https://hal-sciencespo.archives-ouvertes.fr/hal-03587648Bonhomme, StéphaneStéphaneBonhommeRobin, Jean-MarcJean-MarcRobinEconomics department - MIT - Massachusetts Institute of TechnologyUP1 - Université Paris 1 Panthéon-SorbonneModeling Individual Earnings Trajectories Using Copulas: France, 1990-2002HAL CCSD2006earnings dynamicsmobilitycopulas[SHS.ECO] Humanities and Social Sciences/Economics and FinanceSciences Po Institutional Repository, Spire2022-02-24 15:59:342022-04-29 10:12:392022-02-24 15:59:34enJournal articles1We construct a dynamic model of individual earnings which is a natural extension of thestandard discrete Markov chains used in the empirical literature on earnings mobility andwe allow for both observed and unobserved heterogeneity. Using copula representations ofmultidimensional densities we decompose the likelihood of individual earnings trajectories intothe product of two components: the product of marginal–or cross-sectional–densities and thelikelihood of the sequence of individual ranks in marginal distributions. Copula representationsjustify the independent analyses of cross-sectional inequality and relative mobility that onefinds 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 unobservedheterogeneity. To estimate these mixtures, we develop a sequential EM algorithm, which isshown to be root-N consistent and asymptotically normal. The estimation algorithm is simpleto implement and fast enough to converge for bootstrapping to be a recommendable procedurefor estimating standard errors. We then apply our methodology to French Labor Force Surveydata, for 1990-2002. We find that neglecting earnings mobility, individual heterogeneity andunemployment risk has a significant effect on the level of intertemporal earnings inequality butaffects very little their evolution.