The Strength of the Precautionary Saving Motive when Prudence is Heterogenous*

Transcription

1 The Strength of the Precautionary Saving Motive when Prudence is Heterogenous* Bradley Kemp Wilson Department of Economics University of Saint Thomas February 2003 Abstract This paper examines the extent to which conclusions of cross-sectional studies of precautionary saving behaviour are robust to allowing for the possible heterogeneity of prudence across households and the inclusion of dynamics. From an intertemporal model of consumption with precaution heterogeneity and conditional income volatility, a stochastic-parameter model of food consumption with systematic components is developed and estimated using data from the Panel Study of Income Dynamics. This paper shows that neglecting heterogeneity and dynamics in cross-sectional consumption regressions can lead to misleading inferences about the strength of the precautionary motive at the household level. Our results indicate that the degree of prudence, and thus the strength of the precautionary motive, depends on the age, educational attainment and labor supply profiles of households. Moreover, the computed profiles indicate that the smallest ratio of precautionary saving to total saving is 38% with the largest ratio being 94%. Address for correspondence: Bradley Kemp Wilson, Department of Economics, Mail #4246, 2115 Summit Avenue, St. Paul, MN Tel.: ; fax.: ; e- mail: bkwilson@stthomas.edu. Key Words: Precautionary saving behaviour, prudence heterogeneity, panel data, stochasticparameter models. JEL Classifications: D12, D91, C23 *I am grateful to Gregory D. Hess and Kwanho Shin for helpful comments.

2 1. Introduction A good number of empirical studies in the consumption literature have investigated the existence of precautionary saving behavior at the household level. Despite the attention this topic has received, however, a consensus has yet to be reached on the strength of the precautionary saving motive at this level. Dardanoni (1991), Carroll (1994), Carroll and Samwick (1995a, 1995b), and Kazarosian (1997) show precautionary saving behavior to be a significant factor in the accumulation of household wealth. In contrast, Guiso et al (1992) and Dynan (1993) find estimates of only small, negligible precautionary motives. The purpose of this study is to address this discrepancy in the empirical evidence. Using data from the Panel Study of Income Dynamics (PSID), this paper presents an arguably robust test that not only indicates whether households possess precautionary motives, but also provides estimates of the strength of such motives across different households. As is well documented in the theoretical/numerical literature, precautionary saving has several important empirical and policy implications. Skinner (1988) and Caballero(1991) have shown that, with realistic parameter values, precautionary saving is more than half of total life cycle saving. Hubbard et al (1993) demonstrate that the existence of precautionary motives can explain the relatively low saving rates of households nearing retirement. Barsky, Mankiw, and Zeldes (1986) show that if households possess precautionary motives, then government insurance programs and tax policies, which reduce uncertainty about future income, may increase welfare. This study improves on prior empirical research in two important ways. First, we use panel data, as opposed to cross-sectional data, which allows for a more accurate assessment of the fundamental question governing precautionary saving; that is, what is the relationship between consumption and income uncertainty over time? With the exception of Dynan (1993) and Kazarosian (1997), empirical investigations of precautionary saving behaviour at the household level have typically used cross-sectional data to estimate the response of consumption or wealth to income uncertainty. In these studies, income uncertainty is measured by income variances across different household groups. Income variances across households, however, are likely to reflect differences in important demographic characteristics; thus, the response of consumption to such a variable is more likely to reflect interindividual differences than precautionary behavior. The benefit of using panel data is that precautionary saving behavior can be distinguished from

3 such interindividual effects by studying consumption as households experience changes to their income variances over time. 1 The second way this study improves on prior empirical work is by allowing for precaution heterogeneity. Thus far, all empirical research in precautionary saving has assumed that households are homogeneous in their perceptions toward precaution. The consequence of this assumption is to bias any assessment of the magnitude of precautionary saving. In most studies, the strength of the precautionary motive, and thus the magnitude of precautionary saving, is dictated by the coefficient of risk aversion [see Kimball (1990)]. In assuming precaution homogeneity, the coefficient of risk aversion is constrained to be the same for all households. Therefore, magnitudes of precautionary saving across households are solely dictated by differing degrees of income uncertainty. There is no reason to believe, however, that households should be homogeneous in their perceptions toward precaution. To illustrate the potential bias created by such homogeneity, consider Skinner (1988) who showed, according to his parameter values, that salespersons, possessing relatively high income variances, should have relatively high saving rates. He found, however, that this occupation group has relatively low saving rates. He subsequently conjectured that salespersons are likely less prudent than other occupation groups. In addition to allowing for a more accurate assessment of the strength of precautionary motives, precaution heterogeneity permits an investigation of potential life cycle features in precautionary saving behavior. For example, Carroll (1992) conjectured that consumers would switch from buffer-stock saving behavior when young, a form of precautionary saving behavior, to more traditional life-cycle saving behavior as retirement approaches. His conjecture was based on the idea that households would become less impatient as they aged, and therefore less motivated to borrow against their future income, as their income growth rates would begin to fall. In this paper, we investigate the possibility of a life-cycle relationship between saving motives, but focus on the intertemporal elasticity of substitution rather than household impatience as the vehicle. The test proposed in this study yields precise estimates of important precautionary motives across different households. Furthermore, the results identify significant demographic 1 Kazarosian (1997) used panel data in his investigation, specifically the Older Men cohort of the National Longitudinal Survey, but did not allow his measures of income uncertainty to vary over time.

4 characteristics and life cycle features in precautionary saving behavior. In particular, such behavior is shown to be strongly influenced by education, spouse labor supply and age. The remainder of the paper takes the following structure. In Section 2, a model of intertemporal consumption is developed to aid in the development of an empirical test of precautionary saving. In this section, precaution heterogeneity is introduced to allow for the possibility that precautionary saving is influenced by differing degrees of prudence as well as income uncertainty. In Section 3, a description of the data is provided. In Section 4, we present the method used to construct household income uncertainty. In Section 5, we examine the test results, and concluding remarks are presented in Section The Model Our model of intertemporal consumption is setup in standard form. Household i s problem at time t is (1) subject to, (2) where E t represents the expectation conditional on all information available at time t; T represents the time of death; C i,t is consumption, Y i,t is labor income, and A i,t is nonhuman wealth, all in period t; i represents the time preference rate and r i represents the real after-tax interest rate, both of which are assumed nonstochastic and to vary across households. Utility is additive over time, varies across households and is assumed to be continuously differentiable; and labor income is uncertain. Solving the household s problem yields the following first-order condition:. (3) This condition shows that higher levels of saving are linked to greater income uncertainty when the marginal utility of consumption is convex. In other words, the valuation of future

5 consumption rises when income uncertainty increases, for the marginal valuation of consumption is very high when there exists more possible states. As has been demonstrated in the theoretical literature, the existence of precautionary saving behaviour can be assessed by measuring the response of the change in household consumption to changes in the volatility of future labor income [see Caballero (1991)]. Adopting this approach, it is first necessary to make assumptions about the general form of the utility function. I assume that the utility function for each household is of the constant absolute risk aversion (CARA) form, (4) where i is the coefficient of absolute risk aversion for household i. Unlike most previous authors, in addition to allowing the coefficient of risk aversion to vary across households, I also allow it to vary according to movements in demographic and other household characteristics. 2 It is important to note that most studies investigating precautionary saving have avoided the use of CARA utility, for despite its analytical tractability it has been argued to be plagued by a number of dubious properties [see Carroll and Samwick (1995a)]. The particular CARA utility function adopted in (4), however, is immune to much of the common criticism, for the coefficient of absolute risk aversion has been allowed to vary across households. Substituting (4) into equation (3), we get, (5) where for simplicity it has been assumed that r i = i for all i. The final step in relating changes in consumption to the volatility of labor income is to apply a second-order Taylor approximation to condition (5). From Appendix A, such an approximation yields, (6) where C i,t = C i,t - C i,t-1, represents the conditional variance of labor income for household i in time period t, and i,t is the expectation error. If i is positive, then increases in labor income 2. This specification was motivated by the research conducted in Blundell et al (1994).

6 volatility translate into higher consumption growth, which reflects higher saving. The size of i determines the strength of the precautionary saving motive for household i. Therefore, given a measure of conditional labor income volatility, equation (6) suggests a way to assess the strength of the precautionary motive using panel data on consumption. 3. The Data The data for this study come from the Panel Study of Income Dynamics (PSID). They have been used previously by a number of authors including Hall and Mishkin (1982), Zeldes (1989), Carroll (1994) and Carroll and Samwick (1995a,b). The data pose two problems for a study of precautionary saving. First, the only measure of consumption is food consumption, and it has been argued to be measured with error [see Altonji and Siow (1987)]. Second, the frequency of the data is annual where precautionary saving decisions are likely made at a higher frequency. On the other hand, the PSID contains detailed information on income which makes it ideal for a study of precautionary saving. Moreover, the intertemporal model of consumption studied here is one which can really only be applied to food consumption, for it does not explicitly account for the durability of most goods [see Wilson (1998)]. The particular extract used in this paper contains data on labor income, food consumption and demographic characteristics such as education, occupation and age for the years 1981 through 1987 for a balanced panel of 1,280 households who are not part of the poverty subsample of the survey. Since this paper is concerned with how consumption responds to labor income volatility, our criteria for sample selection minimize the amount of income variability not directly attributable to labor market activity. The easiest way to think of linking the PSID data to a model of precautionary saving is to identify the household as the decision-making unit and to examine variability in household non-capital income. Therefore, we excluded from the sample all households which during any time over the sample period had experienced divorce, marriage, a change in household head, the death of a spouse, movers into and out of the family unit other than children, and children older than 18 moving into or out of the household. The sample was further restricted to include only those families whose head was at least 26 years old at the beginning of the sample period and no more than 62 at the end of the period, for which there are valid data on occupation, education, food consumption and disposable labor income.

7 Food consumption was computed as the sum of food consumption at home and food consumption away from home with nominal values deflated by the appropriate CPI component. Real disposable labor income was calculated as total family labor income, minus taxes and plus transfers, deflated by the personal consumption expenditures deflator from the National Income and Product Accounts. A more detailed breakdown of the variables used in this study is given in Appendix B. 4. Method for Estimating Labor Income Uncertainty This section presents the method for estimating labor income uncertainty of households included in the PSID sample. As noted in Section 2, the measure of labor income uncertainty adopted in this study is the conditional variance of labor income. To obtain this measure, we assume that the disposable labor income of household i at time period t can be described by the following model:, (7a), (7b) where v i,t is standard normal, and are constants, and are 1 K 1 and 1 K 2 vectors of constants, respectively, Z and W are 1 K 1 and 1 K 2 vectors of known exogenous variables, and the error term, u i,t, is assumed to possess the following properties: and (8a) (8b) The vectors of known exogenous variables, Z and W, are given by, (9a), (9b) where D is a set of dummy variables indicating the education, occupation, and race of the

8 household head; age i,t indicates the age of household head i in year t, and unmpl i,t indicates the total amount of unemployment hours of household head i in year t. This structure, as given by (9a) and (9b), allows for different age/income, age/uncertainty and unemployment/uncertainty profiles for each combination of occupation, education, and race. 3 Given (9a) and (9b), equations (7a) and (7b) can be estimated by Maximum Likelihood (ML), yielding, where hats denote estimated values, which can then be used to assess precautionary saving behavior. Tables 1A and 1B present the results from estimating (7) using the data described in Section 3. The most notable feature of this estimation are the parameter estimates of the conditional variance equation. Reported in Table 1B, these estimates strongly support the use of this method as a way of constructing labor income volatility. Nevertheless, a likelihood ratio test was performed to better guarantee the validity of this approach. The test strongly rejected the null hypothesis that with a statistic of which is significant at the 1 percent level. 5. Results 5.A Conventional Specification As noted above, all previous empirical studies of precautionary saving have assumed that households are homogeneous in their perceptions toward risk. In terms of a panel analysis of precautionary saving, this assumption amounts to restricting equation (6) by running the following pooled regression:, (10) where is constrained to be the same for all households. Using the conditional variance of labor income generated in the previous section, we estimate equation (10) employing ordinary least squares (OLS). 4 The results of this estimation are summarized in Table 2. According to the pooled regression, income uncertainty affects consumption growth positively and appears to be an 3. Estimation of (7a) and (7b) did not include interactions of the race dummy with age, age 2 and total unemployment hours, for the coefficients on those interactions were insignificant. 4. In practice, all regressions testing precautionary saving did not include intercept coefficients because all such coefficients were insignificant in unconstrained versions of equations (6) and (10).

9 important determinant of saving behavior: The coefficient of risk aversion,, has an estimated value of and is significant at the 1% level. This estimate strongly supports the precautionary saving hypothesis, that is, households with greater income volatility save more. In addition to exhibiting statistical significance, the estimated magnitude of the coefficient of CARA reveals a potentially strong precautionary motive. Babcock et al (1993), using risk premiums and probability premiums to compute comparison ranges for the coefficient of CARA, found that when $10,000 is at risk, a coefficient of CARA taking a value of is associated with a risk premium of 20%. In other words, if $10,000 of a household s annual labor income is at risk, then 20% or $2,000 of that amount will be held as a precaution against such risk. This suggests that precautionary saving comprises 63% of total saving for a family with an annual labor income of $40,000, $10,000 of which is at risk, and a saving rate of 8%. Babcock et al (1993) also show that the risk premium declines as the amount of risk decreases; for example, when the amount of risk decreases to $1,000 a coefficient of CARA taking a value of is associated with a risk premium of only 2%. A modified version of the comparison ranges for the coefficient of CARA computed by Babcock et al (1993) is provided in Table 3. By varying the degrees of risk, saving rates and annual household income, it is clear from this table that for those households facing relatively substantial labor income uncertainty, precautionary saving comprises a significant proportion of total saving, thus indicating strong precautionary motives. However, for households whose labor incomes are moderately to less than moderately uncertain, precautionary saving is small to negligible. 5B Risk Heterogeneity It is the contention of this paper that the restriction imposed by the pooled regression is unnecessary and that by relaxing such constraint a more accurate and thorough assessment of precautionary saving can be conducted. To test the validity of the constraint, we estimate equation (10) for each household and then perform an F-test [see Hsiao (1993)]. 5 The test, rejecting the pooling hypothesis with a statistic of 3.3 which is significant at the 1% level, strongly supports treating households has heterogeneous in their perceptions toward precaution. The rest of this section sets out to determine whether precautionary saving behavior is 5. Substantial pretesting of unconstrained versions of equation (3.6) failed to ever find significant intercepts.

10 influenced by household or other demographic characteristics and whether such behavior displays movements over the life cycle. Because this paper is concerned with the population at large, the following stochastic-parameter model with systematic components is adopted to carry out the rest of this study [see Amemiya (1978) and Hendricks et al (1979)]:, (11a), (11b) where denotes the conditional variance of labor income generated in section 4, X i and are a 1 M vector of known constants and a M 1 vector of unknown constants, respectively, and i,t and i are unobservable random variables. The vector X includes dummy variables for education, age and spouse labor supply. Equations (11a) and (11b) are estimated by generalized least squares employing Amemiya s (1978) two-step procedure. The results are summarized in Table 2. According to these estimates, precautionary saving behavior is significantly influenced by household and other demographic characteristics. Except for the estimate on the age dummy for households between 33 and 39 years old, all estimates are significant at the 5% level. From the estimates on the education dummies, a clear pattern is exhibited: The higher the educational attainment, the greater is the degree of precaution. This pattern is quite intuitive. Generally, we can think of there existing a positive relationship between an individual s educational attainment and the quality of the job one possesses, where job quality is a function of both wages and job security. It is thus reasonable to infer that a household which chooses a high level of education in order to obtain greater job security will act as prudently in its saving decisions. In addition to the evidence from the estimates on the education dummies, the estimates on the age dummies clearly identify life-cycle effects in precautionary saving behavior. The results indicate that the intertemporal elasticity of substitution for each household increases as the household ages, in other words, as households age they become more willing to shift their consumption between different periods. This result is particularly interesting, for it would appear to identify a life-cycle relationship between precautionary motives to save and more traditional life-cycle motives. More specifically, this finding suggests that as households get closer to

11 retirement, saving begins to take on a more traditional life-cycle role than a precautionary one. One reason for this transformation might be the reality of retirement, that is, assuming precautionary wealth is held in highly liquid, short term assets, households, as they approach preretirement years, become more willing to accept larger swings in their consumption to take advantage of better-return saving opportunities. This would be particularly true of those households with strong precautionary motives earlier in life. Lastly, the estimate on the spouse labor supply dummy, a variable included to differentiate between one-earner and two-earner households, indicates that households with working spouses are more prudent than households with either no spouses, or households with spouses that do not work. This finding is consistent with Blundell et al (1994), who found a similar effect, and with the evidence from the literature on intra-family risk sharing which demonstrates that many households choose a two-earner regime in order to minimize household consumption variability. In addition to identifying the effects that household and other demographic characteristics have on precautionary saving behavior, the results from estimating equations (11a) and (11b) reveal important precautionary motives across different households. To illustrate this importance, I consider two household types: A high income risk household, with an educational attainment of a high school diploma; and a low income risk household, with an educational attainment of a college degree. In both cases, the age of the household head is between 33 and 39 years old, and spouses are assumed to work. Furthermore, the high-risk household is assumed to have a saving rate of 6% with an annual labor income of $30,000, and the low-risk household is assumed to have a saving rate of 10% with an annual labor income of $60,000. From Table 2, the estimated coefficient of CARA for the high-risk household is and the estimated coefficient of CARA for the low-risk household is According to Babcock et al (1993), for the high-risk household, when 17% of annual labor income is at risk, a coefficient of CARA equal to is associated with a risk premium of 34%. For the low-risk household, when 8% of annual labor income is at risk, a coefficient of CARA equal to is associated with a risk premium of 36%. Given the saving rates assumed for these two household types, it follows that precautionary saving comprises 94% of total saving for the high-risk household and 32% for the low-risk household. These two computed magnitudes of precautionary saving clearly identify strong precautionary motives. In particular, even for a household facing little income uncertainty,

12 namely a household with high educational attainment, the precautionary motive is an important part of consumer behavior. 6. Conclusion This paper uses the Panel Study of Income Dynamics to test for precautionary saving motives, improving on previous studies by using panel data and allowing for risk heterogeneity which permits an investigation of potential household and other demographic influences on precautionary saving behavior. The test yields precise estimates of important precautionary motives across different households, where the strength of such motives depend not only on the varying degrees of labor income uncertainty, but on the varying magnitudes of risk aversion as well. More specifically, this study finds that the degree of household precaution, and thus the strength of the precautionary motive, is positively related to a household s educational attainment, that is, the greater is a household s education the stronger is their precautionary motive. Furthermore, this study identifies clear life-cycle effects in precautionary saving behavior, where households are found to be less prudent as they approach retirement. Lastly, computed magnitudes of precautionary saving, reported as proportions of total household saving, indicate that precautionary motives are significant determinants of consumer behavior, even for those households facing relatively small income risks.

13 References Altonji, Joseph G., and Aloysius Siow, Testing the Response of Consumption to Income Changes with (Noisy) Panel Data, Quarterly Journal of Economics, vol. 102, p , Amemiya, T., A Note on a Random Coefficients Model, International Economic Review, vol. 19, p , Babcock, Bruce A., E. Kwan Choi, and Eli Feinerman, Risk and Probability Premiums for CARA Utility Functions, Journal of Agricultural and Resource Economics, vol. 18, p , Barsky, R. B., N. G. Mankiw and S. P. Zeldes, "Ricardian Consumers with Keynesian Propensities," American Economic Review, vol. 76, p , Blundell, Richard, Martin Browning and Costas Meghir, "Consumer Demand and the Life-Cycle Allocation of Household Expenditures," Review of Economic Studies, vol. 61, p , Caballero, Ricardo J., Earnings Uncertainty and Aggregate Wealth Accumulation, American Economic Review, vol. 81, p , Carroll, Christopher D., "The Buffer-Stock Theory of Saving: Some Macroeconomic Evidence, Brookings Papers on Economic Activity, no. 2, p , Carroll, Christopher D., "How Does Future Income Affect Current Consumption," Quarterly Journal of Economics, vol. 109, p , Carroll, Christopher D., and Andrew A. Samwick, (a), "How Important is Precautionary Saving?" Review of Economics and Statistics, vol. 80, no. 3, p , Carroll, Christopher D., and Andrew A. Samwick, (b), "The Nature of Precautionary Wealth," Journal of Monetary Economics, vol. 40, no. 1, p , Dardanoni, Valentino, "Precautionary Savings Under Income Uncertainty: A Cross-Sectional Analysis," Applied Economics, vol. 23, p , Dynan, Karen E., "How Prudent are Consumers," Journal of Political Economy, vol. 101, p , Guiso, Luigi, Tullio Jappelli and Daniele Terlizzese, "Earnings Uncertainty and Precautionary Saving," Journal of Monetary Economics, vol. 30, p , 1992.

14 Hall, Robert E., and Frederic S. Mishkin, The Sensitivity of Consumption to Transitory Income: Estimates from Panel Data on Households, Econometrica, vol. 50, p , Hendricks, W., R. Koenker, and D. J. Poirier, Residential Demand for Electricity: An Econometric Approach, Journal of Econometrics, vol. 9, p , Hsiao, Cheng, Analysis of Panel Data. Cambridge University Press, Cambridge Hubbard, R., Jonathan Skinner and Stephen P. Zeldes. "The Importance of Precautionary Motives for Explaining Individual and Aggregate Saving," In Carnegie-Rochester Conference Series on Public Policy, edited by Allan H. Meltzer and Charles I. Plosser, Kazarosian, Mark, Precautionary Saving A Panel Study, Review of Economics and Statistics, vol. 79, no. 2, p , Kimball, Miles S., "Precautionary Saving in the Small and in the Large," Econometrica, vol. 58, p , Skinner, Jonathan, "Risky Income, Life-Cycle Consumption, and Precautionary Saving," Journal of Monetary Economics, vol. 22, p , Wilson, Bradley K., The Aggregate Existence of Precautionary Saving: Time-Series Evidence from Expenditures on Nondurable and Durable Goods, Journal of Macroeconomics, vol. 20, no. 2, p , Zeldes, Stephen P., "Optimal Consumption with Stochastic Income: Deviations from Certainty Equivalence," Quarterly Journal of Economics, vol. 104, p , 1989.

15 Appendix A This appendix shows the details of the closed-form approximation, as presented in equation (6), relating revisions in consumption to the conditional variance of labor income. Following Skinner (1988), the solution to the T-period consumption problem begins with the choice of total consumption in the next to last period. Substituting equation 2 into equation 5 and noting that exp(- i C i,t ) = exp(- i A i,t ), since C i,t = A i,t, yields (A1) The right hand side of (A1) can be expressed as second-order Taylor-series approximation evaluated at the mean of Y i,t, denoted as, conditional on information known at T-1. Note that a second-order expansion of the Euler equation involves a third-order expansion of the utility function, a step beyond quadratic utility. Let the right hand side of (A1) be denoted as Then the expectation of the second-order Taylor-series approximation of J is (A2), (A3) where rearranging yields,,,,. (A4)

16 Letting C i,t = C i,t - C i,t-1 and i,t = text:, equation (A4) becomes equation 6 in the. (A5)

17 Appendix B study. This appendix provides a more detailed breakdown of the data and variables used in this Variables for Household and Labor Market Characteristic Variable Description Comment Age Age of household head in years Sample mean is 38.8 Age 2 Square of age Unmpl Total annual hours of unemployment Sample mean is 83.6 annual hours Indicator Variables for Household and Labor Market Characteristic Variable Description Percent of Sample Default Households with heads 28 to 32 years of age in % A2 Households with heads 33 to 39 years of age in % A3 Households with heads 40 to 49 years of age in % A4 Households with heads 50 to 59 years of age in % SLH Whether spouse worked any time over the sample period 71% (work) Race Race indicator- equal to 1 if white and 0 otherwise 71% (white) Indicator Variables for Education used in section 5 Variable Description Percent of Sample Default Grades 0 through 11 by % E2 High School diploma by % E3 Vocational training and/or some college by % E4 College degree by % E5 Advanced education/professional training by %

18 Variables for Education used in section 4 Variable Description Percent of Sample Default Grades 0 through % ED2 High School diploma 19.7% ED3 Vocational training and/or some college 36.3% ED4 College degree 17.3% ED5 Advanced education/professional training 8.2% Indicator Variables for Occupation Variable Description Percent of Sample Default Not working at time of interview 9.7% O2 Professional, technical 20.3% O3 Managers and administrators 15.2% O4 Sales workers 1.9% O5 Clerical 7.2% O6 Craftsmen 17.5% O7 Operatives (non transportation) 8.2% O8 Transportation operatives 5.1% O9 Laborers (non farm) 3.0% O10 Farmers 0.6% O11 Farm laborers 0.7% O12 Service worker 6.7%

19 Tables Variable TABLE 1A Point Estimates, Standard Errors and t-statistics for the Mean Equation of Disposable Labor Income Estimated Coefficient Standard Error t- statistic Variable Estimated Coefficient Standard Error t- statistic Intercept Age 2 ED Age Age 2 ED Age Age O ED Age O ED Age O ED Age O ED Age O Race Age O O Age O O Age O O Age O O Age O O Age O O Age 2 O O Age 2 O O Age 2 O O Age 2 O O Age 2 O O Age 2 O Age ED Age 2 O Age ED Age 2 O Age ED Age 2 O Age ED Age 2 O Age 2 ED Age 2 O Age 2 ED No te. O2 through O12 and ED2 through ED5 are dummy variables for membership in each of the 12 occupational or 5 education-level groups defined in Appendix B.

20 TABLE 1B Point Estimates, Standard Errors and t-statistics for the Conditional Variance of Disposable Labor Income Variable Estimated Coefficient Standard Error t-statistic Variable Estimated Coefficient Standard Error t-statistic Intercept Age O Age Age O Age Age O ED Age O ED Age O ED4-1e Age 2 O ED5-10e Age 2 O Race Age 2 O O Age 2 O O3-1e Age 2 O O Age 2 O O Age 2 O O Age 2 O O Age 2 O O Age 2 O O9-4e Age 2 O O Unmpl O11-1e Unmpl ED O Unmpl ED Age ED Unmpl ED Age ED Unmpl ED Age ED Unmpl O Age ED Unmpl O Age 2 ED Unmpl O Age 2 ED Unmpl O Age 2 ED Unmpl O Age 2 ED Unmpl O Age O Unmpl O Age O Unmpl O Age O Unmpl O Age O Unmpl O Age O Unmpl O Age O No te. O2 through O12 and ED2 through ED5 are dummy variables for membership in each of the 12 occupational or 5 education-level groups defined in Appendix B. Unmpl, also defined in Appendix B, represents the total number of hours of unemployment.

21 Variables TABLE 2 Regressions of Consumption Growth on Conditional Income Volatility Regressions Estimated coefficient Pooled Regression* Standard error t-statistic Unconstrained Regression Estimated coefficient Standard error t-statistic Intercept E E E E A A A SLH * The F-test of the restriction imposed by the pooled regression yielded a test statistic of F 1279,6400 = 3.3, which is significant at the 1% level. Note. E2 through E5 and A2 through A4 are dummy variables for membership in each of the 5 education-level or 4 age groups defined in Appendix B. SLH, also defined in Appendix B, is dummy variable for spousal labor supply, taking a value of 1 if the spouse worked during any time over the sample period and 0 otherwise.

22 TABLE 3 Risk Premiums, Probability Premiums and Constant Absolute Risk-Aversion Coefficients computed by Babcock et al (1993) Coefficient of CARA Coefficient of CARA Risk Premium Probability Premium h = $10,000 h = $5,000 h = $1,000 Risk Premium Probability Premium h = $10,000 h = $5,000 h = $1, No te. h represents the amount of labor income at risk. This table is a modified version of that which appears in Babcock et al (1993).