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 55105-1096. Tel.: 651-962-5688; fax.: 651-962-5682; email: 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.
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
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.
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 6.
2. 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 Et represents the expectation conditional on all information available at time t; T represents
the time of death; Ci,t is consumption, Yi,t is labor income, and Ai,t is nonhuman wealth, all in
period t; $i represents the time preference rate and ri 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:
.
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
(3)
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 Di 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 ri = $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
,
where )Ci,t = Ci,t - Ci,t-1,
(6)
represents the conditional variance of labor income for household i
in time period t, and ,i,t is the expectation error. If Di is positive, then increases in labor income
2. This specification was motivated by the research conducted in Blundell et al (1994).
volatility translate into higher consumption growth, which reflects higher saving. The size of Di
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.
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. M ethod 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 vi,t is standard normal, " and 0 are constants, ( and 2 are 1 × K1 and 1 × K2 vectors of
constants, respectively, Z and W are 1 × K1 and 1 × K2 vectors of known exogenous variables,
and the error term, ui,t , is assumed to possess the following properties:
and
(8a)
(8b)
The vectors of known exogenous variables, Z and W, are given by
,
(9a)
,
where D is a set of dummy variables indicating the education, occupation, and race of the
(9b)
household head; agei,t indicates the age of household head i in year t, and unmpli,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 602.0 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 D 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, age2 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).
important determinant of saving behavior: The coefficient of risk aversion, D, has an estimated
value of 0.00004 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 0.00004 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 0.00004 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.
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)]:
,
,
where
(11a)
(11b)
denotes the conditional variance of labor income generated in section 4, Xi and N
are a 1 × M vector of known constants and a M × 1 vector of unknown constants, respectively,
and ,i,t and 8i 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
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 0.00015 and the estimated
coefficient of CARA for the low-risk household is 0.00016. 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 0.00015 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 0.00016 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,
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.
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. 293 328, 1987.
Amemiya, T., “A Note on a Random Coefficients Model,” International Economic Review, vol.
19, p. 793 - 6, 1978.
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.
17 - 24, 1993.
Barsky, R. B., N. G. Mankiw and S. P. Zeldes, "Ricardian Consumers with Keynesian
Propensities," American Economic Review, vol. 76, p. 676 - 91, 1986.
Blundell, Richard, Martin Browning and Costas Meghir, "Consumer Demand and the Life-Cycle
Allocation of Household Expenditures," Review of Economic Studies, vol. 61, p. 57 - 80,
1994.
Caballero, Ricardo J., “Earnings Uncertainty and Aggregate Wealth Accumulation,” American
Economic Review, vol. 81, p. 859 - 71, 1991.
Carroll, Christopher D., "The Buffer-Stock Theory of Saving: Some Macroeconomic
Evidence,” Brookings Papers on Economic Activity, no. 2, p. 61 - 135, 1992.
Carroll, Christopher D., "How Does Future Income Affect Current Consumption," Quarterly
Journal of Economics, vol. 109, p. 111 - 48, 1994.
Carroll, Christopher D., and Andrew A. Samwick, (a), "How Important is Precautionary
Saving?" Review of Economics and Statistics, vol. 80, no. 3, p. 410 - 419, 1998.
Carroll, Christopher D., and Andrew A. Samwick, (b), "The Nature of Precautionary Wealth,"
Journal of Monetary Economics, vol. 40, no. 1, p. 41 - 71, 1997.
Dardanoni, Valentino, "Precautionary Savings Under Income Uncertainty: A Cross-Sectional
Analysis," Applied Economics, vol. 23, p. 153 - 60, 1991.
Dynan, Karen E., "How Prudent are Consumers," Journal of Political Economy, vol. 101, p.
1104 - 13, 1993.
Guiso, Luigi, Tullio Jappelli and Daniele Terlizzese, "Earnings Uncertainty and Precautionary
Saving," Journal of Monetary Economics, vol. 30, p. 307 - 37, 1992.
Hall, Robert E., and Frederic S. Mishkin, “The Sensitivity of Consumption to Transitory Income:
Estimates from Panel Data on Households,” Econometrica, vol. 50, p. 461 - 81, 1982.
Hendricks, W., R. Koenker, and D. J. Poirier, “Residential Demand for Electricity: An
Econometric Approach,” Journal of Econometrics, vol. 9, p. 33 - 57, 1979.
Hsiao, Cheng, Analysis of Panel Data. Cambridge University Press, Cambridge. 1993.
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,
1993.
Kazarosian, Mark, “Precautionary Saving–A Panel Study,” Review of Economics and Statistics,
vol. 79, no. 2, p. 241 - 247, 1997.
Kimball, Miles S., "Precautionary Saving in the Small and in the Large," Econometrica, vol. 58,
p. 53 - 73, 1990.
Skinner, Jonathan, "Risky Income, Life-Cycle Consumption, and Precautionary Saving," Journal
of Monetary Economics, vol. 22, p. 237 - 55, 1988.
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. 309 - 323, 1998.
Zeldes, Stephen P., "Optimal Consumption with Stochastic Income: Deviations from Certainty
Equivalence," Quarterly Journal of Economics, vol. 104, p. 273 - 98, 1989.
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(-Di Ci,T ) = exp(-Di Ai,T ), since Ci,T = Ai,T , yields
(A1)
The right hand side of (A1) can be expressed as second-order Taylor-series approximation
, conditional on information known at T-1. Note
evaluated at the mean of Yi,T , denoted as
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
(A2)
Then the expectation of the second-order Taylor-series approximation of J is
,
(A3)
where rearranging yields
,
Y
,
Y
Y
Y
,
,
.
(A4)
Letting )Ci,T = Ci,T - Ci,T-1 and ,i,T =
, equation (A4) becomes equation 6 in the
text:
.
(A5)
Appendix B
This appendix provides a more detailed breakdown of the data and variables used in this
study.
Variables for Household and Labor Market Characteristic
Variable
Age
Age2
Unmpl
Description
Age of household head in years
Square of age
Total annual hours of unemployment
Comment
Sample mean is 38.8
Sample mean is 83.6 annual hours
Indicator Variables for Household and Labor Market Characteristic
Variable Description
Percent of
Sample
Default
A2
A3
A4
SLH
Race
29.1%
35.2%
18.9%
16.7%
71% (work)
71% (white)
Households with heads 28 to 32 years of age in 1984
Households with heads 33 to 39 years of age in 1984
Households with heads 40 to 49 years of age in 1984
Households with heads 50 to 59 years of age in 1984
Whether spouse worked any time over the sample period
Race indicator- equal to 1 if white and 0 otherwise
Indicator Variables for Education used in section 5
Variable Description
Default Grades 0 through 11 by 1987
E2
High School diploma by 1987
E3
Vocational training and/or some college by 1987
E4
College degree by 1987
E5
Advanced education/Professional training by 1987
Percent of Sample
18.3%
19.6%
34.1%
17.8%
10.0%
Variables for Education used in section 4
Variable Description
Percent of Sample
Default Grades 0 through 11
18.2%
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%
Tables
TABLE 1A
Point Estimates, Standard Errors and t-statistics for the Mean Equation
of Disposable Labor Income
Variable
Estimated
Coefficient
Standard
Error
tstatistic
Variable
Estimated
Coefficient
Standard
Error
tstatistic
Intercept
30405
10843
2.8
Age2×ED4
-74
13
-5.7
Age
-916
507
-1.8
Age2×ED5
-57
17
-3.3
Age2
11
6
1.9
Age×O2
195
648
0.30
ED2
-1917
11566
-0.17
Age×O3
4284
1093
3.9
ED3
-38824
10439
-3.7
Age×O4
1637
3679
0.44
ED4
-126412
21350
-5.9
Age×O5
205
923
0.22
ED5
-96619
28864
-3.3
Age×O6
2454
681
3.6
Race
6923
297
23.3
Age×O7
1275
822
1.6
O2
6536
13287
0.49
Age×O8
1473
955
1.5
O3
-72780
22107
-3.3
Age×O9
4176
1528
2.7
O4
-9142
80653
-0.11
Age×O10
727
2290
0.32
O5
1131
18693
0.06
Age×O11
2373
980
2.4
O6
-38274
13830
-2.8
Age×O12
2564
811
3.2
O7
-18351
16125
-1.1
Age2×O2
-0.07
8
-0.01
O8
-17764
20159
-0.88
Age2×O3
-43
12
-3.5
O9
-67606
28398
-2.4
Age2×O4
-20
41
-0.50
O10
-9815
49354
-0.20
Age2×O5
-0.64
11
-0.06
O11
-55860
20656
-2.7
Age2×O6
-26
8
-3.2
O12
-46079
16928
-2.7
Age2×O7
-13
10
-1.3
Age×ED2
481
559
0.86
Age2×O8
-15
11
-1.4
Age×ED3
2436
507
4.8
Age2×O9
-52
19
-2.7
Age×ED4
6817
1089
6.3
Age2×O10
-11
26
-0.40
Age×ED5
5380
1452
3.7
Age2×O11
-24
11
-2.2
Age2×ED2
-8
7
-1.2
Age2×O12
-30
9
-3.3
Age2×ED3
-29
6
-4.9
No te. O2 through O1 2 and E D2 through ED 5 are du mmy va riables for membership in each of the 12 occupational or 5 edu cation-level groups
defined in Appendix B.
TABLE 1B
Point Estimates, Standard Errors and t-statistics for the Conditional
Variance of Disposable Labor Income
Va riable
Estimated
Co efficient
Standard
Error
t-statistic
Va riable
Estimated
Co efficient
Standard
Error
t-statistic
Intercept
698293587
122546053
5.7
A ge× O 8
-4431966
10945496
-0.40
Age
-24179971
5535017
-4.4
A ge× O 9
180300928
18315841
9.8
Age
2
237412
59377
4.0
Age×O10
-156340333
53433429
-2.9
ED2
-380661531
120978466
-3.1
Age×O11
41635928
8598453
4.8
ED3
-729545778
121808623
-6.0
Age×O12
48541465
11547818
4.2
ED4
-1e+10
386094739
-29 .5
Age 2 × O 2
1662903
70599
23 .6
ED5
-10e+09
399792962
-24 .0
Age 2 × O 3
-5677965
221865
-25 .6
2
Ra ce
86401469
2192305
39 .4
Age × O 4
-479174
640651
-0.74
O2
281117697
124860702
22 .5
Age 2 × O 5
171665
135720
1.3
2
O3
-1e+10
400545002
-25 .8
Age × O 6
334848
98630
3.4
O4
269312345
155938084
1.7
Age 2 × O 7
260520
153852
1.7
2
O5
332425865
234001390
1.4
Age × O 8
49875
135316
0.37
O6
138951048
163812503
0.85
Age 2 × O 9
-2158107
230512
-9.4
1713149
552742
3.1
O7
64566159
235491006
0.27
2
Age ×O10
2
O8
109931911
215942202
0.51
Age ×O11
-453924
98080
-4.6
O9
-4e+09
345071380
-10 .2
Age 2 ×O12
-556136
125904
-4.4
O10
327375932
127610404
2.6
Unmpl
-45645
7687
-5.9
O11
-1e+09
179333102
-5.8
U nm pl× E D 2
-22656
13812
-1.6
O12
-999788289
250571889
-4.0
U nm pl× E D 3
25411
18152
1.4
A ge× E D 2
23280425
5720027
4.1
U nm pl× E D 4
-335348
17885
-18 .8
A ge× E D 3
36761055
5850723
6.3
U nm pl× E D 5
-305525
436623
-0.70
A ge× E D 4
553255259
20221579
27 .3
U nm pl× O 2
180393
27241
6.6
A ge× E D 5
484443334
22941000
21 .1
U nm pl× O 3
-161774
246014
-0.66
Age 2 × E D 2
-281014
64193
-4.4
U nm pl× O 4
207188
18524
11 .2
2
Age × E D 3
-377257
66768
-5.7
U nm pl× O 5
-2076
55162
-0.04
Age 2 × E D 4
-5826262
249913
-23 .3
U nm pl× O 6
140745
64931
2.2
2
Age × E D 5
-5242048
322872
-16 .2
U nm pl× O 7
25614
30270
0.85
A ge× O 2
-143871023
6098009
-23 .6
U nm pl× O 8
-39739
71677
-0.55
A ge× O 3
514475640
20096699
25 .6
U nm pl× O 9
-38083
19239
-2.0
A ge× O 4
-24957541
63636583
-0.39
Unmpl×O10
-183906
181056
-1.0
A ge× O 5
-15757897
11595087
-1.4
Unmpl×O11
113099
15820
7.1
A ge× O 6
-17901583
8077559
-2.2
Unmpl×O12
-55393
19805
-2.8
A ge× O 7
-13130524
12243860
-1.1
No te. O2 through O1 2 and E D2 through ED 5 are du mmy va riables for membership in each of the 12 occupational or 5 edu cation-level groups
defined in A ppend ix B . Unm pl, also de fined in Ap pendix B , represents the to tal nu mber of hou rs of unem ploym ent.
TABLE 2
Regressions of Consumption Growth on Conditional Income Volatility
Variables
Regressions
Pooled Regression*
Estimated
coefficient
Standard
error
t-statistic
0.00004
0.000014
2.75
Unconstrained Regression
Estimated
coefficient
Standard
error
t-statistic
Intercept
0.000037
0.000015
2.41
E2
0.000085
0.000015
5.74
E3
0.000087
0.000013
6.55
E4
0.000091
0.000015
5.95
E5
0.000099
0.000018
5.46
A2
-0.0000015
0.0000011
-1.31
A3
-0.000013
0.0000014
-9.47
A4
-0.000017
0.0000014
-12.21
SLH
0.000048
0.000010
4.70
* T he F -test o f the r estrictio n im posed b y th e po oled reg ression y ield ed a test stati stic o f F 1 2 7 9 ,6 4 0 0 = 3 .3, w hich i s significa nt a t 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 App endix B , is dum my v aria ble for spou sal lab or sup ply, tak ing a v alu e of 1 if the spou se work ed du ring a ny tim e over the sam ple
period and 0 otherwise.
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
Prob ability
Premium
h=
$10,000
h=
$5,000
h=
$1,000
Risk
Premium
Prob ability
Premium
h=
$10,000
h=
$5,000
h=
$1,000
.02
.010001
.000004
.000008
.000040
.50
.271844
.000122
.000243
.001219
.04
.020011
.000008
.000016
.000080
.52
.284599
.000129
.000258
.001293
.06
.030036
.000012
.000024
.000120
.54
.297559
.000137
.000274
.001371
.08
.040086
.000016
.000032
.000161
.56
.310723
.000146
.000290
.001455
.10
.050167
.000020
.000040
.000201
.58
.324082
.000154
.000308
.001544
.12
.060289
.000024
.000048
.000242
.60
.337622
.000164
.000328
.001641
.14
.070460
.000028
.000057
.000284
.62
.351322
.000175
.000349
.001745
.16
.080687
.000033
.000065
.000326
.64
.365149
.000186
.000371
.001859
.18
.090980
.000037
.000074
.000368
.66
.379055
.000198
.000396
.001984
.20
.101347
.000041
.000082
.000411
.68
.392977
.000212
.000426
.002122
.22
.111797
.000046
.000091
.000455
.70
.406826
.000227
.000455
.002276
.24
.122338
.000050
.000099
.000500
.72
.420486
.000245
.000489
.002449
.26
.132980
.000055
.000109
.000545
.74
.433806
.000265
.000529
.002647
.28
.143731
.000059
.000118
.000592
.76
.446590
.000287
.000574
.002875
.30
.154601
.000064
.000127
.000639
.78
.458600
.000314
.000628
.003142
.32
.165599
.000069
.000137
.000688
.80
.469552
.000346
.000692
.003461
.34
.176735
.000074
.000147
.000739
.82
.479129
.000385
.000769
.003848
.36
.188017
.000079
.000158
.000791
.84
.487018
.000433
.000866
.004331
.38
.199456
.000084
.000168
.000845
.86
.492971
.000495
.000990
.004951
.40
.211060
.000090
.000180
.000901
.88
.496909
.000578
.001155
.005776
.42
.222837
.000096
.000191
.000959
.90
.499024
.000693
.001386
.006932
.44
.234798
.000102
.000203
.001019
.92
.499827
.000866
.001732
.008664
.46
.246948
.000108
.000216
.001082
.94
.499990
.001155
.002302
.011553
.48
.259295
.000115
.000229
.001149
.96
.500000
.001733
.002441
.017329
No te. h represents the amou nt of labor income at risk. This table is a modified version of that which appears in Babcock et al (199 3).