A La Recherche des Moments Perdus: Covariance Models for Unbalanced Panels with Endogenous Death

We develop a model for decomposing the covariance structure of panel data on firms into a part due to permanent heterogeneity, a part due to differential histories with unknown ages, and a part due to the evolution of economic shocks to the firm. Our model allows for the endogenous death of firms and correctly handles the problems arising from the estimation of this death process. We implement this model on an unbalanced longitudinal sample of French firms which have both known and unknown ages and histories. For firms with unknown birthdates, we find that the structural autocorrelation in employment, compensation and capital is dominated by the part due to initial heterogeneity and random growth rates. Serial correlation in the periodic shocks is less important. For these firms, profitability, value-added and indebtedness have processes in which the heterogeneity components are less important. Firms with known birthdates and histories (which are younger than the censored firms) have autocorrelation structures dominated by the heterogeneity.