Reconciling Estimates of Earnings Processes in Growth Rates and Levels

The stochastic process for earnings is the key element of incomplete markets models in modern quantitative macroeconomics. It determines both the equilibrium distributions of endogenous outcomes and the design of optimal policies. Yet, there is no consensus in the literature on the relative magnitudes of the permanent and transitory innovations in earnings. When estimation is based on the earnings moments in levels, the variance of transitory shocks is found to be relatively high. When the moments in differences are used, the variance of the permanent component is relatively
high instead. We show theoretically that the difference can be induced by the fact that earnings at the start or at the end of earnings spells are lower and more volatile than the observations in the interior of earnings histories. Using large administrative datasets from Denmark and Germany, we show that this property of earnings spells quantitatively accounts for the full amount of discrepancy in the estimates. Using data from the Panel Study of Income Dynamics, we show that this property of earnings induces a substantial upward bias in the estimate of consumption insurance against permanent shocks.