Multivariate regression models for panel data

The paper examines the relationship between heterogeneity bias and strict exogeneity in a distributed lag regression of y on x. The relationship is very strong when x is continuous, weaker when x is discrete, and non-existent as the order of the distributed lag becomes infinite. The individual specific random variables introduce nonlinearity and heteroskedasticity; so the paper provides an appropriate framework for the estimation of multivariate linear predictors. Restrictions are imposed using a minimum distance estimator. It is generally more efficient than the conventional estimators such as quasi-maximum likelihood. There are computationally simple generalizations of two- and three-stage least squares that achieve this efficiency gain. Some of these ideas are illustrated using the sample of Young Men in the National Longitudinal Survey. The paper reports regressions on the leads and lags of variables measuring union coverage, SMSA, and region. The results indicate that the leads and lags could have been generated just by a random intercept. This gives some support for analysis of covariance type estimates; these estimates indicate a substantial heterogeneity bias in the union, SMSA, and region coefficients.