up Final thoughts Are Americans saving optimally? Deliberately provocative title, though we are much closer to saying yes than we were before doing this. Some households in top half of lifetime income distribution are saving too much Bequest motives? Heterogeneity in rates of return or deep preference parameters? Learn more? You can find revisions of this and other papers at 7