Clustering Regression Functions in a Panel
When time series data of a reasonable length for several cross sectional units are available (for example in the analysis of CO2 emission in industrial countries, or the estimation of production functions for 20 manufacturing sectors), researchers begin by testing whether the data can be pooled and a single dynamic model can be built for all cross sectional units. The "pooling restriction" is often rejected, and then researchers usually proceed by estimating separate dynamic regressions for each cross sectional unit. However, it has been noted in many of such situations that using the pooled model, or shrinking the individual models towards the pooled model, produces superior forecasts relative to individual models. We note that rejecting the grand pooling restriction does not necessarily imply that all cross sectional units must be different. This paper suggests a hierarchical clustering algorithm with a global objective function, to partially pool regressions when the overall pooling restriction is rejected by the data. In addition to the lack of fit and lack of parsimony, the objective function also penalizes lack of conformity with theoretical priors and imprecision in the estimated parameters. This algorithm is used for clustering the gasoline demand functions of OECD countries. The results are compared with those of an alternative method based on a classification and regression tree (CART) procedure. Keywords: Medium sized panels, cluster analysis, information criteria, minimum message length, classification and regression tree (CART).
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