Understanding Earnings Dynamics: Identifying and Estimating the Changing Roles of Unobserved Ability, Permanent and Transitory Shocks∗

We consider a general framework to study the evolution of wage and earnings residuals that incorporates features highlighted by two influential but distinct literatures in economics: (i) unobserved skills with changing non-linear pricing functions and (ii) idiosyncratic shocks that follow a rich stochastic process. Specifically, we consider residuals for individual i in period t of the form: Wi,t = μt(θi) + εi,t, where θi represents an unobserved permanent ability or skill, μt(·) a pricing function for unobserved skills, and εi,t idiosyncratic shocks with both permanent and transitory components. We first provide nonparametric identification conditions for the distribution of unobserved skills, all μt(·) skill pricing functions, and (nearly) all distributions for both permanent and MA(q) transitory shocks. We then discuss identification and estimation using a moment-based approach, restricting μt(·) to be polynomial functions. Using data on log earnings for men ages 30-59 in the PSID, we estimate the evolution of unobserved skill pricing functions and the distributions of unobserved skills, transitory, and permanent shocks from 1970 to 2008. We highlight five main findings: (i) The returns to unobserved skill rose over the 1970s and early 1980s, fell over the late 1980s and early 1990s, and then remained quite stable through the end of our sample period. Since the mid-1990s, we observe some evidence of polarization: the returns to unobserved skill declined at the bottom of the distribution while they remained relatively constant over the top half. (ii) The variance of unobserved skill changed very little across most cohorts in our sample (those born between 1925 and 1955). (iii) The variance of transitory shocks jumped up considerably in the early 1980s but shows little long-run trend otherwise over the more than thirty year period we study. (iv) The variance of permanent shocks declined very slightly over the 1970s, then rose systematically through the end of our sample by 15 to 20 log points. The increase in this variance over the 1980s and 1990s was strongest for workers with low unobserved ability. (v) In most years, the distribution of μt(θ) is positively skewed, while the distributions of permanent and (especially) transitory shocks are negatively skewed. ∗We thank Youngmin Park for excellent research assistance, Peter Gottschalk and Robert Moffitt for sharing their PSID data creation programs, and Maria Ponomareva and Steve Haider for their useful suggestions. We also thank seminar and conference participants from Carnegie Mellon University, Florida State University, Montana State University, Ohio State University, University College of London, University of Iowa, University of Wisconsin, Uppsala University, and the MSU/UM/UWO Labor Day Conference. Lochner acknowledges financial research support from the Social Sciences and Humanities Research Council of Canada.