Reexamining the permanent income hypothesis with uncertainty in permanent and transitory innovation states

In this paper, we reexamine the permanent income–consumption relationship analytically and empirically, based on the innovation regime-switching (IRS) model developed in Kuan, C.M., Huang, Y.L., Tsay, R.S., 2005. An unobserved component model with switching permanent and transitory innovations. Journal of Business and Economic Statistics, 23, 443–454]. A novel feature of the IRS model is that it explicitly allows for uncertainty in innovation states. When the labor income follows an IRS process, it is shown that the agent’s perception on the likelihoods of income innovations being permanent and transitory plays a crucial role in determining the optimal forecasts on the change of consumption. The effect of a current labor income innovation on consumption is a weighted average of two distinct effects resulting from permanent and transitory innovations with the weights equal to the perceived likelihoods of the respective states. Also, past innovations may affect consumption when there are revisions in the perceived likelihoods of previous states. Our empirical study on US data shows that consumption indeed reacts significantly to the perceived likelihoods of innovation states. However, even after controlling for the effect of state uncertainty, we find consumption vastly underreacts to permanent innovations in labor income but reacts about the right magnitude to transitory ones when compared with the prediction of the permanent income hypothesis. This evidence is similar to Elwood, S.K., 1998. Testing for excess sensitivity in consumption: A state-space unobserved components approach. Journal of Money, Credit, and Banking, 30, 64–82] but in sharp contrast with that found in Hall, R.E., Mishkin, F.S., 1982. The sensitivity of consumption to transitory income: Estimates from panel data on households. Econometrica, 50, 461–480].