The optimal prediction of cross-sectional proportions in categorical panel-data analysis

Longitudinal study is a powerful tool in many areas of empirical research, including health-care research, environmental monitoring and econometrics. In econometrics, the data generated through longitudinal studies are often referred to as panel data. Such data combine the features of both cross-sectional and time-series measurements. However, the vast literature on panel-data analysis focuses almost exclusively on the treatment of cross-sectional heterogeneity. Few studies address the problem of modeling panel data from a prediction point of view. In this article, we first formulate the prediction problem for categorical panel data. We then argue that prediction methods that are natural for other types of data may not be appropriate for panel data. Our main result shows that the optimal predictor, among a broad class of consistent predictors, is equivalent to a nonrandomized classification procedure that is determined by a set of integral equations.