Myopia, Liquidity Constraints, and Aggregate Consumption: A Simple Test
Journal article by John Shea; Journal of Money, Credit & Banking, Vol. 27, 1995
Journal Article Excerpt
Myopia, liquidity constraints, and aggregate consumption: a simple test. by John Shea THE NEOCLASSICAL life cycle--permanent income hypothesis (LCH/PIH) implies that predictable movements in income should not affect consumption. Recent tests using aggregate time-series data consistently reject this prediction. Campbell and Mankiw (1990), for instance, present significant estimates of the elasticity of consumption with respect to predictable income ranging from 0.351 to 0.713. While the failure of the LCH/PIH in aggregate data is well established, the reason for this failure is not. Two alternative hypotheses that have received considerable attention are myopia and liquidity constraints. This note conducts a simple test of these two alternatives using aggregate time series data.(1) The test exploits the fact that myopia and liquidity constraints have testable implications for asymmetry in consumption behavior, as first noted by Altonji and Siow (1987). Under myopia, consumption tracks current income. Thus, the failure of the LCH/PIH should be symmetric: consumption should respond equally to predictable income increases and decreases. Under liquidity constraints, however, the LCH/PIH fails only because agents cannot borrow when income is temporarily low. In this case, consumption should be more strongly correlated with predictable income increases than declines; liquidity constraints impede borrowing but not saving. The empirical evidence suggests that neither myopia nor liquidity constraints is an adequate characterization of U.S. aggregate consumption behavior. Using quarterly data from 1956-1988, I show that consumption is more sensitive to predictable income declines than increases. This "perverse asymmetry" also arises in my recent study of household consumption (Shea 1995). These findings are inconsistent with myopia and liquidity constraints, but are qualitatively consistent with recent work incorporating loss aversion into intertemporal preferences. 1. SPECIFICATION, DATA, AND RESULTS Following Campbell and Mankiw (1990; hereafter Campbell-Mankiw), one can test the LCH/PIH by running the following OLS regression: [MATHEMATICAL EXPRESSION OMITTED] where [delta]c is consumption growth between t - 1 and t, [delta]y is expected income growth between t - 1 and t, and r is the expected real interest rate between t - 1 and t. Under the LCH/PIH, predictable income movements should not affect consumption, controlling for the return to saving. Thus, under the LCH/PIH [lambda] should equal zero, provided [delta][y.sub.t] and [r.sub.t] are measured using information available at t - 1. Following Campbell-Mankiw, I set [delta][y.sub.t] and [r.sub.t] as linear projections of ex post income growth and the ex post real interest rate on variables in the t - 1 information set. Under myopia, consumption tracks current income. Consumption should respond symmetrically to predictable income increases and decreases. Under liquidity constraints, however, consumption should respond more strongly to predictable income increases than decreases; liquidity constraints do not cause the Euler equation between adjacent periods to fail if optimal frictionless consumption growth exceeds expected income growth.(2) This discussion suggests that one can test for the presence of liquidity constraints and myopia by running the following OLS regression: [MATHEMATICAL EXPRESSION OMITTED] where POS is a dummy variable for periods in which [delta]y > 0, and NEG is a dummy variable for periods in which [delta]y < 0. Under the LCH/PIH, both [[lambda].sub.1] and [[lambda].sub.2] should equal zero. Under myopia, the [lambda]s should be positive, significant, and equal. With liquidity constraints, [[lambda].sub.1] should be significantly positive, and should be significantly greater than [[lambda].sub.2]. For the sake of robustness, I estimate (1) and (2) on two data sets. In the first set, consumption equals quarterly seasonally adjusted per capita real NIPA personal consumption expenditures (PCE) on nondurables and services. Income equals quarterly seasonally adjusted per capita real NIPA disposable personal income, deflated using the PCE deflator for all consumption. The (ex post) real interest rate equals the average secondary market three-month nominal T-bill yield in period t - 1 minus the growth rate of the PCE deflator for all consumption between t - 1 and t.(3) In the second data set, I follow the advice of Blinder and Deaton (1985) by removing the 1975:2 income tax rebate and interest payments from households to businesses from disposable income, and by removing shoes and clothing from nondurables consumption.(4) The sample period is 1956:4 through 1988:4, a total of 129 observations. To form [delta][y.sub.t] and [r.sub.t], I experiment with five lists of instruments, shown in Table 1. These lists include lags of income growth, consumption growth, interest rates, and the log consumption--income ratio; Campbell-Mankiw use similar instruments.(5) [TABULAR DATA OMITTED] Empirical results using the standard NIPA data are shown in Table 2; Table 3 presents results using the Blinder-Deaton data. In each table, column (1) presents a measure of the relevance of each instrument list for income growth. Following Nelson and Startz (1990), estimates of [lambda] in equations (1) and (2) may be imprecise or even spurious if the instruments have low predictive power for income growth. Traditionally, instrument relevance has been measured as the corrected R-squared from regressing the right-hand-side variable of interest on the instrument vector. However, this relevance measure can be misleading in models with multiple endogenous variables if there is multicollinearity among the instruments. The relevance measure reported in column (1) is the "partial R-squared" measure proposed by Shea (1993), defined as the R-squared from regressing the component of [delta]y orthogonal to a constant and r on the component of fitted [delta]y orthogonal to a constant and fitted r; the reported measure is corrected for the number of overidentifying instruments.(6) The results indicate that for both data sets the first instrument list (consisting of lags of income and the real interest rate) is substantially less relevant than the other lists. This suggests that the estimates generated by list 1 may less reliable than estimates generated with other instruments.(7) [TABULAR DATA OMITTED] Column (2) reports estimates of [lambda] from equation (1), in which the response of consumption to expected income is restricted to be symmetric. OLS standard errors and t-statistics are in parentheses and square brackets, respectively, and are not corrected for heteroskedasticity or serial correlation; Campbell-Mankiw report that such correction has little effect on their results. The LCH/PIH is rejected for both data sets and for all instrument lists. The estimated elasticity of consumption with respect to predictable income ranges from 0.374 to 0.528; these are within the range of estimates reported by Campbell-Mankiw, who use a different sample period. Estimates of [micro] and [beta] are omitted to save space; as in Campbell-Mankiw, the estimates of [beta] are negative and/or insignificant in all specifications.(8) Columns (3) and (4) report estimates of [[lambda].sub.1] and [[lambda].sub.2] from equation (2), in which expected income growth is broken down into expected increases and decreases. Column (5) reports the F-statistic for testing [[lambda].sub.1] = [[lambda].sub.2], while column (6) reports the number of sample quarters for which [delta]y is negative. Negative expected aggregate income growth is rare in the postwar United States; the fraction of sample quarters for which NEG = 1 ranges from 1.6 percent (Blinder-Deaton data, instrument list 1) to 14.7 percent (Blinder-Deaton data, instrument list 5). Nevertheless, the estimates tell a reasonably clear story. In most specifications, consumption responds significantly both to expected income increases and declines. However, consumption is much more sensitive to predictable income declines than increases. Not surprisingly, [[lambda].sub.2] is estimated imprecisely; nevertheless, one can still formally reject [[lambda].sub.2] = [[lambda].sub.1] in favor of [[lambda].sub.2] > [[lambda].sub.1] for instrument lists 4 and 5 in the standard data, and for lists 1, 4, and 5 in the Blinder-Deaton data; meanwhile, one can never reject [[lambda].sub.2] = [[lambda].sub.1] in favor of [[lambda].sub.1] > [[lambda].sub.2]. In general, then, these results are inconsistent with both the LCH/PIH and with myopia and liquidity constraints. The lone exception is the specification using the standard data and instrument list 1, for which [[lambda].sub.1] is positive and significant while [[lambda].sub.2] is negative and insignificant. While this finding is consistent with liquidity constraints, there are two good reasons to discount it: first, list 1 generates only five quarters of negative [delta]y in the standard data, the lowest of any instrument list; second, as mentioned above, list 1 is substantially less relevant for income growth than the other lists. In fairness, I must point out that some of the estimates of [[lambda].sub.2] are unrealistically high; in the Blinder-Deaton data using list 1, for instance, the elasticity of consumption with respect to predictable income declines is nine, whereas even an extreme myopic alternative to the LCH/PIH would imply an elasticity of only one. These extreme results can again be attributed to poor instruments and small samples; in the Blinder-Deaton data, for instance, list 1 is virtually irrelevant and generates only two quarters of negative [delta]y. It is comforting to note that in both data sets, instrument list 5--the most relevant list, and the list generating the most quarters of negative [delta]y--produces estimates of [[lambda].sub.2] that are reasonably precise and close to one. 2. COMPARISON WITH PREVIOUS STUDIES To my knowledge, this is the first paper to test for asymmetries in the response of aggregate consumption to expected income growth.(9) Two existing papers, however, test for such asymmetries in household data, with mixed results. Altonji and Siow (1987) find that households expecting income to rise exhibit a somewhat higher sensitivity of consumption to predictable income than households expecting income to fall, although neither sensitivity is significantly different from zero. In my own previous work (Shea 1995), on the other hand, I find that household consumption is much more sensitive to predictable income declines than increases. Instrument relevance may be the key to explaining this contradiction. Altonji and Siow form [delta][y.sub.t] by projecting ex post household income growth on a variety of lagged household-specific variables. Unfortunately, Altonji and Siow's most powerful instruments--lagged hours of unemployment and disability, and lagged wages interacted with dummy variables indicating past quits and layoffs--are far better predictors of income increases than declines. Thus, Altonji and Siow's test arguably has little power to detect asymmetry in consumption behavior. In Shea (1995), on the other hand, I form [delta][y.sub.t] by matching households to particular long-term union contracts. Because my sample runs from 1982 through 1987, a substantial number of sample contracts call for long-term nominal wage freezes, which imply predictable real declines for the affected households. This measure of [delta][y.sub.t] arguably has more power to detect asymmetry than the measure employed by Altonji and Siow. 3. CONCLUSION The life cycle--permanent income hypothesis is not consistent with postwar U.S. aggregate consumption data. This note shows that this rejection of the LCH/PIH is not symmetric: aggregate consumption is more sensitive to predictable income declines than to predictable income increases. This finding is inconsistent with both myopia, which predicts symmetric rejection of the LCH/PIH, and with liquidity constraints, which predict the opposite asymmetry. Bowman, Minehart, and Rabin (1993) propose a model that is potentially consistent with this paper's findings. In their model, preferences exhibit loss aversion: utility is concave when consumption increases above a reference level, but convex when consumption declines below reference levels. This asymmetry reflects the idea that households suffer relatively large psychic losses when forced to cut living standards even a small amount; experimental evidence supporting such preferences is documented in Kahneman, Knetsch, and Thaler (1991). Bowman, Minehart, and Rabin show that loss-averse households may optimally refuse to reduce consumption today in the face of expected but uncertain declines in future income. Intuitively, the cost of not smoothing losses is smaller than the potential benefit of never having to reduce consumption below reference levels; consumption thus is insensitive to predictable income increases, but responds one-for-one to predictable declines. In fairness, I should point out that at this stage loss aversion is consistent with my findings only in a broad, qualitative sense. Bowman, Minehart, and Rabin analyze only a two-period model; results on consumption under loss aversion with infinite horizons and with arbitrary stochastic income processes are not yet available. Furthermore, there are other plausible explanations for the asymmetries found in this paper. For instance, if durable stocks are difficult to adjust downward in the short run due to imperfect resale markets, then under myopia nondurables consumption may have to respond more strongly to income declines than to income increases. Future research should rigorously formulate and test alternatives to the LCH/PIH that go beyond the simple versions of myopia and liquidity constraints examined and rejected in this paper. LITERATURE CITED Altonji, Joseph G., and Aloysius Siow. "Testing the Response of Consumption to Income Changes with (Noisy) Panel Data." Quarterly Journal of Economics 102 (May 1987), 293-328. Blinder, Alan S., and Angus Deaton. "The Time Series Consumption Function Revisited." Brookings Papers on Economic Activity 2 (1985), 465-521. Bowman, David, Debby Minehart, and Matthew Rabin. "Loss Aversion in a Savings Model." University of California-Berkeley mimeo, 1993. Caballero, Ricardo J. "Near-Rationality, Heterogeneity and Aggregate Consumption." National Bureau of Economic Research Working paper no. 4035, 1992. Campbell, John Y., and N. Gregory Mankiw. "Permanent Income, Current Income, and Consumption." Journal of Business and Economic Statistics 8 (July 1990), 265-79. Chah, Eun Young, Valerie A. Ramey, and Ross M. Starr. "Liquidity Constraints and Intertemporal Consumer Optimization: Theory and Evidence from Durable Goods." National Bureau of Economic Research Working paper no. 3907, 1991. Deaton, Angus. "Saving and Liquidity Constraints." Econometrica 59 (September 1991), 1221-48. Flavin, Marjorie. "The Joint Consumption/Asset Demand Decision: A Case Study in Robust Estimation." National Bureau of Economic Research Working paper no. 3802, 1991. Kahneman, Daniel, Jack L. Knetsch, and Richard H. Thaler. "Anomalies: The Endowment Effect, Loss Aversion, and Status Quo Bias." Journal of Economic Perspectives 5 (Winter 1991), 193-206. Nelson, Charles R., and Richard Startz. "The Distribution of the Instrumental Variables Estimator and Its t-Ratio When the Instrument Is a Poor One." Journal of Business 63 (January 1990), S125-40. Runkle, David E. "Liquidity Constraints and the Permanent-Income Hypothesis: Evidence from Panel Data." Journal of Monetary Economics 27 (February 1991), 73-98. Shea, John. "Instrument Relevance in Linear Models: A Simple Measure." University of Wisconsin mimeo, 1993. _____. "Union Contracts and the Life Cycle--Permanent Income Hypothesis." American Economic Review 85 (March 1995), 186-200. Zeldes, Steven P. "Consumption and Liquidity Constraints: An Empirical Investigation." Journal of Political Economy 97 (April 1989), 305-46. (1.)Most existing tests of liquidity constraints have been carried out with household data, with mixed results. Zeldes (1989) and Altonji and Siow (1987) find evidence for liquidity constraints, while Runkle (1991), Flavin (1991), and Shea (1995) do not support liquidity constraints. Most of these papers test for liquidity constraints by comparing the response of consumption to predictable income for poor and rich households. This test exploits the fact that rich households can dissave when income is temporarily low, while poor households cannot. As Shea (1995) points out, however, these tests cannot discriminate between liquidity constraints and myopia if poverty is correlated with myopic behavior. Chah, Ramey, and Starr (1991) test for liquidity constraints in aggregate data by exploiting the predictions of liquidity constraints for the comovements of durables and nondurables purchases; they conclude that liquidity constraints are present. (2.)Deaton (1991) investigates optimal consumption by a liquidity-constrained consumer under various income processes. His findings confirm my conjecture that liquidity constraints imply an asymmetric failure of the LCH/PIH. For instance, when income is stationary, Deaton finds that high income draws are always smoothed by saving, while low income draws are not smoothed unless wealth is high. (3.)Results are qualitatively similar if income and the interest rate are deflated using the PCE deflator for nondurables and services only. (4.)Blinder and Deaton (1985) also recommend adding real nontax payments to state and local governments to both disposable income and consumption. I do not make this correction because real nontax payments are available in NIPA only after 1958. (5.)I avoid t - 1 instruments to avoid misspecification due to time-averaging, information-aggregation bias, and durability; see Campbell and Mankiw (1990) for discussion. (6.)This correction is made to insure that the relevance measure does not automatically increase with the addition of (possibly irrelevant) overidentifying instruments. The correction is performed as follows. Begin with the uncorrected [R.sup.2] from regressing the orthogonal component of [delta]y on the orthogonal component of [delta]y. Let K equal the number of overidentifying instruments, and let N equal the sample size. Then the corrected partial R-squared is given by 1 - (N - 1)(1 - [R.sup.2])/(n - 1 - K0. (7.)Results are qualitatively similar if relevance is instead measured using the simple corrected [R.sup.2] from the regressions of [delta]y on the instrument lists. (8.)Results are qualitatively similar if the coefficient on the real interest rate is allowed to vary with the direction of expected income change, or if the real interest rate is omitted entirely. (9.)Caballero (1992) tests for asymmetries in the relationship between aggregate consumption growth and ex post income growth (that is, [delta]y rather than [delta]y). He finds that consumption is slightly more sensitive to income growth below the sample mean of [delta]y than above the sample mean of [delta]y; this difference is not statistically significant. In previous versions of this paper, I examined the relationship between consumption and expected income allowing for different elasticities above and below the mean of [delta]y. I found that consumption is more sensitive to expected income growth below the sample mean than above, although the asymmetries are not as dramatic as those reported in the current paper. -1- |
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