Liquidity constraints and the permanent-income hypothesis

Journal of Monetary Economics 27 (1991) 73-98. North-Holland

Liquidity constraints and the permanent-income hypothesis Evidence from panel data* David E. Runkle Federal Reserve Bank of Minneapolis, Minneapolis, MN 55480, USA University of Minnesota, Minneapolis, MN 55455, USA

Received July 1989, final version received October 1990

Several recent studies have rejected the permanent-income hypothesis using aggregate time-series data. One explanation for this rejection is that some households are liquidity-constrained. This study directly tests for liquidity constraints using panel data on individual households. It finds no evidence of liquidity constraints and suggests that the failure of the permanent-income hypothesis in aggregate data may be due to aggregation bias. The paper also contains an extended discussion of econometric methods for panel-data rational-expectations models.

.

1. Introduction

The effects of temporary tax cuts, countercyclical spending, and taxes on interest depend on how people choose between present and future consumption. One particularly tractable theory about consumption decisions is the permanent-income hypothesis. This hypothesis states that people base their decisions about current consumption on their expectations about their lifetime income, rather than their current income. If the permanent-income hypothesis is true, then policies such as temporary tax cuts and anticipated *This paper is based on chapter one of my Ph.D. dissertation. I would like to thank Julio Rotemberg, Jerry Hausman, and Robert Solow for their supervision of my thesis. Thanks also to Mike Keane, Greg Leonard, Greg Mankiw, Chris Sims, Steve Zeldes, seminar participants at Brown, Columbia, M.I.T., and the 1985 Winter Meetings of the Econometric Society, and a referee for helpful comments. Outstanding research assistance was provided by Daniel Chin, Ruth Judson, Greg Leonard, and Lorrie Walsh. 0304-3932/91/$03.50

Q 1991-Elsevier

Science Publishers B.V. (North-Holland)

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D.E. Runkle, Liquidity constraints and the permanent-income

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countercyclical spending should have only a limited effect on consumer spending. Some recent attempts to test the permanent-income hypothesis with a stochastic real interest rate on aggregate data have used representative-consumer models. Unfortunately, these attempts have had limited success. This type of model does not seem to fit the data well, and when tested, the restrictions it implies are rejected.’ Two explanations can be postulated for this failure. One leading explanation is that people may be unable to borrow and lend freely; that is, they may be liquidity-constrained. Another explanation is that aggregation problems may invalidate tests of the model on aggregate data. Distinguishing between these explanations is difficult with aggregate time-series data. But there are two reasons to believe that individual data can help show whether liquidity constraints or aggregation bias is responsible for the failure of the permanent-income hypothesis in aggregate data. First, in individual data it may be possible to identify consumers who might be liquidity-constrained. That is impossible with aggregate data. Second, individual data may show directly whether aggregation bias is responsible for the failure of the permanent-income hypothesis. In this paper, I test the permanent-income hypothesis by explicitly modeling individual households’ intertemporal allocations of consumption and saving. To model an individual household’s consumption decision, I set up the intertemporal optimization problem faced by each household and derive the first-order conditions that describe the relationship between the household’s consumption stream and the real interest rate confronting the household. To test the permanent-income hypothesis, I use a linear version of this consumption equation. In modeling these consumption decisions, I consider three econometric issues. First, persistent individual heterogeneity could affect statistical inference, so I determine whether such persistent heterogeneity exists. Second, errors in consumption measurement could also have severe effects, so I test and correct for such errors. Third, aggregate shocks to consumption growth that are not explained by interest rates could result in incorrect statistical inference, so I test for the presence of such shocks. After resolving these issues, I test the permanent-income hypothesis by stratifying the complete data sample in various ways and then testing whether the hypothesis is satisfied for groups that are likely to be liquidity-constrained. For example, people with few liquid assets might have difficulty borrowing and thus might be liquidity-constrained. This study strongly supports the permanent-income hypothesis and shows little evidence of liquidity constraints. These results do not support the ‘Grossman and Shiller (19811, Hansen others, have found these results.

and Singleton (19821, and Mankiw (19811, among

D.E. Runkle, Liquid@ constraints and the permanent-income

15

hypothesis

conclusion that the rejection of the permanent-income hypothesis in aggregate data is caused by liquidity constraints. Instead, that rejection may well have been caused by aggregation bias. There is also evidence of significant measurement error in consumption. There are two other surprising results in this paper. First, there is no evidence of any persistent household-specific effect in the data. Thus, models with persistent household-specific effects are not necessary to test for liquidity constraints. Second, there is no evidence of aggregate shocks in consumption growth after removing the effect of the cross-sectional variation in expected real after-tax interest rates. Thus, Chamberlain’s (1984) warning that aggregate shocks may invalidate the results of panel-data rational-expectations models does not apply here. 2. Theory To test the permanent-income hypothesis, I directly estimate the parameters of a consumer’s utility function. Assuming that changes in government policy do not alter consumers’ preferences, I can use my estimates to calculate the effect of various policy changes. Suppose that the consumer maximizes expected utility and has timeseparable preferences that take the following form:

K,, = E;,,

5PT-‘Wi,,).

(1)

7=t

Eq. (1) is subject to the sequence of constraints Ai.7+*

=

(1 + ri.l)(Ai,+ + Y;.,,- Ci,T),

r=t,t+l,...,

T-l, (2)

and to the terminal condition

Ai,T 2 0, where

E, = mathematical expectation conditional on Zi,,, Z;,, = information available to person i at time t, pi = ith person’s discount rate, T = person’s lifetime, U( >= one-period utility function (strictly concave), C,,, = ith person’s consumption in period t, y;.,, = ith person’s income in period t, Ai,, = ith person’s nonhuman wealth in period t, = ith person’s uncertain one-period real interest rate in period t. ‘i,r In each time period, the consumer

chooses consumption

C,,, to maximize

D.E. Runkle, Liquidity constraints and the permanent-income

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hypothesis

expected utility given the information available at time t. Since consumers face varying marginal tax rates, the real interest rate they face is

[l + it(l -

r, ,,I

=

ei,t)]Pt -

PI+1

1,

(3)

where i, is the one-period interest rate at time t, 8i,r is the consumer’s marginal tax rate at time t, and pt is the price index for nondurable goods at time t. If the consumer plans consumption choices optimally and is not liquidity-constrained, then

Eq. (4) indicates that the consumer plans consumption such that he cannot expect to make himself better off by reducing his consumption today. Eq. (4) also implies that any information available at time t should not be correlated with the equation’s forecast error. From (4) it is clear that the actual values of the variables must obey the following condition:

(5) Note that ri,t is not known at time t and is therefore not part of the information set Zi,,. To make eq. (5) operational, I assume that the consumer has a constant relative risk-aversion utility function of the form U(C,,,) =

F,

where 1 -(Y is the Arrow-Pratt measure of relative specific form of eq. (4) that follows from (6) is

risk aversion.’

The

(7)

‘1 choose this utility function because of its past use in theoretical and empirical studies of asset pricing. See, for example, Rubenstein (1974) and Hansen and Singleton (1982).

D.E. Runkle, Liquidity consrraints and the permanent-income

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Many previous studies of the permanent-income hypothesis have estimated equations such as (7) on aggregate data. Unfortunately, I cannot use this nonlinear equation to test the hypothesis in panel data because of problems caused by measurement error. If consumption were measured with error, I could not consistently estimate the parameters of (7) because the model is nonlinear in its parameters. I therefore test the hypothesis by examining a linearized version of eq. (7). Taking the natural logarithm of both sides of (7) and using the second-order Taylor approximation for In0 +x>, the Euler equation for consumption is ACi,,+i =

ln(ci,t+l>

-

ln(ci,t)

=aiO

+ alri,r

+

ui,f+17

where

E(Vi,t+lIzi,*)= O9 u2 = E(r.&+,). Except where otherwise noted, (Yio is assumed to be the same for all households. To test the permanent-income hypothesis, I use two methods. First, I examine the overidentifying restrictions of the model. Estimating eq. (8) allows me to test directly whether the forecast error in that equation is correlated with instruments chosen from information that each household had when it made its consumption decision. If the errors are correlated with the instruments, then the permanent-income hypothesis is rejected. Hansen (1982) shows how to test whether the forecast error is correlated with the instruments. If the errors are conditionally homoskedastic, Hansen’s test statistic is equivalent to n times the R2 obtained from regressing the residuals from two-stage least squares on the instruments.3 Otherwise, the 3To see this note that in this case Hansen’s test statistic is u’W[‘X’u, where V, = B*(x’X) and X is the matrix of instruments. This statistic is equal to n[(u’X(X’X)-‘X’u)/(u’u)], which is the nR* mentioned.

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minimized value of the generalized-method-of-moments (GMM) criterion function must be used as that test statistic. If the instruments are uncorrelated with the residuals, that statistic is distributed asymptotically xi_,, where 4 is the number of instruments and p is the number of parameters.4 The second, complementary, method of testing the hypothesis is to check whether information besides the household’s expected after-tax real interest rate (other than demographic variables) helps predict the rate of consumption growth? One implication of the hypothesis is that any information available at time t besides the real interest rate should not help predict the rate of consumption growth between time t and time t + 1. That is, no other variable included in an instrumental-variables regression such as eq. (8) should have a significant coefficient. If other variables besides the real interest rate are significant in the regression, then this particular representation of the hypothesis is rejected. If the hypothesis is rejected by the methods described above, one alternative hypothesis is that some consumers are liquidity-constrained: that is, the model fails for these consumers because they cannot borrow enough. Aggregate data cannot be used to test whether liquidity constraints explain the failure of representative-consumer models at the aggregate level. However, with panel data, the sample can be stratified on the basis of some variable (e.g., net worth or home ownership) which might predict whether consumers are liquidity-constrained. I can then test whether the consumption behavior of those who might be liquidity-constrained is different from that of others. For instance, if consumers with low net worth may not have access to credit on the same terms as consumers with high net worth, the former group may be liquidity-constrained.6

3. Data The data for this study come from the Panel Study on Income Dynamics (PSID).’ They have been used previously by Hall and Mishkin (19821, Shapiro (1984), and Zeldes (1989). The data pose two problems. First, their 4Unfortunately, this test statistic may be incorrect for the linearized version of the model due to approximation error. However, since measurement error is probably a larger problem than approximation error, I use the linearized version of the Euler equation. ‘See, for example, Mankiw (1981). %nce an earlier version of this paper was first circulated, other authors [e.g., Zeldes (1989) and Ball (198411 have used this split-sample approach to testing Euler equations in panel data. ‘An earlier version of this paper used data from the Denver Income Maintenance Experiment (DIME) but those data had, at most, four annual observations on consumption. I have since concluded that measurement error is the most important issue to address in testing the permanent-income hypothesis in panel data. Because I argue in the appendix that at least four consecutive observations are necessary to test for the presence of measurement error, I had to abandon the DIME data.

D. E. Runkle, Liquidity constraints and the permanent-income hypothesis

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only measure of consumption is food consumption.**9 Second, they do not provide any direct measure of net worth, so indirect measures must be computed from measures of householder’s asset income. It is important to understand both the criteria used to exclude specific observations and the methods used to construct variables used in the empirical analysis. The sample used in the following analysis consists of an unbalanced panel of 2,830 observations on 1,144 households between 1973 and 1982. Since this paper is concerned with consumption, my criteria for sample selection minimize the noise in the consumption data. I excluded pre-1973 data because information on marginal tax rates was missing before then. If food consumption in an observation grew by more than 300 percent or shrank by more than 75 percent from the previous observation, I excluded it. I included an observation for a household only if all data on consumption, income, and assets were available for that period. Since all data records were kept for heads of households, measurement error in the consumption series would occur if the head of a household divorced, stayed single for a year, and remarried. Therefore, if a couple married or divorced in a given year, I discarded the data for that year and treated the resulting household as a new household. Since data on business equity were unavailable, I excluded farmers and self-employed heads of households. I also excluded heads of households over 65 years old.” The most important household variables used in this study were food consumption, disposable income, asset income, the value of liquid assets, the annual number of hours worked by the householder, and the household’s after-tax real interest rate. Annual hours worked are provided directly in the survey, but all the other variables must be computed from data in the survey. Real food consumption was computed as the sum of real food consumption at home and real food consumption away from home.” Disposable income was computed as reported family-unit income, plus the net cash value of food stamps purchased, minus federal income and social security taxes paid by the householders.‘* 80ther authors [e.g., Shapiro (198411 have noted that measurement error may be a problem with the PSID consumption data, but no one has directly tested or corrected for measurement error. ‘To my knowledge, no panel has a broader measure of consumption than the PSID and more than the four consecutive observations needed to test for measurement error. “Since the selection is based on variables exogenous to the estimated equations, no sampleselection bias will occur. “The nominal data for each element of food consumption was deflated by the appropriate CPI component. Since the food-consumption data refer to consumption during a week in the first quarter of the survey year, the average CPI component for the first three months of the year was used to deflate the nominal quantities. The net cash value of food stamps was included in the nominal value of food consumption at home. “Taxes are computed for both husband and wife if both are present in the family. I computed social security taxes from published social security tax schedules and reported labor income.

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Asset income was computed as the sum of the husband’s and wife’s reported dividend and interest income. The value of liquid assets was computed from asset income. To estimate the stock of assets, the first $200 of interest and dividend income was divided by the annual average commercialbank passbook rate, while the remaining asset income was divided by the annual average of yields on three-month T-bills. The value of liquid assets is computed to be the sum of these two components.13 All nominal values, except for food consumption, were deflated by the annual average of the personal consumption-expenditure deflator for the year before the interview. The after-tax interest rate for each household was computed by multiplying the interest rate by (1 - Oi,t), where 8i.t is the marginal tax rate for household i in period f. The average annual passbook-savings rate for the year before the panel interview was used as the interest rate. The real after-tax interest rate for each household was computed using eq. (3), which subtracts the ex post inflation rate from the after-tax interest rate. 4. Econometric considerations Before the Euler equation for consumption is estimated, the correct estimator needs to be chosen. So far I have assumed that consumption is measured without error. Given that assumption, eq. (8) can be estimated with two-stage least squares if I also assume that the error term in eq. (8) is independent both across households within each time period and across time for each household. That is, E(~J~,,c~,~)=c,’ = 0

if

i=j

and

t=s,

otherwise.

(9)

But if the assumptions in eq. (9) are wrong, then estimates from two-stage least squares will be at best inefficient and possibly inconsistent. Three possible violations of these assumptions that I investigated were the presence of persistent household-specific effects, the presence of measurement error in consumption, and the presence of aggregate shocks to consumption growth that are not accounted for by interest rates. 4.1. Persistent household-specific effects Testing and accounting for persistent differences in household behavior that are not explained by observable variables has been one of the principal issues in the literature on the econometrics of panel data.14 If such persistent 13These calculations for wealth are very similar to those used by Zeldes (1989). 14See Chamberlain (1984) for a review of this literature.

D.E. Runkle, Liquidity constraints and the permanent-income

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81

differences occurred in the PSID, they would affect my tests of the permanent-income hypothesis because they would violate the assumptions made in eq. (9). That violation would imply that two-stage least squares would not be an appropriate estimation method for testing the permanent-income hypothesis. This type of heterogeneity could arise if each household had its own discount rate, which remained constant across time. In this case, eq. (8) implies that ai would differ among households. If I were to falsely assume that czi,, is the same for each household, the difference between c+, and CY,, would be the household-specific component 77i. Thus, the error term in eq. (8) would have two components:

(10) where ni = cvi,,- (Ye. Since persistent household-specific effects could result in incorrect inference, it is important to test for them. A simple test to determine whether household-specific effects occur is to include past values of consumption growth as independent variables or instruments in eq. (8).15 If a household’s rate of consumption growth is high because of a persistent household-specific effect, then a higher-than-average rate of consumption growth for that household several periods ago would imply a higher-than-average rate of consumption growth today, and lagged values of AC,,,+ 1 will be correlated with the household-specific component in the error term. In this case, previous consumption growth will be invalid as an instrument in the equation because it will be correlated with the household-specific effect. If previous consumption growth is uncorrelated with the error term, no persistent household-specific effect exists. If previous consumption growth is correlated with the error term, then additional econometric methods must be used to conduct proper statistical inference. l6 These additional methods are explained in the appendix. 4.2. Measurement error in consumption A more serious potential problem than household heterogeneity is measurement error in consumption.” As noted earlier, the standard deviation of 15Aswill be explained below, the first lag of consumption growth should nor be included in these tests, because of potential measurement error. 16This test can also detect household-specific effects that gradually decay, but fully developing that argument would be an unnecessary complication in this paper. “As long as measurement error in the instruments is uncorrelated with the measurement error in the independent variables, I do not have to consider measurement error in the independent variables.

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D. E. Runkle, Lhuidity constraints and the permanent-income

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the rate of consumption growth was large enough to suggest the presence of measurement error. Other authors’* have done little to test or correct for measurement error, and they report uncorrected standard errors. If the log of consumption were measured with a white-noise error Si,l, this error would further complicate the model. Assuming rational expectations, let us examine how such an error term would affect the estimation procedure if there were no persistent household-specific effects.” If there is measurement error but no persistent household-specific effect, then IJ~,,+*=~i,~+i + 6i,l+i - 6i.r. Thus E(z+ . ,uj,) . =a,*+2a,* =

--(T

= 0

8”

if

i=j,

t =s,

if

i=j,

It-sl=l,

otherwise.

(11)

If this kind of measurement error is present, then using two-stage least squares to estimate eq. (8) will lead to incorrect statistical inference, because the estimate of the covariance matrix of the parameters will be incorrect, because two-stage least squares assumes that CT:= O.*’ If this kind of measurement error exists, correct statistical inference can be made by using a GMM estimator of the form:

where g(p) is the sample average of the orthogonality conditions specified in (8) and W is a weighting matrix. Such an estimator is efficient within the class of estimators that uses only conditional moment restrictions if the optimal weighting matrix W is used.21 In general, the optimal weighting matrix is simply the inverse of the covariance matrix of the orthogonality conditions that are imposed to estimate a particular equation. ** In estimating eq. (8) in the presence of measurement error in consumption, there is an MA(l) error term. Therefore, ‘sAltonji and Siow (1987) and Hayashi (1987) are notable exceptions. lgThe appendix discusses how to test for measurement error in the presence of persistent household-specific effects. zoThis kind of error structure could also arise from random shocks to preferences, as demonstrated by Hayashi (1987) and Attonji and Siow (1987). However, in section 5, I use aggregate time-series data to show that preference shocks are not a significant cause of serial correlation in the errors in these panel-data regressions. *‘See Chamberlain (1984). “See Hansen (1982) for further details.

D. E. Runkle, Liquidity constraints and the permanent-income

the estimate of the covariance matrix of the orthogonality R,+R,

hypothesis

83

conditions is

+a;,

where (13) and K, is the sum of the number of nonmissing cross-products for each of the N individuals at the Ith lag.u*24 I check the adequacy of eq. (11) in describing the covariance of the errors in eq. (8) by examining the autocorrelations of those errors. I obtain an initial consistent estimate of the model by using the identity matrix as the weighting matrix. The residuals can then be used to compute p(l), . . . , p(k - 11, where k is the maximum number of observations per household. This model implies that the errors are MAW. Therefore, it should be true that ~(1) = 0 for 12 1. It is important to note that MA(l) errors in eq. (8) could also result from household-specific random changes in preference in each period.25 So it is not correct to assume that MA(l) errors are necessarily caused by measurement error. But the source of the MA(l) errors has no effect on what methods should be used for statistical inference. In either case, the serial correlation in the errors must be accounted for in computing the weighting matrix for GMM estimation. I continue to call the source of this serial correlation ‘measurement error’ both for convenience and because I believe that measurement error, rather than random changes in preferences, is the most likely cause of MA(l) errors. 4.3. Aggregate shocks The most serious potential problem for estimating eq. (8) is the possible existence of aggregate shocks to consumption growth that are not captured by the expected real after-tax interest rate. Such shocks could lead to inconsistent parameter estimates in eq. (8). Suppose every household had a common component in its consumption growth, 5, + 1, that was not explained by expected interest rates. Then, if there =Because of the moving-average error structure, this estimate is not constrained to be positive definite. Cumby, Huizinga, and Obstfeld (1983), Eichenbaum, Hansen, and Singleton (19881, and Newey and West (1987) discuss consistent estimates that are guaranteed to be positive definite. 24Since I assume that the correlations in the error terms across individuals accumulate each of the R’s on an individual-by-individual basis. “Hayashi (1987) and Ahonji could cause MA(l) errors.

and Siow (19871, among others, have discussed

are zero, I can how taste shocks

84

D.E. Runkle, Liquidity constraints and the permanent-income

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were no measurement error, ui,,+ 1 would be equal to [,+ I + Ed,!+1. If there are a small number of time periods for each household, this kmd of shock would create problems for tests of the permanent-income hypothesis using panel data. Chamberlain (1984) first noted the potential effects of aggregate shocks on rational-expectations models estimated with panel data. He suggests that one result of aggregate shocks in a rational-expectations panel-data model is that the sample version of the orthogonality condition E(Q+, II,,,) converges to zero as the number of time periods increases, but not as the number of households increases, if the number of time periods is held fixed. Thus, in the PSID, where the number of observations per household is small, aggregate shocks would lead to inconsistent parameter estimates.26 A simple GMM specification test can be used to determine whether aggregate shocks exist. If such shocks are present, then time-period-specific dummy variables are not valid instruments for estimating eq. (8), because the time dummies will be correlated with the aggregate shocks. Suppose we have a set of q instruments which we believe are valid for estimating eq: (8). Call the minimized value of the GMM objective function using that set of instruments J,. Now, reestimate eq. (8) adding I time dummies. Call the minimized value of the GMM objective function using that set of instruments Ja. If there are no aggregate shocks, the time dummies should be valid instruments for estimating eq. (8). In that case, J, -.T, should be distributed asymptotically as a x: random variable. 27 If the value of this test statistic is too large, aggregate shocks are present.28 5. Results

My empirical investigation addresses three issues. First, what is the covariante structure of errors in the consumption equation? Second, do the panel data as a whole support the permanent-income hypothesis? Third, is there evidence of liquidity constraints in these panel data? Each of these questions is examined by GMM estimation of the consumption Euler equation (8). Unless otherwise stated, the instrument list includes a constant, the householder’s age, the householder’s hours worked in periods t - 1 and t - 2, the family’s disposable income in periods t - 1 and t - 2, the value of asset income in periods t - 1 and t - 2, the value of liquid assets in periods t - 1 and t - 2, and the value of the after-tax real interest rate for %Keane and Runkle (1990) show that aggregate shocks significantly affect tests of the rationality of price forecasts in panel data. “This form of GMM specification test was developed in Eichenbaum, Hansen, and Singleton (1988). Newey (1985) also developed GMM specification tests. =There is reason to believe, as Michener (1984) suggests, that changes in the interest rate are themselves a summary of aggregate uncertainty. In this case, aggregate shocks that are unrelated to the interest rate may be unlikely.

D.E. Runkle, Liquid& constraints and the permanent-income hypothesis

a5

Table 1 Autocorrelationsof u,, , +, in eq. (8). ~(1) = - 0.380 P(2) = - 0.047 p(3) = 0.012 ~(4) = 0.008

passbook and T-bill interest rates in periods 1 - 1 and t - 2. The head-ofhousehold’s age is also included as a regressor in all equations, but that coefficient is not reported.29 Note that all of these instruments are household-specific data that should have been known by the household when the household made its consumption decisions. 5.1. The covariance structure of consumption-equation errors As I discussed in section 4, three questions need to be answered about the errors in the consumption equation. First, is there evidence of persistent household-specific effects? Second, is there evidence of measurement error in consumption? Third, is there evidence of aggregate shocks in the consumption equation? Each of these questions must be answered before deciding which estimator is appropriate for this model. Section 4.1 showed two simple ways to test for persistent household-specific effects: examining the serial correlation of the errors and testing the explanatory significance of lagged consumption growth. Table 1 shows the autocorrelations of the errors from GMM estimation of (S).3o If there were persistent household-specific effects, all of the lagged autocorrelations would be, significant. But p(2) and p(3) are close to zero. They also have the opposite sign, which should not occur if there were persistent household-specific effects. The regression results in column 3 of table 2 also suggest that persistent household-specific effects do not exist. If a persistent household-specific effect does exist, then the second lagged difference of consumption (AC,,,_,) should be significant in the consumption regression, regardless of whether that effect is random or fixed. But the regression results show that that variable is not significant. Therefore, there is no evidence for any persistent household-specific effect. Since there are no persistent household-specific effects, it is easy to test for measurement error. Eq. (11) in section 4.2 showed the error-covariance structure that would exist if there were measurement error and no house“This amountsto assumingthat time preference depends on age. I also estimated regressions with additional demographic variables and with no demographic variables. The results of those regressions are quite similar to those reported here. mAll regressions in this section use the entire data sample.

86

D. E. Runkle, Liquidity constraints

and the permanent-income

hyporhesis

Table 2 GMM estimates of AC,, t + , = In(Ci,+,)-In(Cir)=ao+alri,,l (1) a0

h2

(2)

+ui,+,.a

(3)

(4)

0.06878 CO.018021

0.09083 (0.01979)

0.10481 CO.022951

0.07089 (0.02090)

0.44582 (0.16380) -

0.35362 (0.16457)

0.48500 (0.20422)

- 0.37098 (0.02226)

- 0.04130 (0.02566)

0.49274 CO.170641 -

J-statistic

17.364 (0.8168)

20.724 (0.9214)

20.919 (0.9255)

19.786 (0.6550)

N Extra regressor(s) Extra instrument(s) No. of instruments No. of MA terms

2830 None None 16

2830 Act.1 ACi,, 17 1

2830 ACi,,-1 ACi,,-r 17 1

2830 None None 21

‘Standard errors are in parentheses under J-statistics.

under coefficients. Significance levels are in parentheses

hold-specific effects. The autocorrelations in table 1 suggest that the covariante pattern in these data has exactly that structure. Eq. (11) shows that, if measurement error were the only source of variance in the growth rate of consumption, we would expect p(l) to be equal to -0.5. A value of -0.38 indicates that approximately 76 percent of that portion of the variance in the growth rate of consumption unexplained by family-specific real interest rates is the result of measurement error. 31 The results in column 2 of table 2 confirm the importance of measurement error. If measurement error were present, we would assume that ACi,, would be significant and that it would have a negative sign. In the regression, the coefficient on lagged consumption growth is negative and highly significant. I therefore assume an MA(l) error structure for all the regressions I report. My tests for household-specific effects and measurement error examined the serial correlation of errors for an individual household. But if there are aggregate shocks in the economy, then errors could be correlated across households within each period. Section 4.3 showed that such correlation would invalidate my statistical inference. Following the discussion of section 4.3, I conduct a GMM specification test for aggregate shocks. Column 4 in table 2 shows the results of adding time dummies to the instrument list. Adding those five instruments increased the value of the J-statistic from 17.36 in column 1 to 19.79. As discussed in section 4.3, if the time dummies are valid instruments, the difference between those J-statistics should be 31Note that measurement error in ri , or other omitted variables would bias the results away from the conclusion that measurement ‘error is severe. This variance decomposition is valid only if there are no random tastes shocks to household utility.

D. E. Runkle, Liquidity constraints and the permanent-income

hypothesis

a7

distributed asymptotically as a ,yg random variable. Since that statistic has a value of 2.43, I cannot reject the null hypothesis that time dummies are valid instruments and that there are no aggregate shocks.32 5.2. Tests of the permanent-income

hypothesis

Before I examine whether liquidity constraints exist, I must see whether these data, as a whole, support the permanent-income hypothesis. I do this by examining the regression results for eq. 031, then testing whether different income variables help predict consumption growth. The main regression result is reported in column 1 of table 2: The estimate of the intertemporal substitution parameter, (pi, is significant and is approximately 0.45. One way to interpret this result is that a one-percent increase in the real interest rate will make consumption grow at a rate 0.45 percent faster than it would have grown without the rate increase. This estimate implies that the coefficient of relative risk aversion is approximately 2.2. The size of the J-statistic (the x2-statistic referred to earlier) indicates that the model is not rejected. Thus the hypothesis that households intertemporally substitute consumption based on variations in expected after-tax real interest rates is not rejected by the data.33 But’other tests must be performed to see whether the data support the permanent-income hypothesis. As long as the instrument list is restricted to only those variables known by the household before time t, no other regressor should be significant in eq. (8). Table 3 reports regressions for the entire data set, including various measures of income as additional regressors. None of the four income variables (In yiI, In I$_ i, In K, - In q,_ i, and In y,_ 1 - In Y;.,_2) is significant in explaining the rate of growth of consumption.34 Together, these results provide strong support for the permanentincome hypothesis. 32Strictly speaking, I need to assume that the data in these regressions come from a mixing distribution, to allow the inclusion of nonstochastic instrumental variables [see White (1984)]. This assumption seems justified, given the previous finding that no family-specific effects exist. 331 cannot include x, as an instrument in the regression because of the timing of data collection. Consumption in periods r and t + 1 refers to consumption in a specific week during the first three months of the year, while income in t refers to income for the whole year. Furthermore, income for the whole year is not necessarily known during the first three months of the year, so income in t could be correlated with the forecast error in consumption growth. Thus, income in time t cannot be used as an instrument. 34These results are quite different from those of Zeldes (1989). There are three main differences between Zelde’s paper and this one: First, Zeldes uses family-specific dummies, which, as Chamberlain (1984) showed, may yield inconsistent parameter estimates in rationalexpectations models. Second, Zeldes ignores the effects on statistical inference of the movingaverage error structure resulting from measurement error in consumption, and therefore incorrectly computes the covariance matrix of the parameters. Third, he uses a different sample than is used here. I restrict my data to the years in which the PSID directly furnishes a marginal tax rate for each family (waves 9-161, and I use other, more stringent, data-selection criteria than Zeldes. Those criteria are described in section 3.

88

D.E. Runkle, Liquidity constraints and the permanent-income

hypothesis

Table 3 GMM estimates of AC,, r+ , = In(Ci,+t) - ln(Ci,)=a,+aIrir,,

+u~,+~.~

(1)

(2)

0.04062 (0.10123)

(0.018649)

(0.09757)

(0.01802)

aI

0.48716 (0.16860)

0.42801 (0.16458)

0.48260 (0.16881)

0.47858 (0.16674)

a2

0.01246 (0.01136)

0.08771 (0.09482)

0.01046 (0.01100)

0.02763 (0.03112)

J-statistic

16.249 (0.8199)

16.175 (0.8167)

16.556 (0.8329)

16.690 (0.8384)

N Extra regressor(s) No. of instruments No. of MA terms

2830 In% 16 1

2830 InV, ,-t lb 1

2830 AK,,-1 16 1

a0

-

%tandard errors are in parentheses under J-statistics.

(3)

0.06369

(4)

- 0.02242

2830 AY., 16 1

0.06785

under coefficients. Significance levels are in parentheses

5.3. Tests for liquidity constraints Even though the permanent-income hypothesis was not rejected for the entire sample, I can still test whether liquidity constraints exist by examining whether the permanent-income hypothesis can be rejected for different groups in my sample that might have trouble borrowing. I used two different criteria to split the sample: whether a household owned or rented its Table 4 Homeowners. GMM estimates of AC,, , + 1=In(Ci,+,)-In(Ci,)=ao+a,r,,,t+~i,+t.a (1)

(2)

(3)

(4)

(5)

a0

0.01210 (0.00886)

0.02735 (0.13096)

0.08688 (0.02003)

0.04295 (0.12369)

(0.01934)

aI

0.38302 (0.19367)

0.41601 (0.18079)

0.38386 (0.17768)

0.41270 (0.18125)

0.41768 (0.18036)

-

0.00698 (0.01443)

0.05274 (0.09592)

0.00528 (0.01370)

0.01414 (0.03134)

J-statistic

11.429 (0.4250)

9.553 (0.3449)

9.350 (0.3272)

9.641 (0.3525)

9.612 (0.3501)

N

2097 None 16 1

a2

Extra regressor(s) No. of instruments No. of MA terms

‘Standard errors are in parentheses under J-statistics.

2097

2097

In yi.t

AK,

16 1

16 1

2097

InL-l

16 1

0.08962

2097

ALI

16 1

under coefficients. Significance levels are in parentheses

D.E. Runkle, Liquidity constraints and the permanent-income

hypothesis

89

Table 5 Households with greater than two months’ income in liquid assets. GMM estimates of ACi,, + 1= In(Ci,+t) - In(Cir)=ao+a,rir,r (1)

(2)

a0

0.00568 (0.01259)

- 0.19675 (0.16580)

al

0.68042 (0.26563)

+uir+r.= (4)

(5)

0.05969 (0.03305)

-0.16786 (0.15800)

0.05930 (0.03286)

0.67054 (0.26079)

0.54288 (0.25122)

0.66778 (0.26136)

0.56033 (0.25054)

-

0.02823 (0.01791)

- 0.00020 (0.12708)

0.02512 (0.01705)

0.01719 (0.06223)

J-statistic

13.654 (0.6013)

12.222 (0.5720)

14.293 (0.7176)

12.464 (0.5908)

14.291 (0.7175)

N Extra regressor(s) No. of instruments No. of MA terms

950 None 16 1

950 InYi,, 16 1

950 AK.1 16 1

a2

-

‘Standard errors are in parentheses

(3)

950 tnL.1 16 1

under coefficients. Significance levels are

950 Ayi,,-1 16 1

in parentheses

under J-statistics. residence and whether the annuitized value of the household’s asset income was greater or less than two month’s income. Homeowners and people with liquid wealth probably would not be liquidity-constrained, so past income should not have much power in predicting their consumption growth. Tables 4 and 5 show exactly that result. In none of those regressions is an income variable significant in explaining consumption Table 6 Renters. GMM estimates of AC,, , + 1=In(Ci,+,)-In(Ci,)=ao+a,ri,,,+r+r+I.a

(1)

(2)

(3)

(4)

(5)

0.03334 (0.01833)

- 0.23412 (0.19674)

0.00015 (0.04489)

-0.19703 to.192021

0.00876 (0.04313)

0.73011 (0.39505)

0.74026 (0.38861)

0.58447 (0.35718)

0.71479 (0.38721)

0.57724 (0.35541)

-

0.02952 (0.02315)

0.17087 (0.18875)

0.02531 (0.02275)

0.04644 (0.06558)

J-statistic

14.862 (0.6840)

14.192 (0.7114)

13.878 (0.6915)

14.537 (0.7322)

14.979 (0.7574)

N Extra regressor(s) No. of instruments No. of MA terms

733 None 16 1

733 tnyl,,, 16 1

733

733 AL, 16 1

a0

a2

aStandard errors are in parentheses under J-statistics.

733

4

16 1

In bl

16 1

under coefficients. Significance levels are in parentheses

90

D. E. Runkle, Liquidity

constraints and the permanent-income

hypothesis

Table 7 Households with less than two months’ income in liquid assets. GMM estimates of AC,, ,+ , = In(Ci,+t) - In(Cir)=a,+a,ri,,I

+u~~+,.=

(1)

(2)

(3)

(4)

(5)

a0

0.02042 (0.01036)

-0.11314 (0.13680)

0.03885 (0.02623)

- 0.09413 (0.13222)

0.04121 (0.02553)

al

0.29585 (0.22812)

0.27877 (0.21910)

0.22928 (0.21719)

0.27772 (0.21939)

0.30580 (0.22355)

0.01762 (0.01519)

0.06313 (0.11447)

0.01558 (0.01476)

0.04011 (0.03442)

19.074 (0.9133)

18.448 (0.8973)

18.110 (0.8876)

a2

-

J-statistic

18.313 (0.8540)

18.220 (0.8908)

N Extra regressor(s) No. of instruments No. of MA terms

1880 None 16 1

1880 In K,, 16 1

‘Standard errors are in parentheses under J-statistics.

1880 4% 16 1 .

1880 In%-t 16 1

1880 AK,,-* 16 1

under coefficients. Significance levels are in parentheses

growth. Note also that the J-statistics are small enough that the overidentifying restrictions of the models cannot be rejected. It is more likely that renters and people without liquid wealth would not have easy access to credit markets and that past income might therefore explain part of their consumption growth. Tables 6 and 7 show that this conjecture is not true. As in the previous regressions, the income variables are not significant in explaining consumption growth. The overidentifying restrictions of the models also cannot be rejected. The data therefore do not support the hypothesis that one group of consumers is liquidity-constrained while another group is not. This finding is important because many authors have asserted that the rejection of the permanent-income hypothesis in aggregate data is due to liquidity constraints. 6. Conclusion The results presented here strongly support the permanent-income hypothesis. They also show that panel data do not support the view that certain consumers are liquidity-constrained and others are not. Further, they also suggest that measurement error in consumption is a serious problem in panel data and that appropriate precautions must be taken to ensure that statistical inference is not affected by that error. It is somewhat puzzling that these results are so strong, given the frequent rejection of the permanent-income hypothesis in aggregate data. One possi-

D.E. Runkle, Liquidity constraints and the permanent-income

hypothesis

91

ble reason for the difference between the time-series and panel-data results is that time-series tests are subject to aggregation biases. Aggregate studies assume a representative agent who conditions expectations on aggregate variables. But households may not find aggregate data useful in predicting their future economic conditions. In this study I assumed only that each household knew its own past economic condition. With this assumption, I could not reject the permanent-income hypothesis. Since the assumptions in this study about what each household knew are more reasonable than the information assumptions in aggregate studies, these results from household data may be better tests of the permanent-income hypothesis than those made with aggregate data.

Appendix: Issues in econometric panel-data models

estimation

of rational-expectations

Although many recent authors have used panel data to test models that assume rational expectations, relatively little has been written about whether traditional panel-data estimators are appropriate in a rational-expectations context.35 This appendix describes correct tests for different types of persistent household-specific heterogeneity in rational-expectations panel-data models. It also discusses tests for persistent heterogeneity in the presence of measurement error in the dependent variable.36 Recall the main equation, eq. (81, from the text: Aci,t+l

The orthogonality that

E(Ui,t+lI’i,t)

=

aiO

+

alri,r

+

‘i,t+l*

conditions for this model are generated by the assumption

=

‘7

i=l

where there are N households instruments that we can use household in time t or before. Correct statistical inference structure of the residuals. The

,..., N,

t=l,...,

T-l,

(A-1)

and T observations per household. Thus, the for estimating (8) are data known by the also demands that we know the covariance only circumstance in which two-stage least

35The most important previous paper is Chamberlain (1984). “I assume there that there are no aggregate shocks. Section 4.3 discusses both the problems that aggregate shocks cause in these models and tests for such shocks.

92

D. E. Runkle, Liquidity constraints

squares are appropriate E(vi,,vj,,)=az

hypothesis

for estimating (8) is when if

= 0

and the permanent-income

i=j

and

t=s,

otherwise.

(A.2)

Unfortunately, if persistent household-specific heterogeneity or measurement error in consumption is present, two-stage least squares will at best produce incorrect test statistics. At worst, it will yield inconsistent parameter estimates. In the text of this paper, I showed how to test and correct for measurement error in ACi,, + 1 if no persistent household-specific heterogeneity exists. In the appendix, I will explain how to estimate panel-data rational-expectations models with persistent household-specific effects. A.1. Estimation with household-specific effects and no measurement error in consumption In eq. (81, persistent household-specific effects could arise if each household had its own discount rate that was constant across time. In that case, ai would differ among households. If I were to falsely assume that (Yio is the same for each household, the difference between (Yio and a0 would be the persistent household-specific component in the error term. Thus the error term ui,l+l? would have two components: vi,r+l

=

77i +

Ei,r+l’

(A.3)

I,,+ i IZ,,,) = 0, while we have made no Thus far we have assumed that EC&. assumptions about the expectation of the persistent household-specific error conditioned on the household’s information set. But the value of this conditional expectation has important implications for determining the correct method to use in estimating eq. (8). I will consider two cases: E(qilZi,,) # 0 and E(~~ll,,~) = 0. A.1.I. Fixed effects: E(~ilZi,,) # 0 If E(q, IZ,,,) # 0, then instrumental-variables estimation will be inconsistent because the household-specific effect is correlated with the instruments. Such an error structure is known as the fixed-effects model. This structure would occur if each household had its own discount rate that was correlated with the household’s income, net worth, or after-tax interest rate. For example, if poor households had a higher discount rate than rich households, Ti would be correlated with income. I can circumvent this problem of inconsistent estimation in several ways, all of which involve eliminating qi.

D. E. Runkle, Liquidity constraints and the permanent-income

hypothesis

93

The most common procedure for eliminating 7,. is to demean every variable for each household and then to estimate the demeaned regression CAci,t

+

1 -dci)

=“l(‘i,r+l

-~)

+&i,t+l

-pi,

where AC,, , + 1 = ln - ln(C,,,). This demeaning has the same effect as adding a separate constant for each family. In a normal regression demeaning might make sense, but in a rational-expectations context, it assumes that households know the mean value of every variable before the end of the sample. In particular, using a demeaned regression requires including a function of future X’s in the regression, which would violate the orthogonality conditions arising from eq. (81, and would yield inconsistent estimates.37s38 If, however, I want to impose only the orthogonality conditions implied by (8), I should difference the data instead of demeaning it. If I estimate the equation

(A-5) I can use any data from time t - 1 or earlier as instruments and be sure that the orthogonality conditions are preserved. Thus, for eq. (13) I can use a GMM estimator of the form:

where g(p) is the sample average of the orthogonality conditions specified in (A.51 and W is a weighting matrix. In general, the optimal weighting matrix is simply the inverse of the covariance matrix of the orthogonality conditions that I impose to estimate a particular equation. Eq. (A.51 has an MAW error term. Therefore, the estimate of the covariance matrix of the orthogonality conditions is

n,+n,+n;, where

(A.6) 37Asimilar point was raised in a different context by Chamberlain (1984). ‘sSuppose that there were two observations on one household. If 1 used eq. (121, the transformed observations would be (AC, 1 -AC, 2) = a,(r, 1 - r, J + e1 , -E, z and (AC, 2 - AC1 ,I = 4h.2 - r*. 1) + El.2 - El. 1. Hawker, E(r;,2aI,I) # b, so this estikator Gould be in’consistek

J.Mon-D

94

D. E. Runkle, Liquidity constraints and the permanent-income

hypothesis

and K, is the sum of the number of nonmissing cross-products for each of the N individuals at the Zth lag.39*40 One simple way to check to see whether the covariance structure implied by eq. (13) is correct is to obtain an initial consistent estimate of the model by using the identity matrix as the weighting matrix and to compute the autocovariance function of the residuals, y(O), . . . , y(k), where k is the maximum number of observations per person. The model implies that y(O) = -2~0) and -y(k) = 0 for k r 2.4’ A.Z.2. Random effects: E(TI~JZ,,,)+ 0 If E(n;lZ, I> = 0, then instrumental-variables estimates are consistent. However, IV estimates are inefficient because the ni term is ignored in computing the covariance matrix for instrumental-variables estimation. As a result, IV estimation yields inconsistent standard errors. If I were using a standard regression model, a simple generalized-least-squares (GLS) transformation could be applied, but I cannot use a standard GLS transformation here because that would violate some of the model’s orthogonality conditions. However, GMM estimation can still be used to increase efficiency. In this case,

E(U;,tujs) =ut+ue:,if =CT

= 0

2 1

if

i =j,

t=s,

i=j,

t zs,

otherwise.

(A.71

Thus, persistence in ui I exists for each household. The persistent household-specific effect is merely a special form of serial correlation such that all of the autocovariances of the orthogonality conditions are nonzero. If the largest number of observations for any household is k, the covariance matrix of the orthogonality conditions is simply

3gBecause of the moving-average error structure, this estimate is not constrained to be positive definite. Cumby, Huizinga, and Obstfeld (19831, Eichenbaum, Hansen, and Singleton (19881, and Newey and West (1987) discuss consistent estimates that are guaranteed to be positive definite. ‘%ince I assume that the correlations in the error terms across individuals are zero, I can accumulate each of the R’s on an individual-by-individual basis. 4’The y(k)% and their covariance matrix can be computed by using the Yule-Walker equations for each household, averaging over ail the households, and weighting by the number of observations per household.

D.E. Runkle, Liquidityconstraintsand the permanent-income

hypothesis

95

where R, is computed exactly as detailed in (A.6k4* The inverse of this covariance matrix is the optimal weighting matrix for GMM estimation. I can determine whether (A.7) is a reasonable covariance structure for the model by using the identity matrix as the weighting matrix to obtain an initial consistent estimate of the model’s parameters. If I compute r(O), . . . , y(k), where k is the maximum number of observations per household, this model implies that y(l) = y(2) = * . * = y(k). A.1.3. Tests for persistent household-specific effects Hausman (1978) and Hausman and Taylor (1981) have developed tests to determine whether the fixed-effects or random-effects model is correct for a particular set of panel data. Their tests are equivalent to comparing fixedeffects estimates with estimates obtained by using a GLS transformation on the random-effects model. However, since both of these estimates will be inconsistent because the instruments are not strictly exogenous, I cannot use their tests. There is, however, a simple Hausman specification test that can be used. Since the random-effects estimator uses additional orthogonality conditions that the fixed-effects differencing estimator ignores, the former is efficient relative to the latter. Under the null hypothesis that the persistent household-specific effect is uncorrelated with the instruments, both estimators are also consistent. If, instead, the persistent household-specific effect is correlated with the instruments, only the fixed-effects differencing estimator will be consistent. Under the null hypothesis the test statistic

(ii ‘RE -cs,FEoY( Wl,,)

-

wlFeo))-1(4RE - 4J

will be distributed asymptotically as a x: random variable. If the value of this test statistic is too large, that suggests that the persistent household-specific effect is correlated with the household’s information set. In this case, the fixed-effects difference estimator must be used to get consistent parameter estimates. Otherwise, both estimators will be consistent, but the random-effects estimator should be used because it will be more efficient.43 A.2. Estimation with persistent household-specific effects and measurement error in consumption One of the principal issues discussed in the body of the paper was how to correctly estimate eq. (8) in the presence of measurement error in consumption. Since no persistent household-specific effects were found in the empiri42This estimate also may fail to be positive-definite. 43The main text of this paper discusses how to test whether any type of persistent householdspecific heterogeneity exists.

96

D. E. Runkle, Liquidity

constraints

and rhe permanent-income

hypothesis

cal results, the paper did not discuss how to estimate rational-expectations panel-data models with both household-specific effects and measurement error. However, since many authors have found evidence for persistent household-specific effects in panel data, it is important for economists to understand how to consistently estimate these models. Suppose, as discussed in section 4.2, that the log of consumption is measured with a white-noise error and persistent household-specific effects are present. In that case, “i,f+l

=

rli

+

&i,f+l

+

8i,r+l

-

si,ta

(A.81

If the household-specific effect is correlated with the household’s information set, then using an IV estimator to directly estimate eq. (8) will result in inconsistent parameter estimates, for the reasons discussed in section A.l.l. But eq. (8) can still be first-differenced to yield (“i,t+l

-Aci,t)

+&i.t+l

=al(ri,r-ri,t-l)

-

Ei,f

+6i,t+l

2Si,, + 6i,r-1.

-

(A-9)

Call the error term in this regression ui,t+l

=&i,,+l

+

6i,r+l

-&i,r

-

26i,t

+

(A.10)

6i,t-**

Given the previous assumptions about orthogonality in eq. (8), it should be true that E( ui f+ I lli ,_ i) = 0. Therefore, instruments from time C- 1 and before can be ‘used ‘to estimate eq. (A.9). Eq. (A.91 also implies a definite structure for the covariance of vi, f, namely, E( ui, ,uj,,) = 2as2 + 6~;

if

i=j,

t=s,

=

if

i=j,

It--sl=l,

if

i=j,

It-s1

=

--(T

E2-4u;

d

= 0

=2,

otherwise.

(A.ll)

Because the error term is now h4A(2), the covariance matrix of the orthogonality conditions is R,+R, One testable

+a;

+n,+n;.

proposition

that emerges is that y(O) = -27(l)

- 2y(2). The

D. E. Runkle, Liquidity constraints and the permanent-income

hypothesis

97

y(k)‘s can be computed easily, and the estimates of the coefficients and their standard errors can be computed using the Yule-Walker equations. However, it is not necessarily optimal to use this first-differenced estimator even if there is a persistent household-specific effect. If the persistent household-specific effect is independent of the household’s information set, then first-differencing will simply cause a loss of efficiency. Eq. (A.8) implies that the error term would be orthogonal to all information available at time t. Therefore it is possible to estimate that equation directly using GMM. Eq. (A.8) also suggests the structure of the autocovariances of the error in that equation, namely, E(ui ,uj,) =u~+u,*+~u~* =u

2 -f7 ?

=(T

2 ?

= 0

a*

if

i=j,

t =s,

if

i=j,

It-s1

if

i=j,

It-8122,

otherwise.

= 1,

(A.12)

One testable proposition that emerges from (A.12) is that y(j) = y(k) for j, k 2 2. Since the residual for each household is still correlated with every other residual for that household, the GMM covariance matrix is formed as it was when I assumed that no measurement error occurred. The single remaining question is how to determine whether a tied- or random-effects estimator is appropriate if both persistent household-specific effects and measurement error in consumption are present. I can test which estimator is appropriate by using exactly the same GMM specification test described in the previous section. If the value of the test statistic is small enough, then the random-effects estimator should be used. Otherwise, the fixed-effect difference estimator must be used to get consistent parameter estimates. References Altonji, J.G. and A. Sow, 1987, Testing the response of consumption to income change with (noisy) panel data, Quarterly Journal of Economics 102, 293-328. Ball, L., 1984, Intertemporal substitution and constraints on labor supply: Evidence from panel data, Unpublished manuscript (M.I.T., Cambridge, MA). Chamberlain, G., 1984, Panel data, in: Z. Griliches and M.D. Intriligator, eds., Handbook of econometrics, Vol. II (Elsevier Science Publishers, Amsterdam) 1247-1313. Cumby, R.E., J. Huizinga, and M. Obstfeld, 1983, Two-step two-stage least squares estimation in models with rational expectations, Journal of Econometrics 21, 333-355. Eichenbaum, MS., L.P. Hansen, and K.J. Singleton, 1988, A time-series analysis of representative agent models of consumption and leisure choice under uncertainty, Quarterly Journal of Economics 102,51-78.

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D.E. Runkle, Liquidity constrainrs and the permanent-income

hypothesis

Grossman, S.J. and R.J. Shiller, 1981, On the determinants of stock market variability, American Economic Review 71, 222-227. Hall, R. and F. Mishkin, 1982, The sensitivity of consumption to transitory income: Estimates from panel data on households, Econometrica 50, 461-482. Hansen, L.P., 1982, Large sample properties of generalized method of moments estimators, Econometrica 50, 1029-1054. Hansen, L.P. and K.J. Singleton, 1982, Generalized instrumental variables estimation of nonlinear rational expectations models, Econometrica 50, 1269-1286. Hausman, J.A., 1978, Specification tests in econometrics, Econometrica 46, 1251-1271. Hausman, J.A. and W. Taylor, 1981, Panel data and unobservable individual effects, Econometrica 49, 1377-1398. Hayashi, F., 1987, Tests for liquidity constraints: A critical survey, in: T. Bewley, ed., Advances in econometrics - Fifth world congress, Vol. II (Cambridge University Press, Cambridge) 91-120. Keane, M.P. and D.E. Runkle, 1990, Testing the rationality of price forecasts: New evidence from panel data, American Economic Review 80, 714-735. Mankiw, N.G., 1981, The permanent income hypothesis and the real interest rate, Economics Letters 8, 307-311. Michener, R., 1984, Permanent income in general equilibrium, Journal of Monetary Economics 13, 297-305. Newey, W.K., 1985, Maximum likelihood specification testing and conditional moments tests, Econometrica 53, 1047-1070. Newey, W.K. and K. West, 1987, A simple, positive semidefinite, heteroskedasticity and autocovariance consistent covariance matrix, Econometrica 55, 703-708. Rubenstein, M., 1974, An aggregation theorem for securities markets, Journal of Financial Economics 1, 224-246. Shapiro, M.D., 1984, The permanent income hypothesis and the real interest rate: Some evidence from panel data, Economics Letters 14, 93-100. White, H., 1984, Asymptotic theory for econometricians (Academic Press, New York, NY). Zeldes, S., 1989, Consumption and liquidity constraints: An empirical investigation, Journal of Political Economy 97, 305-346.