Correlated Random Coefficient Distributions in Linear Panel Models
Coauthor: Jim Powell
Abstract:
We consider a static linear panel model with both correlated and uncorrelated random coefficients, where the former may depend arbitrarily on observable regressors, while the latter are independent of them. In short panels, we derive sufficient conditions for identification of the distributions of the random coefficients without imposing restrictions on the time-series structure of the error terms. Our framework unifies regular and irregular designs. Identification proceeds via a two-step strategy that separates the correlated and uncorrelated components. In the first step, the distribution of the uncorrelated component is identified using transformations that eliminate the correlated coefficients, and which depend on the design. In irregular designs, identification exploits a stayer-based argument based on near-singular regressor realizations, while in regular designs it follows from algebraic annihilation using projections orthogonal to the regressors. In the second step, the distribution of the correlated coefficients is recovered by deconvolution. We focus on the estimation of the density of the correlated random coefficients, which mirrors the identification strategy and involves a regularized inverse problem. We propose a two-step minimum distance sieve estimator with trimming and Fourier smoothing, and a cross-validation criterion for data-driven selection of tuning parameters. An application to household consumption data reveals substantial heterogeneity in calorie-expenditure elasticities masked by average effects and highlights the sensitivity of distributional estimates to violations of the identifying assumptions.
Organized by: Vadim Marmer
