Estimation of a break point in group membership structure

This paper proposes an estimation method for a change in group membership structure. We consider linear panel data models with grouped pattern of heterogeneity. In a panel data context, a structural break can arise when the group membership structure and/or the value of one or more coefficients change during the sample period. In particular, failure to account for a change in the group membership structure may result in detecting a spurious structural break in the values of the coefficients. We propose a least squares estimator for such models that estimates the break point, group membership structure, and coefficients simultaneously. The estimator is consistent under a mild condition on the relative magnitude of the cross-sectional sample size and the length of time series. The asymptotic distribution of the coefficient estimator is identical to that under known break point and known group membership structure. Monte Carlo simulations yield encouraging results.

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