# The permanent income hypothesis with a time varying second moment of income

#### Abstract

The existing research on the Permanent Income Hypothesis (PIH) has discovered two empirical puzzles in consumer behavior. First, consumers appear to ignore old information when deciding their level of spending, resulting in an "excess sensitivity" of the change in consumption to preexisting (lagged) income. Second, the overall variance of the change in consumption is much less than expected given the observed variance of unanticipated income. This finding has been labeled "excess smoothness."^ This dissertation examines the PIH when it is assumed that the consumer's utility function is quadratic and labor income is best described as a random walk in logs with autoregressive conditional heteroscedasticity (ARCH) effects in the income error terms. ARCH income errors imply that both the income innovations and the squared innovations are independent stochastic processes. A random walk in logs implies that it is growth rates--not the levels--of income which matter.^ A model of the PIH is developed where the change in consumption is a function not only of the innovation in the log income process but also of the squared error stochastic process. This model combines the linear constraint of the PM with the log-normal random walk process for income. Various data series are analyzed and it is found that the measure of labor income which is most appropriate to the theoretical construct of the PIH does exhibit ARCH effects in its errors, but is not cointegrated with consumption (as has been suggested in recent literature).^ The model of this dissertation is tested to see if it can explain the empirical consumption puzzles. Both univariate and multivariate models are tested. A VARCH(1) approximation of the model performs was the most promising framework. The results suggest that the PIH with a time-varying second moment of income does offer some improvement in explaining excess smoothness but cannot reject the excess sensitivity to known information which other researcher found. ^

#### Subject Area

Economics

#### Recommended Citation

Connelly, John R., "The permanent income hypothesis with a time varying second moment of income" (1995). *ETD Collection for Fordham University*. AAI9530023.

https://fordham.bepress.com/dissertations/AAI9530023