Panel data models: some recent developments

This chapter focuses on two of the developments in panel data econometrics since the Handbook chapter by Chamberlain (1984).The first objective of this chapter is to provide a review of linear panel data models with predetermined variables. We discuss the implications of assuming that explanatory variables are predetermined as opposed to strictly exogenous in dynamic structural equations with unobserved heterogeneity. We compare the identification from moment conditions in each case, and the implications of alternative feedback schemes for the time series properties of the errors. We next consider autoregressive error component models under various auxiliary assumptions. There is a trade-off between robustness and efficiency since assumptions of stationary initial conditions or time series homoskedasticity can be very informative, but estimators are not robust to their violation. We also discuss the identification problems that arise in models with predetermined variables and multiple effects. Concerning inference in linear models with predetermined variables, we discuss the form of optimal instruments, and the sampling properties of GMM and LIML-analogue estimators drawing on Monte Carlo results and asymptotic approximations.A number of identification results for limited dependent variable models with fixed effects and strictly exogenous variables are available in the literature, as well as some results on consistent and asymptotically normal estimation of such models. There are also some results available for models of this type including lags of the dependent variable, although even less is known for nonlinear dynamic models. Reviewing the recent work on discrete choice and selectivity models with fixed effects is the second objective of this chapter. A feature of parametric limited dependent variable models is their fragility to auxiliary distributional assumptions. This situation prompted the development of a large literature dealing with semiparametric alternatives (reviewed in Powell, 1994's chapter). The work that we review in the second part of the chapter is thus at the intersection of the panel data literature and that on cross-sectional semiparametric limited dependent variable models.