Grouped heterogeneity in linear panel data models with heterogeneous error variances

Abstract

We develop a procedure to identify latent group structures in linear panel data models that exploits a grouping in the error variances of cross-sectional units. To accommodate such grouping, we introduce an objective function that avoids a singularity that arises in a pseudo-likelihood approach. We provide theoretical conditions and numerical evidence that show when allowing for variance groups improves classification. Two applications illustrate the proposed method. First, we revisit the cross-country relationship between income and democracy. We find evidence for a group of high-variance countries, where average democracy has increased slowly over time. Second, we consider the relation between firm-level R&D investments and the business cycle. We find a well-defined group structure in the variances that ex-post can be related to firm size. Our estimates indicate stronger procyclical investment patterns at medium-size firms compared to large firms.

Keywords: panel data, clustering, R&D investment

JEL Classification: C23, D22, E32