Direct tests of the permanent income hypothesis under uncertainty, inflationary expectations and liquidity constraints

JAKOB B. MADSEN MICHAEL McALEER University of Western Australia Nedlancts, Australia

Direct Tests of the Permanent Income Hypothesis under Uncertainty, Inflationary Expectations and Liquidity Constraints* Several studies have argued that the life-cycle permanent income hypothesis (LC-PIH) of Hall (1978) breaks down because of the excess sensitivity of consumption to current income and through consumers failing to exploit information which is available in period t-1. Using direct expectations data based on consumer surveys for the U.S., this study" shows that when uncertainty, in particular, and credit constraints are accommodated in the model, consumption is not sensitive to current income. Moreover, contrary to previous empirical findings, the index of consumer confidence is found to be unable to predict consumption. Thus, the theoretical predictions of the rational expectations LC-PIH are unfounded empirically because they fail to accommodate uncertainty, in particular, and credit constraints.

1. Introduction The life-cycle permanent income hypothesis (LC-PIH) predicts that consumption depends on permanent income, which is the annuity value of lifetime resources, so that consumption is unrelated to current income (Friedman 1957). If rational expectations are also assumed, the LC-PIH implies that consumption follows a random walk, so that only consumption in the previous period contains information which can predict current consumption (Hall 1978). Numerous empirical studies have argued for a rejection of the rational expectations LC-PIH hypothesis because consumption has been found to be excessively sensitive, that is, positively related to current income (see, for instance, Campbell and Mankiw 1989, 1990, 1991; *Helpful comments by an anonymous referee, and seminar participants at the Bank of Japan, Chinese University of Hong Kong, City University of Hong Kong, Hiroshima University, Hong Kong University of Science and Technology, Kyoto University, Osaka University, University of Hong Kong, and Yokohama National University and financial support from the Australian Research Council, are gratefully acknowledged. Richard Curtin kindly provided the University of Michigan Surveys of Consumers Data.

Journal of Macroeconomics, Spring 2000, Vol. 22, No. 2, pp. 229-252 Copyright © 2000 by Louisiana State University Press 0164-0704/2000/$1.50

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Jakob B. Madsen and Michael McAleer Carroll, Fuhrer and Wilcox 1994; Flavin 1981; and Hayashi 1982). Using macroeconomie data, Flavin (1985), Jappelli and Pagano (1989), Vaidyanathan (1993) and Wilcox (1989) have provided empirical evidence which suggests that the excess sensitivity of consumption to current disposable income can be explained, to some extent, by credit constraints. It follows that limited access to credit markets prevents young consumers, as well as other consumers who are experiencing a temporary loss in income, from borrowing against their expected lifetime incomes. Although these studies provide empirical support for the credit constraint hypothesis, and hence seem to suggest that a modification of the standard rational expectations LC-PIH is needed, they are nevertheless subject to several problems, which are discussed in greater detail in Section 3 below. First, Campbell and Mankiw (1991) find that there has not been a discernible decline in the excess sensitivity of consumption to income for six major countries over the past two to three decades, despite the fact that credit markets have developed substantially since WWII. Consequently, they suggest that this issue deserves further investigation. Second, measures such as the rate of unemployment (Flavin 1985; Wilcox 1989), total consumer credit to consumption ratio (Jappelli and Pagano 1989; Vaidyanathan 1993) and nominal interest rates (Wilcox 1989) have been used to approximate credit constraints. However, there is no guarantee that these proxies are adequate approximations and, indeed, they may be detecting movements other than credit constraints. For instance, Juster and Taylor (1975) use the rate of unemployment as a proxy for uncertainty in estimating their consumption functions, so that it is not entirely clear whether the rate of unemployment accurately reflects uncertainty or credit constraints, or possibly both. Third, the credit constraint hypothesis has not been tested against its alternatives, for instance, that uncertainty may induce consumers not to obey the LC-PIH. Income uncertainty leads both to more prudent behavior and to higher sensitivity of consumption to current income: a large increase in expected income lowers the need for precautionary saving, and hence increases consumption (Blanchard and Fischer 1989, pp. 290-91; Muellbauer and Lattimore 1995). A large decrease in income, by contrast, increases precautionary saving, thereby establishing a positive correlation between income and consumption. Ignoring the effects of uncertainty in model estimation yields an omitted variables bias. More importantly, such an omission ignores the possibility that consumers may be credit constrained because of the uncertainty attached to their future capacity to repay their debts, and not through any failure of credit markets. Consequently, the presence of credit constraints is affected by uncertainty, and if uncertainty is not incorporated adequately in

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Direct Tests of the Permanent Income Hypothesis the consumption function, then the credit availability variable will not capture the underlying effects of credit constraints on excess sensitivity_ The empirical estimates provided in this paper reveal that the significance of the credit constraint variable in the eonsumplion function depends on whether uncertainty and inflationary expectations are accommodated in the model. Finally, even though the liquidity constraint hypothesis may be true, it is unlikely to account for all the excess sensitivity in consumption. Only 12% of households in the 1983 Survey of Consumer Finances for the U.S. (see Kennickell and ShaekMarquez 1993) held zero liquid assets, and the excess sensitivity parameter is typically estimated to be in the region of 0.4 for the U.S. In this paper, the extent to which excess sensitivity in consumption can be explained by uncertainty, real interest rates, inflationary expectations and credit constraints are tested using the University of Michigan Surveys of Consumers data. Specifically, it is tested whether: 1) uncertainty causes excess sensitivity; 2) excess sensitivity reflects some income accruing to consumers who do not obey the LC-PIH, as advocated by Campbell and Mankiw (1989); 3) excess sensitivity can be explained by the real interest rate and/or inflationary expectations (Miehener 1984); and 4) excess sensitivity is caused by credit constraints. The Michigan Survey contains information regarding expected inflation, uncertainty, and credit constraints. 1 Since consumers are asked explicitly in the Michigan Survey whether their consumption has been constrained by credit or by an uncertain future, both of which are detailed in Section 4, it enables discrimination between the various hypotheses that have been outlined above. The empirical estimates in Sections 4 and 5 indicate that consumption is not sensitive to current income when the influences of uncertainty (broadly defned), in particular, and also credit constraints are accommodated in the model. Furthermore, it is found that, although the consumer confidence indicator is a significant predictor in a simple consumption function, as suggested by Carroll, Fuhrer and Wilcox (1994), it loses its forecasting ability when the influences of uncertainty and credit constraints on consumption are incorporated in the model. In Section 6, we expand the empirical analysis with expected real income to implicitly test the extent to which excess sensitivity reflects credit constraints, using the test suggested by Antzoulatos (1994, 1997). In Section 7, it is concluded that the rational expectations LCPIH is not rejected because of excess sensitivity or because consumption is 1Whereas survey evidence on inflationary expectations has been used in consumption functions (for instance, Wilcox 1989), survey evidence on credit constraints and uncertainty have, to the best of our knowledge, not previously been used to discriminate between competing theories of consumption.

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Jakob B. Madsen and Michael McAleer predicted by consumer confidence, but because the hypothesis fails to accommodate uncertainty, in particular, and also the lack of access to adequate credit facilities, in both estimation and testing.

2. Consumption, the LC-PIH and Excess Sensitivity Campbell and Mankiw (1989, 1990, 1991) propose that the consumption function can be represented as a weighted average of consumers who base their decisions on current income and permanent income. They assume that a fraction of consumers, i-L, obey the LC-PIH, whereas the fraction L do not. The primary issue addressed in this paper is whether a non-zero reflects the breakdown of the LC-PIH, or rather the omission of factors, such as uncertainty and the presence of credit constraints, which prevent consumers from conforming to the LC-PIH. The representative LC-PIH consumer chooses consumption, Clt, to maximize expected utility from the discounted stream of real consumption. ACtt is a zero mean, independently and identically distributed random variable and is uncorrelated with all variables known to the consumer at time t - 1. Let C,2~be the real consumption of the representative rule-of-thumb consumer, who is assumed to spend all of their current income. Thus, AC2t = EAYt, where £, the excess sensitivity parameter, is the fraction of income accruing to rule-of-thumb consumers, and Y is real disposable income. The change in aggregate real per capita consumption is given by the following equation: ACt = ACu + AC2t = ~,AYt + u l t ,

(1)

where uzt is a stochastic error term. This equation states that the change in consumption is given by the change in real disposable income and the change in permanent income, which follows a stationary white noise process.

3. Causes of Excess Sensitivity in Consumption A substantial body of empirical evidence suggests that Z > 0. It has been argued by some that a positive ~ reflects the fraction of the population that does not obey the LC-PIH, whereas others have argued that market imperfections prevent consumers from obeying the LC-PIH. More precisely, a positive £ may reflect some or all of the following factors, which need not be mutually exclusive:

a. Non-life-cycle behavior. According to this hypothesis, the fraction k of income is earned by rule-of-thumb consumers who are unlikely to change 232

Direct Tests of the Permanent Income Hypothesis their behavior, even in a market without imperfections (Campbell and Mankiw 1989, i991). b. Variable real interest rate. The LC-PIH model discussed in the previous section is derived under the assumption of a constant real interest rate. However, Miehener (1984) has demonstrated that intertemporal optimization gives rise to an endogenous interest rate response at an aggregate level, which in turn leads to excess sensitivity to income. If all consumers try to divert consumption to the future, the real interest rate will decrease because the supply of loanable funds increases. Consequently, a failure to take account of the endogenous real interest rate response will yield an excess sensitivity of consumption to income. c. Uncertainby. This hypothesis, which revolves around the uncertainty concerning income and spending, has not previously been accorded much attention, especially in the empirical literature. Under the uncertainty hypothesis, consumers are less likely to obey the LC-PIH and are more likely to behave in a myopic manner, the greater is the uncertainty faced (Blanchard and Fischer 1989; Muellbaner and Lattimore 1995). For example, a large decrease in income increases uncertainty, and hence the need for precautionary savings, and lowers consumption; when income increases, uncertainty is decreased, the need for precautionary savings is lowered, and consumption increases. A positive relationship between current consumption and current income is thereby established, and the relationship is an increasing function of uncertainty. Blanchard and Fischer (1989) demonstrate that uncertainty increases the excess sensitivity parameter under the assumption of intertemporal optimization. Their result is reinforced if it is also assumed that consumers have adaptive expectations. In such a case, consumers expect the decrease in their income to continue, which enhances their saving, so that the excess sensitivity parameter will increase even further. Closely related to this uncertainty concept is the buffer stock theory of saving, which has been advocated by Carroll (1992, 1994). According to the buffer stock theory, consumers with greater uncertainty about future income have lower current consumption. According to this theory, consumption growth will be negatively correlated with contemporaneous uncertainty, but positively correlated with lagged uncertainty (Carroll

1992). d. Credit constraints. This hypothesis has gained popularity as a (partial) explanation of a non-zero L (Flavin 1985; Hall and Mishkin 1982; Hayashi 1985; Hubbard and Judd 1986; Jappelli and Pagano 1989; Vaidyanathan 1993; and Wilcox 1989). According to this hypothesis, credit constraints prevent consumers from allocating their intertemporal consumption optimally. 233

Jakob B. Madsen and Michael McAleer

In the next section the influences of these factors on consumption are investigated. In particular, some variables that have been found to predict consumption in other empirical studies are reexamined after inclusion of the factors mentioned above.

4. Empirical Estimates Stochastic Specification

To discriminate between the various hypotheses outlined in the previous section, consumption functions are estimated for the U.S. using variables which are taken from the University of Michigan Surveys of Consumers. For that purpose, Equation (1) is augmented to allow for credit constraints, uncertainty and the real interest rate, as follows: AC t = i10 -t- )~AYt q- o:lrt q- o:2UNt q- 113CC~ q- u2t ,

(2)

where C is the log of real per capita consumption of non-durables and services, Y is the log of real per capita disposable income, r is the real after-tax interest rate, UN is uncertainty, and CC is credit constraints. The survey data are given as follows. Measurement o f Uncertainty, Inflationary Expectations and Credit Constraints

Data from the University of Michigan Surveys of Consumers are used to measure: (a) inflationary expectations; (b) UN; and (c) CC. The specific questions that relate to these three variables are as follows: a. "During the next 12 months, do you think that prices in general will go up, or go down, or stay where they are now?" and "By about what percent do you expect prices to go up, on average, during the next 12 months?" b. "Spealdng now of the automobile market--do you think that the next 12 months or so will be a good time to buy a car?" and "Why do you say so?": "Bad times ahead; uncertain future.'" c. "Speaking now of the automobile market--do you think that the next 12 months or so will be a good time to buy a car?" and ''Why do you say so?": "Interest rates are high; credit is tight.'" The expected mean increase in prices is reported, which can readily be used as a measure of inflationary expectations. However, the uncertainty and credit constraints variables, which are needed to estimate the consumption function, are less straightforward to measure because the queslions are conditional. Consumers are not asked directly whether or not they consider 234

Direct Tests of the Permanent Income Hypothesis the future to be uncertain, although this is the essential variable for the consumption choice. Instead, the question is conditional upon the response "bad time" to the question "Do you think that the next 12 months or so will be a good time or a bad time to buy a car?" It is, therefore, not appropriate to use only the frequency of consumers responding "bad times ahead, uncertain future" relative to the consumers responding "bad time" to the question "Do you think that the next 12 months or so will be a good time or a bad time to buy a car?" If only 5% of the consumers think that it is bad time to buy a car, then the response of the 95% of the consumers is suppressed. To deal with this problem, uncertainty is measured by multiplying the percentage of those responding with "bad time" to the question "Do you think that the next 12 months or so will be a good time or a bad time to buy a car?" with the percentage of those responding in the affirmative to the question "Bad times ahead; uncertain future." The degree to which consumers find themselves credit constrained is measured by multiplying the percentage of those responding with "bad time" to the question "Do you think that the next 12 months or so will be a good time or a bad time to buy a car?" with the percentage of those responding in the affirmative to the question "Interest rates are high; credit is tight." Finally, there are two issues which need to be addressed concerning the survey questions. The first issue is whether to measure UN and CC in levels or in first differences. Estimation is undertaken with UN and CC measured in levels because the survey questions indicate that they are intended to measure changes. The questions "good times" or "bad times" refer to the current state as compared with the normal state. If the respondent answers "good times," a positive change is indicated relative to normal experience. This formulation suggests that UN and CC are trend stationary, as opposed to difference stationary. The second issue is why consumer opinions about buying conditions for cars are used as opposed to buying conditions for houses or large household goods. There are several reasons for this choice, as follows: a. The consumer has to make the decision whether or not to buy a new car at reasonably regular intervals. Together with the fact that the purchase of a new car can be easily postponed, it is likely that the consumer has actively thought about whether or not times are good to buy a car when answering the survey questions. By contrast, the consumer makes the choice about whether or not to buy a house at highly infrequent intervals. b. The degree of uncertainty is unlikely to be reflected in survey questions about purchases of houses. Only a minor proportion (at most 2-4%) of consumers responding negatively to the question of whether it is a good time to buy a house respond "Bad times ahead; uncertain future," which 235

Jakob B. Madsen and Michael McAleer likely reflects the fact that houses are safe investments in times of uncertainty. c. Over 60% of new cars are purchased partially or entirely on credit (Evans 1969, 151). Hence, most consumers have to consider credit availability whenever they contemplate buying a car. d. Purchases of large household goods involve only a fraction of the outlay as compared with purchases of cars. Therefore, aspects of uncertainty and credit terms are likely to be less important for purchases of large household goods other than cars. The question which comes readily to mind is how the estimation resuits will be affected by the choice of variables. If consumer opinions about the purchase of large household goods are used to calculate CC and UN, results are obtained which are almost identical to those presented below. If consumer opinions for purchases of houses are used, the uncertainty variable becomes slightly less insignificant as compared with the estimates provided below, and the credit constraint variable becomes insignificant.

Data and Estimation Method The quarterly data on income and consumption of non-durables and services are seasonally adjusted and are measured on a per capita basis using total population. The models are estimated over the period 1972:i to 1997:i: the data period commences in 1972:i because survey data on CC and UN before that period are available only one, two, or three times a year. Per capita income is instrumented using 1-3 lags of the instruments (the instruments are indicated in the notes to Table 1). Following Campbell and Mankiw (1989, 1990, 1991), it has become customary to lag the instruments at least two periods to avoid the problems associated with an MA(1) error process_ If the residuals are found not to exhibit an MA(1) process when instruments lagged one period or more are used, then the instrument set is not optimal if only the instruments lagged two periods or more are included. Thus, it is preferable to also include instruments lagged one period in the instrument set and then to test for an MA(1) error process in the errors. The non-income regressors in Equation (2) were not instrumented because Hausman tests could not reject the null hypothesis of exogeneity.2 z2"qae estimation period is 1972:i-1997:i. Absolute t-tests for the weak exogeneity of the variables UNt, CCt, rt, it and 'p~, where it is the nominal interest rate (3-month Treasury Bill rate) and "p7 is expected inflation, are 0.17, 0.63, 1.42, 1.44, and 1.33, respectively. The tests were performed using the unrestricted estimate of Equation (2) with the real interest rate partitioned into 'p~ and it (Model 7 in Table 1), for all variables except for rt, where the unrestricted estimate of Equation (2) was used (Model 4 in Table 1). The following instruments were used: UNt: UNt_I, UNt_2, UN,_3, ACt_l, ACt_2~ and ACt_3; CC~: CCt_I, CCt_~, CCt_a, AC t 1,

236

Direct Tests of the Permanent lncome Hypothesis If instruments are used for variables that are exogenous, then the estimates become inefficient as compared to least squares estimates. Estimation Results The results from estimating Equation (2), and restricted versions thereof, are presented in Table 1. White's heteroscedasticity consistent standard errors are used in the two cases where heteroscedasticity is present at the 1% significance level. The remaining diagnostic tests do not suggest any inadequacies in the models at the 1% level. However, the F-tests for structural instability suggest a structural break in 1981/82 in two cases at the 5% level. These cases will be discussed in the presentation of the results. Note that the Lagrange multiplier tests for first-order serial correlation, LM(S), do not suggest an MA(1) process in the estimates of Table 1, which suggests that it is appropriate to include only one-period lags in the instrument set. In the estimates in the first row of the table, the restriction ~1 = ~2 = aa = 0 is imposed in Equation (2) to inspect the sensitivity of ~, the estimated coefficient of AYe, to the inclusion of the other variables. The estimated value of L is 0.38, which is virtually identical to the estimate given in Flavin (1981) but is slightly lower than most of the estimates in Campbell and Mankiw (1989, 1991). However, since income is negatively correlated with uncertainty, it is biased upward, as confirmed by the other estimates. In the second row, where CC is omitted from the estimates of Equation (2), the estimated coefficient of uncertainty is negative and highly significant, the excess sensitivity parameter is 0.22 and significant, and the estimated coefficient of the real interest rate is positive and significant, an issue which is explored further below. In the third row, where the coefficient of uncertainty is omitted, the estimate of L is 0.25 and is significant. Both CC and the real interest rate are significant at the 5% level, with the coefficient of credit constraints having the expected sign. The F-test indicates structural instability at the 1% level, which may indicate that the model is misspecified. Unrestricted estimates of Equation (2) are presented in row 4. The coefficients of UN and CC have the expected signs and are significant, although the significance of CC is only marginal. In this case, the estimated excess sensitivity parameter has decreased further to 0.16, but is still significant at the 5% level. From these results it can be concluded that consumption is only marginally sensitive to current income when the influence of ACt_2, ACt_3, it_l, it_2~ and it_~; it: AYt_I, AYt_2, AYt_~ ACt_l, AC~ ~, ACt_3, it_l, it_z, it-3, rt I, rt 2, and r~_ 3; rt: AYt-1, AYt- 2, AYt- 3, ACt-l, ACt- 2, ACt-3, it- l, it-2, A/t-a, rt-1, rt- 2, and rt_3; AYt: AYt-1, AYe-2, AYt 3, ACt-l, AC~_ 2, ACt-a, it-l, it-2, and it_3; "p~: "P~-I, P~-2, "P~-3~AYt-I, AYt-2, AYt-3, ACt-l, ACt-2, ACt-a, it-l, it 2, it 3, AMlt 1, AMlt_z, and AMlt 3237

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Jakob B. Madsen and Michael McAleer uncertainty, credit constraints and the real interest rate have been accommodated in the model, a The estimated coefficient of the real interest rate is positive and significant in the estimates given in rows 2-4. This result is consistent with the rational expectations LC-PIH because future consumption becomes cheaper relative to current consumption. However, a condition that must hold for this result to be consistent with the LC-PIH is that, when the real interest rate is decomposed into two components, namely the inflation rate that in time t is expected to persist at time t + 1, 'p~+l, and the nominal after tax interest rate, it, their estimated coefficients are equal but opposite in sign. Parameter estimates with the real interest rate decomposed into its two components are shown in rows 5-9 of Table 1. The estimates associated with uncertainty and excess sensitivity are very similar to the corresponding estimates given in rows 2~1. However, the estimated coefficients of credit constraints are insignificant at the 5% level when uncertainty is accommodated in the estimates. The coefficient estimates of tile nominal after tax interest rate are insignificant in each of rows 5-7, whereas the estimated coefficient of inflationary expectations is consistently negative and highly significant in each of rows 5-9. Thus, the estimated effect of the real interest rate is positive in rows 2--4 because inflationary expectations have a negative effect on consumption, and not because consumers maximize their intertemporal utility. This result may suggest that consmners suffer from money illusion in believing that real income and wealth decrease permanently as a result of increasing inflation. This hypothesis seems to be supported by a recent survey study by Shiller (1997), where the reasons why consumers dislike inflation are examined. Shifler finds that a major reason why consumers dislike inflation is that they are uncertain whether or not income compensation will take place, or if it does whether the adjustment will be sufficient. Juster and Taylor (1975) provide a similar explanation. They argue that if the price level is expected to increase, income earners become uncertain about their expected real income because of the lack of formal indexation rules for wages (the same argument would probably apply to tax indexation rules for all consumers). Consequently, consumers increase their saving, which establishes a negative relationship between inflationary expectations and changes in consumption. The real income uncertainty that is associated with inflationary expec3It remains a possibility that the insignificance of the coefficient of current income reflects the choice of instruments for AYt. Since we have already included one-period lags in the instrument set, these instruments are probably superior to those used previously. Using different instrument sets that are often used in the literature yields results, which are approximately similar to the results above, except that the estimated coefficient of CC becomes less significant.

240

Direct Tests of the Permanent Income Hypothesis

tations is likely to be different from the income uncertainty that is associated with the UN variable. Whereas inflationary expectations reflect real income uncertainty, which is caused by inflation, the UN variable is likely to reflect real income uncertainty, which is associated with unemployment or, more generally, the business cycle. Hence, both variables appear to be important determinants of consumption and, therefore, an important explanation for the excess sensitivity of consumption to income. In rows 5-6, the estimated coefficients of income, uncertainty, credit constraints and inflationary expectations are all significant at the 5% level. If all the variables are included in the model simultaneously, then the coefficients of income, credit constraints and the nominal rate of interest are all insignificant at the 5% level, as is shown in row 7. Furthermore, the F-test for structural instability indicates a structural break at the 5% level in the estimates in row 6, where uncertainty has been omitted. This result seems to indicate that the model is misspecified when UN is excluded from the consumption function. Starting from row 7, the estimates in rows 8-9 show the results of sequentially deleting the insignificant nominal interest rate and then the insignificant credit constraint, with all the remaining variables being insignificant at the 5% level. Deleting the nominal interest rate from row 7 yields the estimates in row 8. Deleting the insignificant CC from row 8 yields the estimates in row 9, in which all coefficients are significant at the 5% level. From the estimates in rows 1-9, it can be concluded that the significance of CC and income in the consumption function are highly sensitive to the model specification, and that CC tends to render the model structurally unstable. However, the estimates suggest that consumption is highly dependent on uncertainty and inflationary expectations, which may also reflect uncertainty. The coefficients of uncertainty and inflationary expectations are consistently highly significant, and the magnitudes of their estimated effects are not sensitive to the model specification. As a final cheek of model (9.), it is tested whether consumers exploit the information which is available to them when they form their expectations about their permanent income. Carroll, Fuhrer and Wilcox (1994) find that the LC-PIH breaks down because current spending does not fully reflect the consumer sentiment, which is denoted eonf below, in the previous quarter. They find that the consumer confidence indicator of the University of Michigan Surveys of Consumers predicts consumption, where the change in consumption is regressed on changes in income and the consumer confidence indicator lagged one period. The estimates in row 9 of Table 1 indicate that their results can be replicated using our data. In particular, the eoeffleient of lagged consumer confidence is positive and significant at the 5% level, as found in Carroll, Fuhrer and Wilcox (1994), and ~, is estimated 241

]akob B. Madsen and Michael McAleer to be 0_33 and significant. However, the estimated coefficient of the consumer confidence indicator becomes negative and remains significant when uncertainty, credit constraints and inflationary expectations are accommodated in the model, as indicated by the estimates in row 10. Therefore, the consumer confidence indicator does not contain any information that earl predict current spending when the influences of uncertainty, credit constraints, and inflationary expectations on consumption are considered. 4 It is noteworthy, however, that the residuals become heteroscedastic mad serial correlated when the consumer confidence indicator is included in the model, as seen in rows 9 and 10. This provides further evidence against the hypothesis that the consumer confidence indicator contains information which may be useful in predicting consumption. The clear implication of these results is that empirical testing of the rational expectations LC-PIH model of Hall (1978) has led to rejection, not necessarily because consumption does not follow a random walk, but because factors such as uncertainty and credit constraints have been ignored. Therefore, the model breaks down primarily because uncertainty, in particular, and credit constraints prevent consumers from obeying the LC-PIH, and not because of excess sensil~vity and the presence of other important economic indicators which can predict eonsmnption, as has been highlighted in the literature to date.

5. Decomposition of Income for Life-Cyclers and Non-Life-Cyclers The previous section showed that the estimated values of ~ dechned substantially when uncertainty, inflation expectations and credit were accommodated in the estimates. However, there may be two problems associated with the estimates given in the previous section. The first problem is that may be biased for L because the fraction of total disposable income going to rule-of-thumb consumers is likely to change over time (Christiano 1989; Ando 1989). If this is true, then real disposable income is mismeasured, which results in an errors-in-variables bias. The second problem is that the Campbell and Mankiw model suggests that consumers are either life-cyclers or they are not. Such a demarcation rules out the possibility that some consumers are pargal life-cyclers in the sense that consumption is fractionally sensitive to current income for this category of consumers. 4Hall (1978) finds that real share prices can predict consumption when the model is estimated in levels. Changes in share prices deflated by the disposable income deflator were not significant predictors of consumption in our model, regardless of whether income, uncertainty or credit constraints were included in the model.

242

Direct Tests of the Permanent Income Hypothesis To cater for these issues, income is partitioned into income of nonlife-cyclers and income of life-cyclers, who may potentially be partial lifecyelers. Following Carroll, Fuhrer and Wilcox (1994), it is assumed that the rule-of-thumb consumer's income consists of wage and salary income. More specifically, the income of the rule-of-thumb (non-life-cycler) consumer is given by yNLe = log[(W(1 - T)/Pr)/POP], where W is wages and salaries, T is the average income tax rate, POP is the population and pr is the implicit disposable income deflator. The income of the life-cycle consumer is computed as the difference, yLC = (y _ yNLC). The results of estimating restricted and unrestricted versions of Equation (2) using income partitioned into that of potential-life-cyclers and of non-life-cyclers are presented in rows 1-5 of Table 2. Inflationary expectations are used instead of the real interest rate because of the problems discussed in the previous section. The nominal interest rate has been omitted from all regressions because it was consistently insignificant at the 5% level. Diagnostic tests do not suggest any inadequacy in any of the model specifications at the 5% level, except for structural instability in row 3. In the first row, consumption is regressed only on income of the two groups. As expected, the estimated coefficient of wages and salaries of non-life-cyclers is highly significant and very high at 0.66. The estimated coefficient of the income of life-cyclers is insignificant in all estimated models (rows 1 4 ) in Table 2. If uncertainty and inflationary expectations are added to this regression, then the estimated coefficient of wages and salaries decreases to a marginally significant 0.32, while uncertainty and inflationary expectations are highly significant (row 2). If credit constraints and inflationary expectations are included in the model, then the effect of wages and salaries changes to 0.44 (row 3). Note that the estimated coefficients of credit constraints and inflationary expectations are insignificant at the 5% level, and structural instability suggests that the model is misspecified. In the estimates given in row 4, where UN, CC, and inflationary expectations are included with the income variables, neither the effect of wages and salaries nor credit constraints is significant, whereas uncertainty and inflationary expectations are highly significant. The results in row 5 show that the coefficient of CC becomes marginally significant when both the insignificant variables are deleted from the model. These results provide two important insights. First, credit constraints are not consistently a significant cause of excess sensitivity when income is partitioned into the income of non-life cyclers and that of life-cyclers. Second, the excess sensitivity and the significance of consumption to income are highly sensitive to the model specification. The excess sensitivity parameter is significant at the 5% level when uncertainty and inflation expectations are

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Direct Tests of the Perraanent Income Hypothesis included in the model (row 2). However, if credit constraints are also included in the model (row 4), then the excess sensitivity parameter becomes insignificant. Finally, UN¢_1 is included in the model to test whether the significance of the uncertainty variable reflects the buffer stock theory of saving behavior. As noted in Section 3, the buffer stock theory predicts that consumption growth is negatively correlated with contemporaneous uncertainty, but is positively correlated with lagged uncertainty (Carroll 1992). Thus, the coefficient of UN¢ should be negative and that of U N t _ 1 positive. These results are presented in row 6 of Table 2. The coefficient of lagged uncertainty, although positive, is highly insignificant, and the excess sensitivity parameter is estimated to be a low 0.17 and only marginally significant. Moreover, the presence of heteroscedasticity in the residuals suggests that the model is misspecified. Hence, the consistently negative and statistically significant impact of contemporaneous uncertainty in Tables 1 and 2 would not seem to reflect the buffer stock theory of saving behavior. Overall, the estimates are fairly consistent with the estimates in Table 1. The excess sensitivity parameter declines significantly in magnitude when uncertainty, credit constraints, and inflationary expectations are accommodated in the various models. Hence, the estimates of excess sensitivity of Campbell and Manldw are biased upwards because they have omitted important determinants of consumption.

6. Alternative Measurement of Credit Constraints The estimates in the previous section indicate that uncertainty is an important reason for excess sensitivity, whereas the importance of credit constraints was shown to be sensitive to model specification. In this section we examine the possibility that these results arise because survey data on credit constraints do not adequately capture whether consumers are credit constrained. For this purpose, the test developed by Antzoulatos (1994, 1997) is used to examine the extent to which excess sensitivity reflects whether consumers are liquidity constrained, and whether the hypothesis of uncertainty loses significance when credit constraints are accommodated in the model. Since Antzoulatos' test involves expected real income growth, the survey data on expected real income growth is ideal for testing the implications of the LC-PIH model. Antzoulatos (1994, 1997) demonstrates that, if the consumer is credit constrained, then the growth in consumption will be correlated with both current and expected income growth, even if the consumer obeys the LCPIH. However, the growth in consumption will not be correlated with future income growth if consumers do not obey the LC-PIH. The intuition behind 245

Jakob B. Madsen and Michael McAleer these results is the following. Suppose that a forward-looking consumer expects an increasing income. If the consumer is credit constrained, then consumption will not adjust to the expected growth in income. It follows that consumption is correlated with future income growth. However, if the ruleof-thumb hypothesis is correct, then consumption growth is not correlated with expected income growth as the consumer spends all current income independently of expected income growth. Incorporating the test of Ant_zoulatos into Equation (2), and using inflationary expectations instead of the real interest rate, yields the following equation:

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where YT+1 is expected real per capita disposable income in period t + 1, which is measured as the proportion of consumers expecting an increase in their real income minus the propor~on of consumers expecting a decrease in their real income over the next 12 months. Specifically, consumers are asked the following question: "How about the next year or two---do you expect your (family) income will go up more than prices will go up, about the same, or less than prices will go up?" Restricted and unrestricted estimates of Equation (3) are presented in Table 3. The estimation period commences in 1975: i since survey data on expected real income were not available prior to that date. Comparing rows 1 and 2, it is seen that the excess sensitivity parameter decreases substantially when expected real income growth is accommodated in the model and the estimated coefficient of expected income is statistically significant. This result concurs with the liquidity constraint hypothesis and the finding of Antzoulatos (1994, 1997). However, the F-test of structural stability indicates that the model is misspeeified, so that important regressors may have been omitted. The structural instability vanishes if uncertainty is included in the estimates (row 3), where all the estimated coefficients are statistieally significant. Ineluding CC instead of uncertainty in row 4 renders the model structurally unstable again. This result suggests that uncertainty is a crucial factor in estimating models of consumption. When both pe and AY~ are included in the model their estimated coefficients lose significanee, especially the estimated coefficient ofp ~ (rows 5, 6, 7 and 9). This result is consistent with the discussion above that an increase in expected inflation is likely to lower the expected value of real income and increase its variance. Together with the fact that the survey question on expected real income is quoted as expected inflation deducted from expected nominal income growth, an increase in expected inflation will automatically 246

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Jakob B. Madsen and Michael McAleer lower expected real income. Hence, expected inflation is rendered unimportant when expected income is included in the model. If AY, AY e, UN and p~ are included as regressors, then all coefficient estimates are statistically significant, except the estimated coefficient of AYe, as shown in the estimates in row 7. Together with the result above, this finding suggests that expected income was influential in the estimates only because uncertainty and inflationary expectations were not accommodated in the model. It can, therefore, be concluded that credit constraints do not appear to be the most important reason why there is excess sensitivity in consumption, but rather than uncertainty prevents consumers from obeying the LC-PIH. Finally, if AY, AYe, CC and UN are included as regressors, then all coefficient estimates are statistically significant, except the estimated coefficient of AY, as shown in row 8. It is remarkable that the estimated excess sensitivity is insignificant when the effects of credit constraints and uncertainty are accommodated in the models. However, since the estimated excess sensitivity parameter is significant in almost all the estimates in Tables 1 and 3, this result should be interpreted eantiously. What can be concluded about the excess sensitivity parameter is that its relevance is reduced significantly when uncertainty, particularly, and liquidity constraints are accommodated in the model.

7. Concluding Remarks It has long been debated whether the rational expectations LC-PIH is untenable because of the excess sensitivity of consumption to income, limited access to credit, and/or because consumers do not incorporate all publicly available information when they form their expectations regarding permanent income. Using the Michigan Surveys of Consumers data, the estimates provided in this paper suggest that none of these factors is likely to be very important when uncertainty and inflationary expectations are accommodated in the competing models of consumption. Consistent with many other studies in the literature, the estimates given in this paper indicate that consumption can, in fact, be sensitive to income. However, the excess sensitivity of consumption ceases to be important, almost to the point of disappearing altogether, when uncertainty, inflationary expectations and the availability of credit are modeled explicitly in the consumption function. Furthermore, the empirical results show that both consumption and excess sensitivity, in some circumstances, are curbed by credit constraints. However, the statistical significance of the credit constraint variables are sensitive to the specification of the model, which sug248

Direct Tests of the Permanent Income Hypothesis gests that credit constraints are unlikely to be especially important in explaining the systematic breakdown of the rational expectations LC-PIH. The only two variables that were found to be consistently significant in the consumption function are consumer's perceptions of uncertainty and their inflationary expectations. Since both variables had negative and significant coefficients, it follows that an increase in uncertainty and expected inflation leads to lower consumption. Whereas theory predicts that the excess sensitivity is a positive function of uncertainty, there are no strong microeconomic foundations as to why consumption and its excess sensitivity to income should be negatively related to inflationary expectations. However, Juster and Taylor (1975), and the survey of Shiller (1997), suggest that inflationary expectations have a negative impact on consumption because of the absence of formal indexation rules for wages. Therefore, the influence of inflationary expectations on consumption reflects a real income uncertainty which is associated with expected inflation, whereas the consumer survey measure of uncertainty is likely to reflect real income uncertainty which is not associated with inflation. Finally, the estimates reported in the paper indicate that consumer sentiment ceases to be a significant predictor of consumption when uncertainty, inflationary expectations and credit constraints are accommodated in the model. This result reinforces the importance of allowing for uncertainty, broadly defined, in estimating the consumption function. The findings of the paper have two important macroeconomic implications. First, since consumption is found to be much less sensitive, if at all, to current income as compared with other studies, it implies that the simple Keynesian income multiplier is much lower than is usually considered, namely 1 instead of 1/(1 - ~). Second, a stable macroeconomic environment is a precondition for consumers to behave prudently according to the LCPIH. An unstable environment with high (expected) inflation, possibly also pronounced deflation, and high uncertainty induces consumers to act myopically, thereby amplifying the multiplier effects of demand and supply shocks. This may, to some extent, explain the propagation of the Great Depression in the 1930s, where shocks had such large ramifications for the economy, because the period was characterized as being extraordinarily uncertain with respect to macroeconomic policies and price fluctuations. Received: September 1998 Final version: July 1999

References

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Jakob B. Madsen and Michael McAleer Antzoulatos, Angelos A. "Borrowing Constraints, Income Expectations and the ELder Equation: Theory and Evidence." Economics Letters 45 (July 1994): 323-27. --. "On Excess Sensitivity in Consumption." Journal of Macroeconomics 19 (Summer 1997): 539-53. Blanchard, Olivier j., and Stanley Fischer. Lectures on Macroeconomics. MA: MIT Press, 1989. Campbell, John, and N. Gregory Mankiw. "Consumption, Income, and Interest Rates: Reinterpreting the Time-Series Evidence." In NBER Macroeconomics Annual, edited by Olivier Blanchard and Stanley Fischer, 185-216. MA: MIT Press, 1989. --. "Permanent Income, Current Income, and Consumption." Journal of Business and Economic Statistics 8 (July 1990): 265-79. --. "The Response of Consumption to Income: A Cross-Country Investigation." European Economic Review 35 (May 1991): 723-56. Carroll, Christopher D. "The Buffer-Stock Theory of Saving: Some Macroeconomic Evidence." Brookings Papers on Economic Activity (No. 2 1992): 61-135. --. "How does Future Income Affect Current Consumption?" Quarterly Journal of Economics 109 (February 1994): 111-47. Carroll, Christopher D., Jeffrey c. Fuhrer, and David W. Wilcox. "Does Consumer Sentiment Forecast Consumer Spending? If so, Why?" American Economic Review 84 (December 1994): 1397-1408. Christiano, Lawrence J. "Comment." In NBER Macroeconomics Annual, edited by Olivier Blanchard and Stanley Fischer, 216-33. MA: MIT Press, 1989. Evans, Michael K. Macroeconomic Activity. New York: Harper and Row, 1969. Flavin, Marjorie. "The Adjustment of Consumption to Changing Expectations about Future Income." Journal of Political Economy 89 (October 1981): 974-1009. --. "Excess Sensitivity of Consumption to Current Income: Liquidity Constraints or Myopia?" Canadian Journal of Economics 18 (February 1985): 117-36. Friedman, Milton. A Theory of the Consumption Function, Princeton NJ: Princeton University Press, 1957. Hall, Robert E. "Stochastic Imphcafions of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence." Journal of Political Economy 86 (December 1978): 971-87. Hall, Robert E., and Frederic S. Mishkin. "The Sensitivity of Consumption to Transitory Income: Estimates from Panel Data on Households.'" Econometrica 50 (March 1982): 461-81. 250

Direct Tests of the Permanent Income Hypothesis Hayashi, Fumio. "The Permanent Income Hypothesis: Estimation and Testing by Instrumental Variables." Journal of Political Economy 90 (October 1982): 895-916. --. "The Effects of Liquidity Constraints on Consumption: A CrossSectional Analysis.'" Quarterly Journal of Economics 10 (February 1985): 183-206. Hubbard, R. Glenn, and Kenneth L. Judd. "Liquidity Constraints, Fiscal Pohcy, and Consumption." Brookings Papers on EconomicsActivity no. 1 (1986): 1-59. Jappelli, Tulho, and Marco Pagano. "Consumption and Capital Market Imperfections: An International Comparison." American Economic Review 79 (December 1989): 1088-1105. Juster, Thomas F., and Lester D. Taylor. "Towards a Theory of Saving Behavior." American Economic Review 65 (May 1975): 203-09. Kennickell, Arthur B., and Janice Shack-Marquez. "Changes in Family Finances from 1983 to 1989: Evidence from the Survey of Consumer Finances." Federal Reserve Bulletin 78 (1993): 1-18. Michener, Ron. "Permanent Income in General Equilibrium." Journal of Monetary Economics 13 (May 1984): 297-305. Muellbauer, John, and Ralph Lattimore. "The Consumption Function: A Theoretical and Empirical Overview." In Handbook of Applied Econometrics: Macroeconomics, edited by M. Hashem Pesaran and M. R. Wickens, 221-311. Oxford: Blackwell, 1995. Shiller, Robert j. "Why Do People Dishke Inflation?" In Reducing Inflation, edited by Christina D. Romer and David H. Romer, 13-65. Chicago: The University of Chicago Press, 1997. Vaidyanathan, Geetha. "Consumption, Liquidity Constraints and Economic Development." Journal of Macroeconomics 15 (Summer 1993): 591-610. Wilcox, James A., "Liquidity Constraints on Consumption: The Real Effects of 'Real" Lending Policies." Federal Reserve Bank of San Francisco Economic Review (Fall 1989): 39-52.

Appendix Description of Variables r = real after-tax interest rate is measured as the after-tax 3-month Treasury Bill rate minus expected inflation; and the tax rate is computed as [total income taxes/(YN + total income taxes)], where yN is nominal after-tax personal disposable income. C = log of real per capita consumption of non-durables and services. 251

]akob B. Madsen and Michael McAleer Y = log of real disposable income per capita. ynLC = log of per capita real labor income, computed as log[(W(1 T)/Pr)/POP], where W is wages and salaries, T is the average income tax rate, POP is the population, and P~"is the implicit disposable income deflator. yrC = log of per capita non-labor income, computed as (Y - yNLC). YT+1 = expected real per capita disposable income at period t + 1, measured as the proportion of consumers that expect an increase in their expected real income minus the proportion of consumers that expect a decrease in their real income over the next 12 months. ']9~+ 1 = the rate of inflation at time t that is expected to prevail one year ahead. i = 3-month Treasury Bill rate. UN = Uncertainty. Percentage responding "Bad times to buy a car" multiplied by the proportion responding "Bad times ahead, uncertain future." CC = Credit constraints. Percentage responding "Bad times to buy a car" multiplied by the proportion responding "Interest rates are high, credit is tight." All the data, except for the consumer survey data, are taken from The Federal Reserve Bank of St. Louis data bank. The consumer survey data are from the Michigan Surveys of Consumers.

252