Spectral clustering with variance information for group structure estimation in panel data

Consider a panel data setting where repeated observations on individuals are available. Often it is reasonable to assume that there exist groups of individuals that share similar effects of observed characteristics, but the grouping is typically unknown in advance. We first conduct a local analysis which reveals that the variances of the individual coefficient estimates contain useful information for the estimation of group structure. We then propose a method to estimate unobserved groupings for general panel data models that explicitly accounts for the variance information. Our proposed method remains computationally feasible with a large number of individuals and/or repeated measurements on each individual. The developed ideas can also be applied even when individual-level data are not available and only parameter estimates together with some quantification of estimation uncertainty are given to the researcher. A thorough simulation study demonstrates superior performance of our method than existing methods and we apply the method to two empirical applications.