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).
Keywords. Earnings process, persistent-transitory shocks, ARMA model, permanent-
transitory shocks.
JEL classification. C23, D31, J31.