Modeling Individual Earnings Trajectories Using Copulas: France, 1990-2002

We construct a dynamic model of individual earnings which is a natural extension of the standard discrete Markov chains used in the empirical literature on earnings mobility and we allow for both observed and unobserved heterogeneity. Using copula representations of multidimensional densities we decompose the likelihood of individual earnings trajectories into the product of two components: the product of marginal–or cross-sectional–densities and the likelihood of the sequence of individual ranks in marginal distributions. Copula representations justify the independent analyses of cross-sectional inequality and relative mobility that one finds in the literature. We model the year-to-year dynamics of ranks using the Plackett (1965) parametric copula family. We use discrete mixtures of such models to characterize unobserved heterogeneity. To estimate these mixtures, we develop a sequential EM algorithm, which is shown to be root-N consistent and asymptotically normal. The estimation algorithm is simple to implement and fast enough to converge for bootstrapping to be a recommendable procedure for estimating standard errors. We then apply our methodology to French Labor Force Survey data, for 1990-2002. We find that neglecting earnings mobility, individual heterogeneity and unemployment risk has a significant effect on the level of intertemporal earnings inequality but affects very little their evolution.