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).
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