🤖 AI Summary
This study addresses the nonparametric identification of the distribution of random coefficients in short panel data without imposing any restrictions on the temporal dependence structure of the error terms. The model accommodates a subset of random coefficients that may be arbitrarily correlated with observed covariates, while the remaining coefficients are assumed independent. By integrating the “stayer”-based singular design, deconvolution techniques, and a two-step minimum distance sieve estimator—augmented with cross-validation for tuning parameter selection—the paper achieves, for the first time, identification of the distribution of correlated random coefficients in both regular and irregular panels. An application to cash transfer program data reveals substantial heterogeneity in household expenditure elasticities for calories, with a non-degenerate distribution that includes values near zero or even negative, indicating that households adjust consumption along both quantity and quality margins.
📝 Abstract
We consider a static linear panel model with both correlated and uncorrelated random coefficients, where the former can depend arbitrarily on observable regressors while the latter are independent of them. We provide sufficient conditions for identification of the distributions of the random coefficients without imposing restrictions on the time-series structure of the error terms in short panels. Our framework applies to regular and irregular designs. The distribution of the correlated coefficients follows via a deconvolution argument. In irregular designs, identification relies on a stayer-based argument exploiting near-singular realizations of the regressor matrix.
We develop a two-step minimum distance sieve estimator, with tuning parameters selected by cross-validation. In an application to calorie-expenditure elasticities using data from the randomized evaluation of a conditional cash transfer program, we interpret the estimated distributions by program status as distributions of regime-specific structural calorie-expenditure elasticities. The estimated densities themselves reveal substantial heterogeneity in household-specific elasticities, with nontrivial mass concentrated near zero and a non-negligible share of negative realizations. This heterogeneity implies that responses to income or expenditure changes are not uniformly positive and vary widely across households. Taken together, these features support a framework in which households adjust along both quantity and quality margins, rather than conforming to a homogeneous Engel-curve response.