Heterogeneity, omitted variable bias, and duration dependence

Abstract

This chapter will discuss models for longitudinal data in which a sample of individuals or firms is followed over time. A primary advantage of such data is that they allow us to test and relax assumptions that are implicit in a cross-sectional analysis. Section 1 considers the main issue in the context of the familiar linear model. Here a basic specification test is a comparison of a regression based on changes with a cross-sectional regression. This test is put in a general framework that relates it to tests for strict exogeneity in time series analysis. We show that the failure of strict exogeneity may be due to heterogeneity, which suggests a reformulation in which there is a mixture of strictly exogenous processes. The assumption of strict exogeneity in a mixture model is itself testable, and such tests should be routine whenever the standard analysis-of-covariance estimator is used.