🤖 AI Summary
This paper addresses the identification and estimation of dynamic random-coefficient linear models with individual heterogeneity in short panel data. Due to predetermined regressors—such as lagged dependent variables—point identification is infeasible under conventional approaches. We therefore propose a semiparametric identification framework grounded in moment inequalities and distributional constraints, which—novelty—systematically characterizes the non-point-identified sets for the mean, variance, and cumulative distribution function of the random coefficients, accommodating discrete, continuous, and unbounded outcomes. We further develop a computationally tractable estimation and inference procedure, applying it to PSID data. Empirically, we find substantial unobserved heterogeneity in U.S. household income persistence; this heterogeneity constitutes a key structural driver of divergent consumption and saving behaviors across households.
📝 Abstract
I study panel data linear models with predetermined regressors (such as lagged dependent variables) where coefficients are individual-specific, allowing for heterogeneity in the effects of the regressors on the dependent variable. I show that the model is not point-identified in a short panel context but rather partially identified, and I characterize the identified sets for the mean, variance, and CDF of the coefficient distribution. This characterization is general, accommodating discrete, continuous, and unbounded data, and it leads to computationally tractable estimation and inference procedures. I apply the method to study lifecycle earnings dynamics among U.S. households using the Panel Study of Income Dynamics (PSID) dataset. The results suggest substantial unobserved heterogeneity in earnings persistence, implying that households face varying levels of earnings risk which, in turn, contribute to heterogeneity in their consumption and savings behaviors.