imperfect insurance and differing propensities to consume across households

ELSEVIER Journal of Monetary Economics 36 (19951 301 327

JOURNALOF Monetary ECONOMICS

Imperfect insurance and differing propensities to consume across households

Jonathan McCarthy Federal Reserve Bank of New York, New York, N Y 10045, USA

(Received March 1992; final version received August 1995)

Abstract

This paper extends previous tests of consumption insurance by splitting the sample to examine whether the marginal propensity to consume (M PC) out of idiosyncratic income shocks is larger for low-wealth households than it is for high-wealth households. Using data from the PSID, I find: (1) The M P C of low-wealth households is higher than that of high-wealth households. There are indications that both precautionary savings behavior and liquidity constraints contribute to this difference. (2) Splitting the data using two different measures of wealth indicates that households perceive housing equity as illiquid. (3) When low-wealth households are split into two subgroups, the M P C of the very-low- wealth group is smaller, reflecting the insurance aspects of means-tested safety-net programs.

Key words: Precautionary savings; Liquidity constraints; Marginal propensity to consume

J E L class!fication: E21; D91

This is a substantially revised version of the last essay of my Ph.D. dissertation at the University of Wisconsin-Madison. I would like to thank the members of my committee Mark Gertler, Tom Holmes, and Ken West for their patience and guidance. I would also like to thank John Cochrane. Charles Steindel, Michael Boldin, Patricia Mosser, Brock Blomberg, the referee and editor, and seminar participants at the University of Wisconsin Madison and the New York Fed for their comments and suggestions. All errors remaining are solely my responsibility. The views expressed herein are my own and do not reflect those of the Federal Reserve Bank of New York nor the Federal Reserve System.

0304-3932/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0 3 0 4 3 9 3 2 9 5 0 1 2 1 4 9

302 .Z McCarthy~Journal of Monetary Economics 36 (1995) 301-327

1. Introduction

This paper investigates the capability of households to insure their consumption against income shocks such as losing a job, the differences across households in this capability, and the implications of any such differences for the marginal propensity to consume (MPC) out of individual income shocks. Among the questions which I at tempt to answer are: (1) How much insurance to households is provided by institutions such as asset markets, medical and disability insurance, unemployment insurance, etc.? (2) How does the capability to insure vary across households? (3) Is the MPC of poorer households larger than that of richer households?

Whether households can insure against personal income risks has important macroeconomic consequences. For example, Lucas' (1987) calculation of the welfare costs of business cycles uses a model of a representative agent subject to aggregate shocks only. However, the losses from a recession, and thus concerns about mitigating its effects, may be greater than Lucas' calculation if income decreases are concentrated on a portion of the population who cannot insure those risks.

Whether households differ in their capability to insure and in their MPCs also has significant macroeconomic consequences. For example, suppose that low- wealth households cannot insure as well as high-wealth households. This difference across households implies that an income shock affects the consumption of low-wealth households more than the consumption of high-wealth households; that is, the MPC of low-wealth households is higher. Under this circumstance, an income shock which is concentrated on low-wealth households has a greater effect on aggregate consumption than a shock concentrated on high-wealth households, even if each shock has the same effect on aggregate income.

To investigate whether households are insured against idiosyncratic shocks, this paper uses a test developed by Cochrane (1991). 1 The test is based on the observation that if insurance is perfect only aggregate shocks affect a household's consumption and so its propensity to consume out of an idiosyncratic shock to income is zero. Using this test, Cochrane rejects the perfect insurance hypothesis; however, he did not investigate whether households differ in their capability to insure against these shocks.

This paper splits households in the sample according to their wealth and uses Cochrane's test to examine whether low-wealth and high-wealth households differ in their M P C out of individual income shocks. I believe this provides some

1Similar tests have been done by Mace (1988, 1991), who uses panel data from the U.S. Consumer Expenditure Survey, and Townsend (1989), who uses panel data from village India. Abel and Kotlikoff (1988) and Altonji, Hayashi, and Kotlikoff (1992) use similar methods to test for intergenerational altruism.

J. McCarthy~Journal of Monetary Economics 36 (1995) 301 327 303

insight into why the perfect insurance hypothesis is rejected, whether household behavior is consistent with self-insurance, and whether the cross-section distribution of wealth is important to the behavior of aggregate consumption.

By splitting a sample to examine differences in consumption behavior across households, this paper is closely related to Zeldes (1989a). Zeldes investigated the presence of liquidity-constrained households by examining the overidentify- ing restrictions of the Euler equation. In contrast, this paper investigates whether households are perfectly insured by examining the cross-sectional restriction of the risk-sharing condition. The difference in methodology between these tests is the choice of instruments to use to test an orthogonality condition involving consumption growth: lagged variables for liquidity constraints versus 'exogenous shock' variables for perfect insurance.

Besides the similar methodologies, this paper and Zeldes (1989a) are closely related because liquidity constraints, as well as precautionary savings behavior, can explain why the MPC of poorer households may be higher than that of richer households when insurance is not perfect. These explanations for differing MPCs are not exclusive; in fact, they are closely related, a fact that has been used in the 'buffer stock' models of saving behavior. 2 Although the basic results in this paper can be explained using liquidity constraints, an extension of the model plus some additional results indicate that more than liquidity constraints are behind the differing MPCs across households.

The balance of the paper is organized as follows. Section 2 describes the model and tests, and Section 3 describes the data from the Panel Study of Income Dynamics (PSID). Section 4 presents the results. The principal results are: (1) Insurance is imperfect and low-wealth households are less capable of insuring against idiosyncratic shocks. (2) Households appear to perceive housing wealth, the major asset for many households, as illiquid. 3 (3) Households with nonpositive wealth appear to be better insured than those households with low but positive wealth, possibly reflecting insurance aspects of means-tested safety-net programs. Section 5 has concluding remarks.

2. A simple theoretical model

2.1. Cochrane model and perfect insurance

I illustrate the theory underlying Cochrane's test in a single-good economy where consumers receive endowments and have equal access to a linear storage

2See Deaton (1991) and Carroll (1991, 1992). 3For the bottom 90 percent of the wealth distribution in the 1983 Survey of Consumer Finances, housing equity comprises over 50 percent of their net worth (Avery, Elliehausen, and Kennickell, 1988).

304 J. McCarthy~Journal of Monetary Economics 36 (1995) 301-327

technology. The economy has N consumers and lasts for T periods. 4 Consumers maximize discounted expected utility and have a discount rate of p. Their single-period utility function is u(c , 3), where c is consumption and 6 is a preference shift. Uncertainty is summarized by the variable s t, which takes on a count- able number of values. The probability of a state s t is n(s t ) .

In each period, a consumer receives a state-contingent endowment Yl and output from the linear storage technology. The storage technology transforms al units of the good not consumed in period t - 1 into (1 + r) al units in period t. Each consumer also receives a state contingent payment ('insurance benefit') zl from a social planner (negative values indicate the consumer pays a 'premium' to the social planner). 5 A consumer's budget constraint in period t is then

ct = fit + (1 + - at + l + zt . (1)

The allocation of consumption across consumers and across time can be solved from the planner's problem of maximizing a social welfare function. If 2 i is the planner's weight for consumer i, this problem is

max E ,

subject to the consumer budget constraints (1) and the aggregate resource constraints in each period (i.e., the sum of the contingent insurance payments in each period is nonpositive),

N i Z z, _< 0. (3)

i=1

i (the'wealth' a consumer The control variables for the social planner are at+ 1

holds at the beginning of period t + 1) and zl. 6 The first-order condition for i is the usual intertemporal condition, while the first-order condition for z~ is at+ 1

*This model is presented here in a less elegant form than in Cochrane (1991) in order to be comparable to the imperfect insurance case presented below.

5The social planner is introduced to avoid solving for equilibrium prices in the perfect insurance model, relying on the second welfare theorem.

6Actually, the social planner only needs to control aggregate 'saving' to determine aggregate consumption in a period, and then optimally distribute the aggregate among consumers. Since all consumers have access to the same storage technology, the planner can distribute 'wealth' according to each individual's intertemporal first-order condition and still satisfy the aggregate optimality condition.

J. McCarthy~Journal of Moneta~ Economics 36 (1995) 301 327 305

where P, is the Lagrange multiplier associated with constraint (3) divided by zt(d). Divide Eq. (4) at t + 1 by Eq. (4) at t to remove the fixed effect associated with the planner's weight 2 i,

1 uc(ci+ 1,61+ 1) /t,+, - - - ( 5 )

1+/ , uc(ci, al) t*,

The right-hand side of (5) consists only of aggregate variables, and so it is the same for all consumers. This then is the basic implication of perfect insurance: consumers' marginal utilities grow at a common rate. 7

To test for perfect insurance empirically using (5), suppose the utility function is constant relative risk aversion (CRRA) with parameter 7 and multiplicative preference shift a~,

,i "i ~[( CI)1-7 - 1 u(c,, 03 = (6)

1 - -7

As in Zeldes (1989), the preference shift is assumed to be a function of the consumer's age, age-squared, a measure of household size and composition (ln(AFN~)), and an unobserved component el,

6~ = exp [bo agel + b'~ (age~) 2 + b 2 In (AFNI) + eli. (7)

After substituting (6) and (7) into (5), taking logarithms, rearranging, and adding a measurement error term {~+ 1, the perfect insurance hypothesis can be stated as the following equation:

(,) ln\~7-.~ 1 = - l n 2 P, / + l n ~ +b,agel

, . ( A F N , + ) ] ~ • - i ( 8 ) _ 1 i - e ' , ) + ~ , + 1 + o 2 m ~ +(et+l _ •

The test for perfect insurance takes the following form. Suppose a consumer receives an exogenous idiosyncratic shock to income Yl + ~. Eq. (8) implies that if insurance is perfect and Y~+I is cross-sectionally independent of unobserved preference shifts and measurement error in consumption growth, then Y~+ 1 should have no effect on consumption growth. Therefore, in the following regression (9), the coefficient on income (fl), which can be interpreted as the MPC out of idiosyncratic shocks to income, should be zero,

ic,, J \ ) ln(C,+ [] I/ AFN~+ I i = :~ + bt aoe~ + b2 In { - ~ + [3yi+ ~ + U,+l. (9) \

7Note that this equation holds ex post, and not in expectation like the usual intertemporal condition.


There are two points to be made about the test for perfect insurance embodied in Eq. (9). The first point is that under the perfect insurance hypothesis, the coefficient on the income shock is zero for any subgroup of households. Specifi- cally, if households are split into low- and high-wealth groups and regressions like (9) are done for each group, the coefficient on the income shock is zero in each regression under the perfect insurance hypothesis.

The second point concerns the existence of liquidity constraints. The constraint on aggregate contingent insurance payments in a period [inequality (3)-I is independent of whether households face borrowing constraints. So even if households face borrowing constraints, the cross-sectional condition (4) remains the same. Therefore, the coefficient on income in (9) is zero under the perfect insurance hypothesis irrespective of whether households face liquidity constraints.

2.2. Imperfect insurance and the marginal propensity to consume

Now suppose that perfect insurance is not available to households. One alternative for households in this case is to self-insure using the asset market. Under this circumstance, the MPCs of low- and high-wealth households may differ.

To illustrate this, suppose that no insurance is available to households so that self-insurance is the only alternative. Also, assume that the effect of an idiosyncratic shock to income on the distribution of future income is the same for low- and high-wealth households. 8 This simplifies the comparison of MPCs out of income shocks between low- and high-wealth households, since the MPC out of income shocks depends on the M P C out of wealth and the income shock's effects on the distribution of future income. 9 The latter assumption then implies that the difference between the MPCs out of income shocks depends only on the difference between MPCs out of wealth.

Therefore, to show that MPCs across households differ according to their wealth, we need to show that the consumption function is not linear. Carroll and Kimball (1995) have examined the conditions under which the consumption function is concave. They find that when the utility function is of the class that exhibits Hyperbolic Absolute Risk Aversion (HARA) and income is stochastic, the consumption function is concave; and it is strictly concave in most cases

81 know a little empirical evidence concerning this assumption. The closest study I know of is Hubbard, Skinner, and Zeldes (1995), who divide the PSID sample by education. They find little difference in the persistence of the earnings process between high school dropouts (who tend to have low wealth income ratios) and college graduates (who tend to have high wealth income ratios). I thus believe that any differences in persistence will be small. 9See Kimball (1990b) and Zeldes (1989b).

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where households engage in precautionary savings behavior, including when utility exhibits CRRA and labor income is stochastic. A strictly concave consumption function implies that the MPC is declining in wealth. Therefore, the MPC of low-wealth households will be greater than the MPC for high-wealth households when households exhibit precautionary savings behavior.

Preferences which exhibit prudence are not only possible source for precautionary savings behavior. Liquidity constraints also can lead to precautionary savings behavior even if preferences do not exhibit prudence; e.g., see Aiyagari (1994). 1° As stated at the end of the previous section, liquidity constraints have no effect on the MPC under perfect insurance. However, when there is no insurance, liquidity constraints can affect the MPC because they restrict the ability of households to use borrowing as self-insurance against current shocks.

What are the implications of liquidity constraints for the differences of MPCs across households? If liquidity constraints remain binding, the MPC for constrained (low-wealth) households is one. The MPC of households who expect to remain unconstrained over their lifetimes (high-wealth) is [assuming r = p; see Zeldes, 1989b, Eq. (6)]

dC~'dy, - K~--,+a (1 + r)-i\ Oy, /j , (1o)

where

' ] Kr-t+l = 1 - (1/(1 + r)) r - ' ÷ l •

Using (10), the MPC of high-wealth households is less than the MPC of low-wealth households if the income process is less persistent than a random walk, as has been estimated from panel studies of household earnings.l t Given this, the two possible sources for precautionary savings behavior have similar implications on the MPC in the regression model (9). 12

Even though the basic regression (9) probably cannot distinguish liquidity constraints from other sources of precautionary savings behavior, the perfect

J°See also Deaton's (1991) discussion of Zeldes (1986). 'Buffer stock' models like Deaton (1991) and Carroll (1992) exploit the similar behavior induced by prudent preferences and liquidity constraints.

11 For example, see MaCurdy (1982).

12On the other hand, if the income process is more persistent than a random walk, the MPC of the unconstrained group would be higher than the MPC of the constrained group. Campbell and Deaton estimated an ARI(1,1) process for U.S. aggregate income that is more persistent than a random walk. Since it is possible to aggregate individuals whose income processes are IMA(1,2) (MaCurdy's, 1982, preferred representation) to an aggregate process that is ARI(I,1)(see Deaton, 1991), the MaCurdy estimates are appropriate for this analysis.

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insurance test differs f rom the liquidity constraints test of Zeldes (1989a). The perfect insurance test examines the effect of exogenous income shocks on the relation between income and consumpt ion whereas the Zeldes test examines the effect of lagged information on the relation. For the most part, Eq. (9) is used to examine whether imperfect insurance causes M P C s to differ across households in a manner consistent with households self insuring th rough precaut ionary savings - whatever the ultimate source for the precaut ionary savings. 13 However, we would expect that differing M P C s are caused by more than liquidity constraints. To examine this supposition, an extension of (9) that a t tempts to control for the effect of liquidity constraints is estimated in Section 4.4.

To this point, the assumptions concerning household insurance opportuni t ies have been all-or-nothing; however, insurance opportuni t ies intermediate to the two extremes are certainly conceivable. Two such intermediate alternatives and their implications are discussed next.

The first alternative is that insurance contracts may require a premium to be paid before the resolution of uncertainty. The premium could be a ' good faith' measure to ensure that households do not walk away from the contract when the ou tcome is not favorable to the household. If only high-wealth households are able to pay the premium, then low-wealth households will be less well- insured and the M P C s of low-wealth households will be greater than those of high-wealth households.

The second alternative is a means-tested social p rogram which insures poor households and is financed by taxes levied on n o n p o o r households. 14 Depend- ing on the size and payment scheme of the program, the poor households could have a lower M P C than the n o n p o o r households, an implication opposite that of the no-insurance case.

This second alternative illustrates a case where the perfect insurance test may have results that are inconsistent with liquidity constraints. Households eligible for means-tested social p rograms have little wealth and at least some of them are usually thought to be liquidity-constrained. So if means-tested social programs do insure some households and if these households can be identified, then the estimated M P C s of these households would not fit the profile implied by the

13In some ways, the distinction between liquidity constraints and imperfect insurance is rather artificial. Both liquidity constraints and imperfect insurance result from missing markets: at a basic level, it is a matter of semantics whether to call the missing markets insurance markets or capital markets. It is difficult to imagine that some households could be liquidity-constrained without those households also being unable to perfectly insure against idiosyncratic shocks. 14If the program was financed by an income tax on nonpoor households, then the tax would reduce the variance of income and so partially 'insure' these households (e.g., see Barsky, Mankiw, and Zeldes, 1986), However, such a tax probably would be an inefficient insurance mechanism.

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l iquidi ty cons t ra in t s model . This is tested in Sect ion 4.3 by s tudying househo lds with nonpos i t ive weal th . l 5

2.3. Empirical implications and tests"

The previous subsect ion suggests that if househo lds canno t insure agains t id iosyncra t ic shocks, the M P C of low-weal th househo lds should be greater than that of h igh-weal th households . This p ropos i t i on is tested in the fol lowing manner : split the sample into low- and h igh-weal th g roups and es t imate Eq. (9) for each of the subsamples .

If the coefficient/3 # 0 in at least one of the subsamples , then the difference between the es t imates of/3 in the subsamples indicates the extent to which low- and h igh-weal th househo lds differ in their capabi l i ty to insure. The null hypothesis to be tested is that there is no difference in insurance capabil i t ies . The a l te rna t ive hypothes i s is that low-weal th househo lds are less capab le of insur ing agains t income shocks. A test of null hypothes is versus this al ter- nat ive hypothes is consists of examin ing whether the difference between the coefficients is s ignif icantly posi t ive using a one-tai l test. This is done in Sect ion 4.

There are two add i t i ona l issues to cons ider in do ing such a test. The first is the defini t ion of wealth. The theory assumes that n o n h u m a n weal th is held in a single l iquid asset and does not p rov ide guidance as to wha t should be included in an empir ica l weal th definit ion. I will use two different def ini t ions of wealth to split the sample to deal with this problem.l~"

The second issue is the use of income as a regressor in (9). The under ly ing theory assumes tha t income shocks are exogenous and are uncor re la ted with the unobserved preference shocks (and thus the regression errors). However , a househo ld ' s income is par t ly affected by its decisions, which makes income growth a less desi rable regressor in (9). 17 Moreover , there m a y be cor re la t ion between unobserved preference shocks and income, which would lead to an

5I can think of two other reasons why wealth could vary across households. Neither reason has implications for the MPC consistent with the self-insurance models. The first is that high-wealth households have been more patient and thus more willing to save. In this case, the lower discount rate would imply a higher MPC and so we would expect that the MPC of high-wealth households to be higher than that of low-wealth households. The second reason is that high-wealth households expect their future income to grow more slowly. However, slower expected income growth does not affect the MPC out of wealth, nor does it necessarily affect the persistence of an income shock. Thus differences in expected income growth have little effect on the differences between the MPCs of the two groups.

l~See the next section for the definitions of these two measures.

17This was noted by Cochrane (1991).

310 J. McCarthy/Journal of Monetary Economics 36 (1995) 301-327

inconsistent estimate of ft. For example, a preference shift could lead a household to consume more today and to work more (to pay for the higher consumption). This would cause an upward bias of the OLS estimate of ft. On the other hand, a preference shift could lead a household to consume less today and to work more (e.g., to pay for a child's future college education). This would cause a downward bias of the OLS estimate of ft. To determine the direction and the magnitude of this bias, I estimate (9) using both OLS and instrumental variables. The instruments for income growth are shocks like involuntary job loss which one can plausibly argue are exogenous to an individual but correlated with income growth.

3. Data

The data for this study come from the 1984-1987 waves of the Panel Study of Income Dynamics (PSID) conducted by the Survey Research Center at the University of Michigan.18 The survey has been conducted during the spring of each year since 1968, and has followed the same families and their 'splitoffs' (new families formed by members of the original study) over this period.

I briefly describe the variables used and sample selection in this section. Complete definitions of the variables and the criteria to be included in the sample are contained in the Appendix.

3.1. Variables used

Consumption Growth. The most comprehensive measure of consumption in the PSID is food consumption, which is equal to food eaten at home plus meals away from home plus food stamps used. I follow most previous work (for example, Hall and Mishkin, 1982; Zeldes, 1989a; Cochrane, 1991) and use this as the measure of consumption.

Consumption growth is calculated as the percentage change in consumption between 1984 and 1987. A period longer than one year is chosen for two reasons. First, more families receive shocks, which is important for some of the instruments used. Second, problems resulting from the different timing of some of the PSID variables are reduced.19

Regressors. Two different measures of income are used: household disposable income and labor income. Labor income fits the theory better but it cannot

laThe data were made available by the Inter-University Consortium for Political and Social Research. Neither the original source or collectors of the data nor the consortium bears any responsibility for the analyses or interpretations presented here. i 9 F o r example, the income question in the PSID refers to the previous year, while the consumption question refers to the time of the interview (which is usually around March).

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be calculated net of taxes wi thout some s t rong assumptions. Income growth is calculated as the percentage change in the average of income between 1983-84 and 1985-86. 20 This measure is similar to that used by Cochrane, and is an a t tempt to reduce the effects of possible measurement error. 21

The other regressors are variables to capture observable preference shifts. The first is the age of the head of household. The second is the growth of the annual food needs (GAFN). The annual food needs variable calculated by the P S I D is an index of family composi t ion and its growth proxies for preference shifts caused by changing family composit ion.

Instruments. As stated in Section 2.3, instruments for income growth should be uncorrelated with unobserved preference shifts (thus they should not be decision variables like quitt ing a job) and measurement error in consumpt ion growth, and should be well-measured. Most of the instruments are variables used by Cochrane as regressors in his test since these variables come as close as any variables in the P S I D to meeting these criteria. These variables are days of work missed by the head of the household due to illness, involuntary moves, involuntary job loss, and length of job search given involuntary job loss. I also include the number of nights the head spends in a hospital as another instrument.

Wealth. In the 1984 wave of the PSID, a special wealth supplement module was included, which is why I have chosen 1984 as the base year. 22 As stated in Section 2.3, I use two measures of wealth. The first is liquid wealth, which consists of 'cash assets' (checking and savings accounts, money market mutual funds, Treasury bills, etc.) plus stocks and mutual funds minus household debts (excluding mortgages and vehicle loans). The second is 'total' wealth, which consists of liquid wealth plus bonds and life insurance cash value plus housing equity.

3.2. Sample selection

The P S I D in 1968 included a 'pover ty sample' that oversampled low-income families. I exclude these families and their splitoffs as I wanted a sample which is

2°The PSID income questions refer to the year immediately preceding the interview, so the 1984 wave asks about 1983 income, the 1985 wave asks about 1984 income, etc. 21Results using income growth from 1983 to 1986 as a regressor are similar qualitatively to those presented in the next section. 22The PSID is not well-designed as a comprehensive wealth survey since its original design oversampled low-income households because of its research and policy interests related to poverty. Since wealth in the U.S. is skewed, a wealth survey should oversample high-income households (as the Survey of Consumer Finances does) to get a more accurate picture of wealth holding, Still, as wealth is used only to split the sample, the 1984 PSID wealth survey should be sufficient (see Curtin, Juster, and Morgan, 1989, for corroboration).


representative of the U.S. population. A family is tracked by following the head of the family, and so I include only families with the same head throughout the sample period and exclude any subsequent splitoffs from the 1984 families. Families are excluded if they lived with another family in 1984.

Families are excluded if there is missing data for wealth or any of the other variables, if consumption is reported to be zero in 1984 or 1987, if income is nonpositive in 1983 + 1984 or 1985 + 1986, or if the interviewer assigned values to some component of consumption or income or to some other variable. The construction of the involuntary job loss instrument meant that all families whose head was not employed in 1984 were excluded from the sample.

3.3. Splitting the sample

The sample is split on the basis of wealth-to-income ratio. I use the two wealth measures defined in Section 3.1 and divide each by the average of 1983 and 1984 disposable income to arrive at the two ratios used. A family is placed in the low-wealth group if the ratio is less than one-sixth and in the high-wealth group if the ratio is greater than or equal to one-sixth. 23 For the liquid wealth split, approximately five-eighths of the sample is placed in the low-wealth group. For the ' total ' wealth split, slightly over one quarter of the sample is placed in the low-wealth group.

Summary statistics for the sample and the subsamples are presented in Table 1. As expected, high-wealth families tend to be older and have fewer composit ion changes (as measured by GAFN). Disposable income growth has similar means in the two subsamples, although the standard deviation is slightly higher in the low-wealth group. The labor income growth mean is considerably higher in the low-wealth group, but the standard deviations are about equal. F rom this table, it appears that the differences between the two groups are not sufficient to affect the validity of the test described in Section 2.3.

One facet of the data displayed in Table 1 is relevant to how well the self-insurance models fit the data. The means of consumption growth in the two subsamples of the liquid wealth split are approximately equal, but the standard deviation in the low-wealth group is larger. This is contrary to the predictions of the self-insurance models. In the precautionary savings model, the argument establishing that low-wealth households have a higher M P C also implies that these households should have higher expected consumption growth. 24

2aThis is the same criterion used by Zeldes (1989a) in his basic split and is similar to a question asked in some previous waves of the PSID about savings balances. It also approximates a rule of thumb for a minimal contingency fund, although financial planners do suggest a greater amount (see the quote on p. 17 of Carroll, 1992). Results using one-third instead of one-sixth as the criterion to split the sample (available from the author) are similar to those reported in the paper. 24This is also shown in Zeldes (1989b); see his Fig. III.

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Table 1 Summary statistics

313

Liquid wealth split Total wealth split

Full Low High Full Low High wealth wealth wealth wealth

Disposable income regressions

Number of cases 1268 795 473 1137 326 811

Age: mean 37.20 33.80 42.93 37.14 30.28 39.90 (std. dev.J (11.36) (9.36t (12.11) (11.48) (8.03) (11.5t)

GAFN: mean 0.0246 0.0377 0.0025 0.0269 0.0714 0.0091 (std. dev.) (0.2322) (0.2384) (0.2199) (0.2346) (0.2501) (0.2258}

Income growth: mean 0.1245 0.1304 0.1147 0.1223 0.1483 0.1118 (std. dev.) (0.2912) (0.3005) (0.27511 (0.2961} (0.3482) (0.2719)

Consumption growth: 0.1133 0.1122 0.1150 0.1142 0.1380 0.1047 mean (std. dev.) (0.4082) (0.4402) (0.3481) (0.4061) (0.4793) (0.37261

Labor income regressions

Number of cases 1624 1028 596 1399 384 1015

Age: mean 3Z77 34.69 43.08 3?.50 30.61 40.11 (std. dev.) (11.34) (9.74) (11.93) (11.39) (8.38) (11.29)

GAFN: mean 0.0116 0.0181 0.0004 0.0170 0.0602 0.0006 (std. dev.I (0.2515) (0.2613t (0.2335) [0.2488) (0.2692) (0.2387)

Income growth: mean 0.0951 0.1266 0.0406 0.0922 0.1477 0.0712 (std. dev.) (0.4596) (0.4199) (0.5170) (0.4570) (0.4824) (0.4455)

Consumption growth: 0.1054 0.1074 0.1020 0.1070 0.1254 0.1000 mean (std. dev.) (0.4141) (0.4414) (0.3625) (0.4109) (0.4805) (0.3812)

Furthermore, if the higher cross-section variance also implies that low-wealth households face greater uncertainty, then these households should undertake more precautionary saving and have higher expected consumption growth. In the liquidity constraints model, constrained households should have higher expected consumption growth because they cannot borrow as much as they desire. If the regressions in the next section are consistent with the self- insurance models, these features of the data and the regression results have to be reconciled.

314 J. McCarthy~Journal of Monetary Economics 36 ('1995) 301-327

Table 2a Regression of consumption growth on disposable income growth; liquid wealth split

Income Sample Constant Age GAFN growth R 2

Least squares results

Full 0.1087"* - 0.0005 0.4553** 0.1068" 0.084 (0.0416) (0.0010) (0.0545) (0.0507)

Low wealth 0.1155 ~ - 0.0012 0.4782** 0.1423" 0.093 (0.0609) (0.0016) (0.0747) (0.0701)

High wealth 0.1591"* - 0.0011 0.4001"* 0.0289 0.073 (0.0609) (0.0013) (0.0674) (0.0572)

Instrumental variables results

Full 0.0417 - 0.0003 0.4621"* 0.5754** (0.0587) (0.0011) (0.0750) (0.2155)

Low wealth - 0.0021 - 0.0015 0.4705** 1.1349"* (0.0938) (0.0019) (0.1275) (0.3710)

High wealth 0.1520 # - 0.0011 0.4010"* 0.0657 (0.0842) (0.0015) (0.0871) (0.2457)

Test of equality of income 9rowth coefficients in low- and hiyh-wealth samples

Least squares regression Instrumental variables regression

Test statistic 1.253 2.404 p-value 0.1050 0.0081

Standard errors are in parentheses below the coefficient estimate. The standard errors for the least squares regressions are the heteroskedastic-consistent standard errors. The standard errors for the instrumental variables regressions are the three-stage least squares standard errors.

Asterisks denotes that the coefficient is significantly from zero at the 1% (**), 5% (*), and 10% (#) levels, respectively.

The test statistic for the significance of the difference is distributed asymptotically standard normal. The p-values are from the standard normal distribution.

4. Results

4.1. Liquid wealth split

Disposable Income. T a b l e 2a p r e s e n t s t he r e su l t s w h e n d i s p o s a b l e i n c o m e

g r o w t h is a r e g r e s s o r a n d t h e s a m p l e is sp l i t u s i n g l i q u i d wea l t h . T u r n i n g f i rs t to

t h e l eas t s q u a r e s resu l t s , t h e coef f ic ien t o n i n c o m e g r o w t h in t h e full s a m p l e is

p o s i t i v e a n d s i g n i f i c a n t l y d i f f e ren t f r o m z e r o a t t he 5 p e r c e n t level. I t s size is

J. McCarthy~Journal of Monetary Economics 36 (1995) 301-327

Table 2b Regression of consumption growth on labor income growth; liquid wealth split

315

Sample Constant Age GAFN Income growth R 2

Least squares results

Full 0.1117** -- 0.0005 0.5124** 0.0587 # 0.108 (0.0390) (0.0009) (0.0464) (0.0308)

Low wealth 0.1073 # - 0.0007 0.5243** 0.1116" 0.119 (0.0562) (0.0015) (0.0615) (0.0422)

High wealth 0.1577"* 0.0013 0.4638** - 0.0049 0.096 (0.0590) (0.0013) (0,0670) (0.0388)

Instrumental variables results

Full 0.0923" -- 0.0003 0.5143"* 0.1826"* (0.0441) (0.0010) (0.0402) (0.0618)

Low wealth 0.0713 - 0.0008 0.5226** 0.4180"* (0.0584) (0.0015) (0.0535) (0.1011)

High wealth 0.1409" - 0.0010 0.4646** 0.0648 (0.0684) (0.0015 ) (0.0619) (0.0683)

Test of equality of income 9rowth coefficients in low- and high-wealth samples

Least squares regression Instrumental variables regression


See notes to Table 2a.

s imi la r to C o c h r a n e ' s e s t ima te a n d is e c o n o m i c a l l y s ignif icant . 2~ Th i s regress ion

rejects the perfect i n s u r a n c e hypothes i s . Sp l i t t ing the sample , the e s t ima ted coefficient on i n c o m e g r o w t h in the

l ow-wea l th s ample is s igni f icant ly different f rom zero a t the 5 pe rcen t significance level a n d is five t imes the size of the ins ign i f i can t coefficient in the h igh -wea l th sample . Th i s is wha t was p red ic ted by the n o - i n s u r a n c e models . However , a s ta t is t ical test c a n n o t reject (even at the 10 pe rcen t level) equa l i ty of the coefficients in favor of the a l t e rna t ive tha t the l ow-wea l th coefficient is

g rea te r t h a n the h igh -wea l th coefficient.

251ts value implies that a 1 percent increase in income results in about a 0.2 percent increase in consumption. A transitory 1 percent shock to income in a simple permanent income model would lead to a change in consumption of 1 percent times the interest rate.


Turn ing to the ins t rumenta l var iable results, the es t imates of the coefficient on income g rowth differ cons ide rab ly f rom the least squares est imates. 26 This indicates tha t cor re la t ion between income growth and the regression e r ro r is a p rob lem; still, these results reinforce those f rom the least squares regressions. The coefficient on income growth is now over 0.5 in the full sample, and is s ignif icant ly different from zero at the 5 percent level. This coefficient is over one and significant at the 1 percent level in the low-weal th sample, while it is small and insignif icant in the h igh-weal th sample. The hypothes is of equa l i ty is rejected in favor of the a l te rna t ive that the low-weal th coefficient is grea ter than the h igh-weal th coefficient at the 1 percent level of significance.

Labor Income. Table 2b presents the results using l abo r income growth as a regressor. The results are s imilar to those for d i sposab le income. The coefficient on l a b o r income g rowth in the whole sample is s ignif icant ly different f rom zero (at the 10 percent level for the least squares regression and at the 1 percent level for the ins t rumenta l var iables regression), and so the perfect insurance hypothes is is aga in rejected. 27 The coefficient in the low-weal th sample is cons ide rab ly grea ter than the coefficient in the h igh-weal th sample, and this difference is s ta t is t ical ly significant at higher confidence levels than is the case for d i sposab le income.

4.2. 'Total' wealth sprit

The results when the sample is spli t on the basis of ' t o ta l ' weal th are presented in Tab le 3. 28 The results for the full sample remain the same as before: the coefficient on income growth is posi t ive and significant, and thus perfect

26In the first-stage regressions, the coefficients on the instruments have the expected sign when they are significant (all instruments except the illness variable are significant in at least one of the samples; only the lost job variable is significant in every sample). The adjusted R 2 is small, around 0.040.07. This is not surprising given the number of sources of cross-sectional variation that are not 'exogenous' or 'insurable': e.g., measurement error, occupation, and industry choice. Some additional variables were added to the first stage to provide more power; they had minimal effect on the substantive results. Since the instruments best fit the theoretical construct for exogenous idiosyncratic shocks the empirical work uses these.

27For labor income, the coefficients on the instruments in the first-stage regressions have the expected sign when significant (all the instruments are significant in some of the samples, but only the lost job variable is significant in every sample). The adjusted R 2 is considerably higher than that for disposable income, between 0.10q3.23. The fact that the substantive results hold strongly when labor income is used provides some more confidence in the instruments.

28In the rest of the paper, I present only the instrumental variables regressions. The substantive conclusions from the least squares regressions are similar.

J. McCarthy/Journal of Monetary Economics 36 (1995) 30l 327 317

insurance is rejected. 29 However, when the sample is split, the difference between the coefficients on income growth in the low-wealth and high-wealth samples is smaller and statistically insignificant at the usual significance levels. 3° This occurs mostly because the coefficient on income growth in the high-wealth sample is higher in this split than it is in the liquid wealth split.

This result may reflect that households consider housing equity to be illiquid. If households are self-insuring against unanticipated shocks, they need to be able to convert quickly the assets they are using for this purpose into consumption. So if housing equity is perceived to be illiquid, households with large housing equity and few other assets may not be particularly well-insured. 31 In the liquid wealth split, these households are placed in the low-wealth group; and in the total wealth split, they are placed in the high-wealth group. Therefore, if housing is not liquid, the coefficient on income growth for the high-wealth sample should be larger when the sample is split using total wealth since the high-wealth sample in this case includes households that are not well-insured. This is what is observed when compar ing Tables 2 and 3.

To explore this interpretat ion further, I split the sample into three groups. The first g roup consists of those families in the low-wealth group of the total wealth split (all of these families are also in the low-wealth group in the liquid wealth split). The second group consists of those families placed in the low-wealth group of the liquid wealth split and in the high-wealth g roup of the total wealth split. The third g roup consists of those families placed in the high-wealth group of both the liquid wealth and total wealth splits. If the analysis of the previous paragraph is correct, the MPCs of the first two groups should be about equal and there should be a significant difference between MPCs of the first and third groups as well as between those of the second and third groups.

The results for this three-way split in Table 4 support the hypothesis that households do not treat housing equity as liquid. The coefficient on income growth in the first two groups is large and significant (at the 10 percent level), while it is small and insignificant in the third group. Equali ty of income growth

29The estimates in the full sample for the total wealth split differ slightly from those in the liquid wealth split because additional households are excluded because of missing data concerning housing and other categories of wealth.

3°Note that Zeldes (1989a) also found less significant differences between low- and high-wealth groups when his sample was split on the basis of 'total wealth', which included housing equity.

3 J A model that formalizes this intuition is Aiyagari and Gertler ( 1991). Their asset pricing model has two assets: The first is liquid, while the second is illiquid because of trading costs. There is uninsured endowment risk that gives rise to a precautionary demand for savings. Consumers in the model demand the liquid asset for precautionary savings, resulting in a low risk-free interest rate. The unattractive aspect of acquiring the illiquid asset (which has a constant dividend) for precautionary savings is having to turn around and sell the asset when there is a bad shock, and incur additional transactions costs.

318 J. McCarthy~Journal of Monetary Economics 36 (1995) 301 327

Table 3 Regression of consumption growth on income growth; total wealth split (instrumental variables regression results only)

Income Sample Constant Age GAFN growth

(a) Disposable income 9rowth

Full 0.0242 0.0001 0.4530** 0.6043** (0.0599) (0.0012) (0.0767 (0.2126)

Low wealth 0.0164 -- 0.0016 0.4911"* 0.9160 '~ (0.1532) (0.0036) (0.1839) (0.4962)

High wealth 0.0369 0.0004 0.4237** 0.4390* (0.0644) (0.0012) (0.0784) (0.2108)

(b) Labor income 9rowth

Full 0.0721 # 0.0002 0.5032** 0.1976** (0.0456) (0.0011) (0.0436) (0.0636)

Low wealth 0.0495 - 0.0004 0.5126"* 0.3913" (0.1128) (0.0032) (0.0915) (0.1454)

High wealth 0.0915 ~ - 0.0001 0.4890** 0.1198 ~ (0.0510) (0.0012) (0.0491) (0.0646)

Test of equality of income 9rowth coefficients in low- and hiqh-wealth samples

Disposable income growth Labor income growth



coefficients cannot be rejected between the first two groups, but it can be rejected (at the 10 percent level) between the first and third groups and between the second and third groups.

This three-way split also provides some evidence to reconcile the regression results consistent with the self-insurance models with the approximately equal average consumption growth rates of low- and high-wealth households in the liquid wealth split. The average consumption growth rates for each of the samples in the three-way split when disposable income is the income measure are: 0.1380 for the low-liquid, low-total wealth sample; 0.0920 for the low-liquid, high-total wealth sample; and 0.1160 for the high-liquid, high-total wealth sample. 32 The anomalous sample is the low-liquid, high-total wealth sample

32The comparable numbers for the samples of the three-way split using labor income as the income measure are: 0.1254 for the low-liquid, low-total wealth sample; 0.0901 for the low-liquid, high-total wealth sample; and 0.1095 for the high-liquid, high-total wealth sample.

.]. McCarthy~Journal of Monetary Economics 36 (1995) 301 327 319

Table 4 Regression of consumption growth on income growth; three-way split (instrumental variables regression results only)

Income Number of Sample Constant Age GAFN growth cases

(a) Disposable income growth

Low liquid wealth, 0.0164 -- 0.0016 0.4911"* 0.9160 ~' 326 low total wealth (0.1532) (0.0036) (0.1839) (0.4962)

Low liquid wealth, 0.0024 - 0.0008 0.3907** 1.033"* 384 high total wealth (0.1035) (0.0023) ( 0 . 1 3 8 3 1 (0.3788)

High liquid wealth, 0.1325 - 0.0006 0.4010"* 0.0627 427 high total wealth (0.0903) (0.0016) (0.0964) (0.2597)

(b) Labor income growth

Low liquid wealth, 0.0495 - 0.0004 0.5126"* 0.3913" 384 low total wealth (0.1128) (0.0032) (0.0915) (0.1454)

Low liquid wealth, 0.0770 - 0.0003 0.5308** 0.2831" 498 high total wealth (0.0728) (0.0019) (0.0739) (0.1243)

High liquid wealth, 0.1349 # -0 .0007 0.4101'* 0.0750 517 high total wealth (0.0729) (0.0016) (0.0687) (0.0687)

Test of equality of income growth coefficients in the samples

Disposable income growth Regressions test statistic (p-value)

l) vs. 2) 0.1876 (0.4256) 1) vs. 3) 1.524 (0.0638) 2) vs. 3) 2.113 (0.0173)

Labor income growth test statistic (p-value)

0.5656 (0.2858) 1.951 (0.0255) 1.450 (0.0735)


which has a high MPC and a low average consumption growth rate. The consumption growth rates for the other two subsamples are consistent with the predictions of the self-insurance models.

My explanation for the anomalous behavior of the low-liquid, high-total wealth households involves the expenses of home ownership. These households may have large debt service payments to pay off mortgages and other debt incurred to purchase such goods as furniture, refrigerators, etc. Since these households have little liquid wealth, such payments comprise a large proportion of their current resources. Under these circumstances, these households may economize on their food expenditures to free up additional resources for debt repayment. These households then would have a low consumption growth rate,


while at the same time they remain would sensitive to income shocks and thus have a high MPC.

4.3. Very-low-wealth consumers and social insurance

As stated in Section 2.2, safety-net programs like Aid to Families with Dependent Children (AFDC), Supplemental Security Income (SSI), and food stamps may reduce the effect of shocks for eligible households and so provide some insurance to them. Households must hold very few assets to be eligible for these programs. This suggests that the behavior of families with 'very low' wealth may differ from those with 'merely low' wealth in a way not consistent with the self-insurance models, particularly the liquidity constraints model. 33

The insurance aspects of these programs are evaluated by splitting low-wealth families into merely-low-wealth households and very-low-wealth households. Very-low-wealth households are defined as those with negative liquid wealth, and is the group which should include households eligible for the safety-net programs. 34 The results are presented in Table 5. The coefficient on income growth for the very-low-wealth group is smaller than the coefficient for the merely-low-wealth group. The difference between the coefficients of the two groups is significant at about the 5 percent level. The insurance aspect of means-tested safety-net programs appears to be significant.

These results are not consistent with the self-insurance models, especially the liquidity constraints model. The very-low-wealth sample is defined in a similar manner as the low-wealth group in Zeldes' (1989a) 'extreme' split. Zeldes found that this group contained liquidity-constrained households. If differing MPCs then were a consequence of liquidity constraints only, the coefficient on income ~rowth for the very-low-wealth sample should have been positive. The insignificant coefficient that I find indicates that differing MPCs can result from something other than liquidity constraints.

4.4. Precautionary savings, liquidity constraints, or both?

With the exception of the last section, the results presented here have been consistent with a liquidity constraints hypothesis as well as a precautionary

33In fact, such programs may 'pervert' savings motives such that households save much less than they would if the social insurance program was not means-tested (see Hubbard, Skinner, and Zeldes, 1995). 34These programs set liquid asset limits in the range between $1000 and $3000 (Committee on Ways and Means, 1992). Thus the very-low-wealth sample should include only eligible households based on asset levels, while the merely-low-wealth sample may include both eligible and ineligible households. This should reduce the estimated MPC for the merely-low-wealth sample, and thus this test may underestimate the insurance component of such programs.

J. McCarthy/Journal of Monetao, Economics 36 (1995) 301 327 321

Table 5 Regression of consumption growth on income growth; split of low-wealth consumers (instrumental variables regression results only)

Income Number of Sample Constant Age GAFN growth cases

(a) Disposable income 9rowth

Merely low wealth 0.0010 - 0.0041 ~ 0.4819"* 1.492"* 452 (0.1200) (0.0023) (0.1520) (0.4520)

Very low wealth - 0.0643 0.0044 0.4226** 0.4426 343 (0.1296) (0.0030) (0.1724) (0.4399)


Merely low wealth

Very low wealth

0.1342 # - 0.0035 # 0.5248** 0.5818"* 585 (0.0717) (0.0018) (0.0694) (0.1419)

--0.0855 0.0053* 0.5369** 0.2603 ~ 443 (0.1009) (0.0026) (0.0832) (0.1420)

Test (~f equality ~f income growth coefficients in very-low-wealth and merely-low-wealth samples




savings hypothesis. As discussed in Section 2.2, this is not surprising since liquidity constraints and precautionary savings are closely related. Although some results in this paper cannot be explained easily using liquidity constraints, further work is needed to disentangle these effects. This section presents one attempt to disentangle these effects.

With regards to liquidity constraints, a test for their presence such as Zeldes (1989a) tests (in the reduced form) whether past information such as income is correlated with consumption. In contrast, the perfect insurance test examines whether information from exogenous shocks affects the correlation between income and consumption. The problem in disentangling is that under the alternative of imperfect insurance, liquidity constraints and precautionary savings affect the MPC similarly.

The similar form of the liquidity constraints and perfect insurance tests and the different instruments used in each test suggest that one way to control for liquidity constraints effects may be to add past information variable(s) to the basic regression (9). Adding such a variable may control for the effect of past information on consumption indicative of the presence of liquidity constraints.


Table 6 Regression of consumption growth on income growth and lagged income; liquid wealth split (instrumental variables regression)

Lagged Income Sample Constant Age GAFN income growth

(a) Disposable income growth

Full - 0.4632 - 0.0007 0.4469** 0.0488 '~ 0.5149"* (0.2843) (0.0011) (0.0665) (0.0250) (0.1805)

Low wealth - 0.8622* - 0.0016 0.4454** 0.0839* 0.9036** (0.4422) (0.0017) (0.0970) (0.0387) (0.2654)

High wealth 0.1908 - 0.0010 0.3990** - 0.0044 0.1070 (0.4214) (0.0015) (0.0849) (0.0354) (0.2285)


Full - 0.4233* -- 0.0003 0.5112"* 0.0479** 0.1502"* (0.1731) (0.0010) (0.0400) (0.0149) (0.0562)

Low wealth - 0.9058** - 0.0007 0.5195"* 0.0919"* 0.3226** (0.2531) (0.0014) (0.0523) (0.0221) (0.0851)

High wealth 0.2629 -- 0.0010 0.4650** - 0.0109 0.0702 (0.2600) (0.0015) (0.0619) (0.0212) (0.0664)

Test of equality of income growth coefficients in low- and high-wealth samples



2ee notes to Table 2a.

As in Zeldes (1989a), I use (the log of) lagged income as the past in format ion variable to be included in the regression.

The results from this extended model for the liquid wealth split are presented in Table 6. 35 They indicate the presence of both l iquidity constra ints and precaut ionary savings. The coefficient on lagged income is significant for the low-wealth sample and insignificant for the high-wealth sample. This is consistent with Zeldes' results and indicative of l iquidity constraints. As for the coefficient on income growth, adding lagged income to the regression decreases the coefficient slightly for the low-wealth sample and has little effect on the coefficient for the high-wealth sample. Still, the coefficient on income growth is significant for the full sample and the low-wealth sample; thus the perfect

35The qualitative results for other splits presented in this paper provide similar conclusions about imperfect insurance as previous results.

J. McCarthy/Journal of Moneta~ Economics 36 (1995) 301 327 323

insurance hypothesis is rejected. Moreover, the difference between the income growth coefficients in the low- and high-wealth samples is still highly significant; therefore, the differences in MPCs across households is consistent with precautionary savings behavior when some controls are placed on liquidity constraints effects.

5. Summary and conclusion

This paper has used Cochrane's (1991) test of consumption insurance in a split sample to test whether the MPCs of low- and high-wealth households differ. I find that the MPC of low-wealth households is greater than that of high- wealth households, which is consistent with self-insurance. Indications are that precautionary savings behavior as well as liquidity constraints contribute to the differing MPCs across households. Using two splits of the sample based on different wealth measures, I find evidence that households perceive housing equity as illiquid. When low-wealth households are divided into two subgroups, I find that the MPC of very-low-wealth households is less than that of other low-wealth households, an indication that means-tested safety-net programs provide eligible households some insurance against income shocks.

Besides the obvious extensions concerning robustness of the results to different data sets, using this test to study different periods may provide answers to some interesting questions. For example, has greater promotion of home equity loans and mortgage refinancing in recent years caused households to perceive housing equity as more liquid? Did falling home prices in some areas during the late 1980s and the 1990s affect the perception of housing equity liquidity? Also, more work needs to be undertaken to disentangle the effects of liquidity constraints and precautionary savings on the MPC. If we can identify periods where liquidity constraints have become tighter or looser, this may contribute to progress on this issue.

The results in this paper indicate that poorer households face another ob- stacle in smoothing consumption compared to the representative agent in the simple permanent income model. Zeldes (1989a) had shown that such households are not able to smooth future consumption relative to present consumption to the extent they desire because of liquidity constraints. This paper has shown that these households are not as well-insured against current income risk as high-wealth households. This may be another step in reconciling the empirical consumption data with the predictions of the permanent income model.

Appendix: Variable definitions

Consumption Growth: The percentage change in food consumption, ln(1987 consumption / 1984 consumption). Consumption is total food consumption:


food eaten at home plus food away from home plus food stamps. A family observation is rejected if: (1) there is an assignment by the interviewer of a component of food consumption in 1984 or 1987; (2) consumption is reported to be zero in 1984 or 1987; (3) the family was a splitoff between 1984 and 1987; (4) there is an interview refusal; (5) there is a bad quality of match; (6) there is a different head between 1984 and 1987; (7) the family is living with another family in 1984; or (8) there is missing wealth data in 1984.

Regressors

Disposable lncome Growth: The percentage change in the average of disposable income between 1983-84 and 1985 86, ln(1985 + 1986 income/ 1983 + 1984 income). As in Zeldes (1989a), disposable income is defined as total family money income plus food stamps minus federal income taxes of head and wife minus federal income taxes of others minus property taxes minus social security taxes of head and wife. All information except for social security taxes comes directly from the PSID tape. Social security taxes are computed by multiplying the appropriate social security tax rate by the lesser of annual wages and the social security tax ceiling. If the head or wife is self-employed, I use the self-employed tax rate for that member. An observation is rejected if disposable income is nonpositive in 1983-84 or 1985-86, or if some component of disposable income is assigned by the PSID in 1983, 1984, 1985, or 1986.

Labor Income Growth: The percentage change in the average of labor income between 1983-84 and 1985-86. Labor income is labor income of the head of the household plus labor income of the wife as reported in the PSID. An observation is rejected if labor income is nonpositive in 1983-84 or 1985-86, or if some component of labor income is assigned by the PSID in 1983, 1984, 1985, or 1986.

Age: The age of the head of the household as reported in the 1984 wave. GAFN: The percentage change in the annual food needs (AFN) variable

between 1984 and 1987, ln(1987 AFN/1984 AFN). This variable is included as a proxy for preference shifts caused by changes in family composition. The AFN variable is calculated by the PSID and is included in the tapes. Its value depends upon the number of members in the family, the age of each member, and their sex. For further details, see the data appendix in Zeldes (1989a).

Instruments

Involuntary Job Loss: A dummy variable which equals one if the head of the household was employed in 1984, lost the job in 1985, 1986, or 1987, became unemployed, and gave as a reason: (1) 'company folded / changed hands / moved out of town; employer died / went out of business', (2) 'strike; lockout', or (3) 'laid off; fired'. This variable equals zero if the head was employed in 1984 and stayed

J. McCarthy/Journal of Moneta~. Economics 36 (1995) 301 327 325

employed or lost his/her job for other reasons; in particular, because of quitting. An observation is rejected if the head was not employed in 1984.

Length of Job Search: The number of weeks spent looking for work in 1984, 1985, and 1986 if involuntary job loss equals one. An observation is rejected if it was rejected for involuntary job loss or if the number of weeks spent looking for work is recorded as missing in 1984, 1985, or 1986.

Illness: The number of days of work missed by the head of the household because of illness to self and others in 1984, 1985, or 1986. An observation is rejected if the PSID assigned a value to either component of the variable.

Hospital Stay: The number of nights the head of household stayed in a hospital in 1984, 1985, and 1986. An observation is rejected if the PSID recorded a missing value for the variable in 1984, 1985, or 1986.

Involuntary Move: A dummy variable which equals one if the head moved in 1984, 1985, or 1986 because of 'response to outside events (involuntary reasons): [household unit] coming down, being evicted, armed services, etc., health reasons, divorce, retiring because of health'.

Wealth

As stated in the text, wealth variables are constructed using data from the special wealth supplement to the 1984 wave of the PSID. While brief, this supplement does provide enough information to create the wealth variables used to split the sample.

The PSID used three categories of financial assets in its wealth supplement. One category is comprised of liquid assets including checking and savings accounts, money market mutual funds, certificates of deposit, government savings bonds, and Treasury bills. 36 A second category includes stocks, mutual funds, and investment trusts. 37 The last category includes bonds, rights in trusts or estates, life insurance cash value, and collectibles held for investment purposes.

The PSID also collected data on tangible assets, which were also placed in three categories. One category is housing equity (house value mortgage principal outstanding). 38 A second is real estate other than one's home. The third includes the value of vehicles owned net of any debt owed on those vehicles.

Other categories of assets included in the PSID wealth supplement are ownership of businesses (including farms) and the value of pension rights. The only category for liabilities is outstanding household debts excluding mortgages and vehicle loans.

36The total in this category includes the amount of these assets which are held in IRA and Keogh accounts. 37Again, this amount includes the amount of these assets held in IRA and Keogh accounts. 38This data has been collected in most waves of the PSID.


Liquid Wealth: 'Cash' assets plus stocks, mutual funds, etc. minus household debts. This is a fairly close counterpart to Zeldes' definition of liquid wealth. The wealth variable for a family is treated as missing if for any of the components listed above, the PSID recorded the variable as: (1) 'missing', (2) respondent refusing to answer, or (3) respondent 'doesn't know'. 39

Financial plus Housin9 Wealth: Liquid wealth plus bonds, life insurance cash value, collectibles, etc. plus housing equity. The wealth variable is treated as missing if: (1) it is missing for liquid wealth; (2) the bonds, etc. variable is recorded as 'missing', 'refused to answer', or 'don't know'; (3) the house value or mortgage principal variables were assigned values by the PSID; or (4) the family reports a second mortgage on the home (since the size of the second mortgage is not reported).

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