Introduction

Recent studies have developed econometric procedures for the analysis of the time series properties of panel data sets consisting of large numbers of short individual time series (e.g., Anderson and Hsiao (1981), Chamberlain (1984), Holtz-Eakin, Newey, and Rosen (1988), and Arellano and Bond (1991)). The analysis is typically based on empirical autoregressive equations including time and individual effects, and possibly observed time-varying exogenous variables. Individual effects are removed by differencing and lagged variables are used as instruments in order to retrieve consistent estimators of the autoregressive coefficients of the levels equation. Alternatively, one could choose moving average processes and components of variance to model the autocovariance matrix of the data in first differences, using methods of moments estimation and testing as well (as done, for example, by Abowd and Card (1989)). In either case, the motivation for this type of analysis with micro data is often to establish a mapping between the observed dynamic interactions and those implied by a theoretical model, or at least to test particular time series implications of such model.

The purpose of this chapter is to formulate procedures for the analysis of the time series behavior of panel data subject to censoring. We apply these methods to analyze the dynamics of female labor supply and wages using PSID data. We follow the standard latent variable approach to models with selectivity and assume a linear autoregressive model for a latent variable which is only partly observed due to a selection mechanism.