Average Propensity to Consume Out of Total Wealth

1. Average Propensity to Consume Out of Total Wealth Laurie Pounder June 28, 2006

2. Talk Outline • Literature & Framework • Data description • Previous Paper – describes A (average propensity to consume) & tests on Merton model • Original hypotheses & preliminary results regarding preferences & cognition • Subsequent questions/issues

3. Some related literature • Optimal saving for retirement literature (Engen, Gale, Uccello 1999; Scholz, Seshadri, Khitatrakun 2005) • Wealth accumulation (Venti & Wise 1998; Lusardi 1999) and consumption profile (Bernheim, Skinner, Weinberg 2001; Hurst 2004; Ameriks, Caplin, & Leahy 2002; Lusardi 2003) literature • Savings rate decline & wealth effect (numerous) → Lifecycle household consumption literature (immense)

4. Basic Lifecycle Consumption Framework to Keep in the Back of Our Mind Under Certainty where r=real interest rate y= income, including earnings, pensions, and transfers F=current assets, including housing = time preference

5. Data - HRS Health and Retirement Survey • Nationally representative panel of ages 50+ • Seven waves since 1992 • Sample updated with new 51-56 year-olds in 1998 • Detailed socioeconomic, income, wealth, health, employment history, family • Some attitudes, subjective expectations, plans etc. • Complete Social Security earnings histories • Employer-reported pension formulas

6. Data - Wealth Expected Present Value of Wealth: Deterministic W = Human Capital + Net Worth Human Capital= Earnings+Pensions+Social Security+Other Transfers Net Worth = 10 categories of assets less 3 categories of debt

7. Data – Wealth, continuedHuman Capital • Components • Expected earnings for non-retired – projected from current earnings based primarily on experience and tenure • Present value of defined benefit and defined contribution pension plans – HRS pension calculator with adjustments & using survey report of expected retirement age • Present value of Social Security benefits • Government benefits – veterans, disability, approximate “income floor” based on SSI • All human capital is after-tax (approximate year-specific tax rates) and discounted, including an age and gender-specific mortality hazard

8. Data - Consumption 2001 & 2003 Consumption and Activities Mailout Survey (CAMS) • Sent to approximately ½ of the household in the HRS sample • 2001 response rate 77% = 3,866 househoId obs • My sample: approx 2,000 households • In CAMS, in the HRS or WB cohorts, Social Security match, and still in the sample for the 2002 wave • 26 expenditure categories covering equivalent of >90% of total expenditures measured by the CEX • I also impute rental equivalence and vehicle consumption with predicted values based on CEX

9. Previous Paper • Describe distribution of C/W • Test a Merton model for optimal consumption and asset allocation

10. Merton Model Subject to: Taylor approximation of the Bellman Equation: Solutions: where A=C*/W

11. Average Propensity to Consume Infinite Horizon: In the special case where r, μ, and σ are constant, then α* is constant and dA/dt=0 which gives: Finite Horizon:

13. Previous Paper Findings • Simple Merton model has very little ability to predict actual C/W using representative agent values for time preference and risk aversion • Solving the Merton equation for the time preference parameter and using the actual survey value for C/W generates an implied distribution for the time preference parameter that compares well to other distribution estimates (Samwick 1996; Barsky et al 1997) • C/W does co-vary as expected with model enhancements such as subjective mortality (life expectancy) and bequests

14. Covariates of A • Previous paper: subjective survival expectancy; health; expected bequests (see Table 1) • New demographics: (some shown Table 1) • Female financial respondent • Divorce & widowhood (remove divorced households because not capturing wealth transfer from male to female) • Retirement status (not shown – small negative coefficient) • Education dummies (not shown, lower education has positive & significant coefficients) • Race (not shown, nonwhite has sizeable positive coefficient)

15. Table 1

16. Explaining Distribution of C/W • My hypothesis generated by the 1st paper was that much of the variation in A, which is not well explained by Merton, may be heterogeneous preferences and/or, for the bottom group, an inability to plan or form expectations • Heterogeneous Preferences: Time & Risk Aversion (EIS – not currently separated) • Correlate two distinct measures of preference • Directly test explanatory power of survey measures and related questions • Cognition, Expectation Formation & Planning • Directly test survey measures • Numeracy • Word recall • Precision of expectation formation • Planning Horizon

17. Two Residuals Containing Preferences:Wealth Residuals and Post-Merton C/W • Wealth residuals a la Hurst’s “Ants and Grasshoppers” (2004) • Residual after regressing financial wealth on income path, employment/health shocks, demographics (“opportunities to save”) – residual accumulated wealth is a variable that reflects past choices, independent of future shocks, should primarily reflect preferences Ft-1 =f(Yh, rh, Ch, γ,ρ) • If consumption adjusts quickly, then C/W should be independent of past shocks. After accounting for age, expected returns, life expectancy , and bequests, under the Merton model, the residual should primarily reflect preferences C/W=f(E[μ], r, age, γ,ρ, bequests) • If both statements are accurate then the wealth residuals (from a previous wave to minimize measurement error correlation) should be highly correlated with the residual of C/W as described above

18. Calculating Wealth Residuals • Regress previous period net worth on everything we have to predict wealth accumulation “opportunities to save”: quadratic in average income over previous 20 years (measured at 2 intervals); coefficient of variation of income; health shocks over previous 10 years; recent employment shocks; education; etc. – residual reflects unexplained propensity to save • Use residual as independent variable to predict C/W controlling for bequests, life expectancy, etc.

19. Table 2 Both regressions include education and race dummies. Observations are lost due to eliminating divorced and about 100 observations for which too much information is missing to calculate wealth residuals. • Conclusion: wealth residuals matter in the direction we expect, but don’t make much difference in explaining variation

20. Table 3 Preference & Cognition Measures • All regressions include demographics, life expectancy, bequests, etc. as above • Conclusion: Results Not Striking

21. Problem: Level of Wealth Highly Correlated

22. Other Preference/Planning Measures • The HRS question about financial planning horizon (not shown in table) has a significant negative coefficient. Those with longer planning horizons have lower C/W • I haven’t yet tried to use other direct measures of preferences and planning (other than risk aversion) from the experimental modules because sample size would be so low (1/2 or less or original module sample size).

23. Perhaps trying to measure preferences (at least directly) and cognition is not the best question to ask here. • At the least, the correlation between level of wealth and C/W potentially skews the answers to these measures → Have to deal with wealth correlation to answer anything correctly • Broadening the scope and/or thinking about confounding issues:

24. List (Questions & Preliminary Results) • Fungibility/Liquidity: How does consumption relate to fraction of W in current versus future assets • Fraction of wealth in current assets has significant positive association with C/W. But counter-intuitively, much of that is from positive coefficient on high fraction of wealth in housing • Pensions: Some studies suggest that, rather than being a substitute for pre-retirement asset accumulation, people with pensions save as much or more than people without pensions (back to preferences?) • Dummy for anyDB plan significantly negative, as is value of DB (DC negative but not significant) • Wealth: Do the rich save more? Possible reasons for co-variance of C/W with level of W • Measurement error • Preferences: high savers=high wealth & low C • Incomplete adjustment to shocks • Wealth sources riskier for wealthier?

25. Modeling Considerations • Within Model • CRRA doesn’t allow risk/EIS variation by wealth – Use HARA?? • Separate Risk & EIS: Epstein-Zin/Kreps-Porteus preferences • Specifying alternative such as “mental accounting”, myopia, or hyperbolic discounting??