A Reappraisal of Recent Tests of the Permanent Income Hypothesis

Hall (1978) showed that the permanent income hypothesis implies that consumption (1) follows a random walk, and (2) cannot be predicted by past income. Reexamination of Hall's data results in rejection of the random walk hypothesis in favor of the alternative hypothesis of positively autocorrelated changes. Evidently this is due to Hall's choice of a quadratic utility function. A logrithmic utility function implies a random walk in the log of consumption which is supported by the data. Hall reported that past income had a negative but insignificant relation to consumption. Changes in the log of income, however, do have a positive predictive relation to changes in the log of consumption. The adjustment of consumption to income seems to be spread over two quarters. Flavin's (1981) test of the theory is formally equivalent to Hall's except for assuming stationarity around a time trend. Mankiw and Shapiro (1984) have pointed out that the effect of detrending may be to tend to rejection of the theory when it is in fact correct. For Hall's data the effect of detrending is to reverse the sign of the coefficient on past income. Its magnitude is what the Mankiw-Shapiro analysis predicts under the permanent income hypothesis.