The persistent-transitory representation for earnings processes

Abstract

We consider the decomposition of shocks to a dynamic process into a persistent and a transitory component. Without additional assumptions (such as zero correlation) the decomposition of shocks into a persistent and transitory component is indeterminate. The assumption that is conventional in the earnings literature is that there is no correlation. The Beveridge-Nelson decomposition that is widely used in time series analysis assumes a perfect correlation. Without restrictions on the correlation, the persistent-transitory decomposition is only set-identified. For reasonable autoregressive moving average (ARMA) parameters the bounds for widely used objects of interest are very wide. We illustrate that these disquieting findings are of considerable practical importance, using a sample of male workers drawn from the Panel Study of Income Dynamics (PSID).