Econometrica, Vol. 70, No. 2 (March, 2002), 781–799 SEMIPARAMETRIC BAYESIAN INFERENCE IN AUTOREGRESSIVE PANELDATAMODELS By Keisuke Hirano 1 1 introduction: full probability models for earnings dynamics This paper develops Bayesian methods for inference in dynamic panel data models with individual effects, and applies them to study longitudinal data on earnings from the PanelStudyofIncomeDynamics(PSID).Westudysemiparametricversionsofcommonly used random effects autoregressive models, in which the distribution of the disturbances is not restricted to fall in a parametric class. To model the unknown distributions without resorting to strong parametric assumptions, we draw upon recent advances in the theory and computation of nonparametric Bayesian models using Dirichlet process priors. The overall approach can be viewed as an application of the general semiparametric Bayesian approach of West, Müller, and Escobar (1994) which in turn makes use of results on Bayesian density estimation by Escobar (1994) and Escobar and West (1995). Most conventional panel data methods (e.g., Anderson and Hsiao (1981), MaCurdy (1982), Chamberlain (1984), Hsiao (1986), Holtz-Eakin, Newey, and Rosen (1988), Arel- lanoandBond(1991),AhnandSchmidt(1995),BlundellandBond(1998))eitherassume normalityforthedisturbanceterms,orrelaxthisassumptionbutdonotprovideestimates of the distribution of the disturbance terms. For some purposes, these distributions can- notbetreatedasnuisanceparameters.Forexample,solvingoptimalconsumptionmodels with stochastic earnings (as in Deaton (1991) and many other studies) requires a com- pletespecificationoftheprocessforearnings.Inaddition,alargepartoftheeconometric work on longitudinal earnings data has focused on forecasting transitions into and out of poverty (see, for example, Lillard and Willis (1978), Horowitz and Markatou (1996), and Geweke and Keane (1997)). The main contribution of this paper is to adapt semiparametric Bayesian methods to a random effects autoregressive model with nonparametric idiosyncratic shocks. Estimat- ing panel data models without parametric assumptions on the disturbances is difficult, because the idiosyncratic disturbance is convoluted with the individual effects. The panel data estimator of Horowitz and Markatou (1996) estimates the underlying distributions nonparametrically, by applying the Fourier inversion theorem to smoothed estimates of the densities of the model residuals. Their approach requires the data analyst to make judgments about smoothness in choosing bandwidth parameters in a generally ad hoc manner, as conventional optimal smoothing results do not apply in this context. The Bayesian approach taken here also requires some judgments about the likely smoothness 1 This paper is based on Chapter 2 of my Ph.D. dissertation, Hirano (1998a), and extends ear- lier work reported in Hirano (1998b). I am grateful to Siddhartha Chib, Ronald Goettler, Caroline Hoxby, Guido Imbens, Lawrence Katz, Katerina Kyriazidou, Arthur Lewbel, Peter Müller, Sendhil Mullainathan, Daniele Paserman, Jack Porter, Charles Romeo, three anonymous referees, and espe- cially Gary Chamberlain for their comments and suggestions. I acknowledge support from the National Science Foundation. 781