Panel Data and Unobservable Individual Effects

TLDR

Pooled panel data enable control of individual‑specific unobservable effects that may correlate with explanatory variables, such as latent ability in schooling‑earnings or managerial ability in firm cost functions. The study employs instrumental variables and the time‑invariant characteristics of the latent variable to derive tests and identification conditions for panel models. It develops a test for the presence of individual effects and over‑identifying restrictions, establishes necessary and sufficient identification conditions, and proposes an asymptotically efficient IV estimator that can differ from the within‑groups estimator. Efficient estimates from Michigan income dynamics data show substantially higher returns to schooling than within‑groups or Balestra‑Nerlove estimates, underscoring the importance of accounting for unobservable individual effects.

Abstract

Abstract An important purpose in pooling time-series and cross-section data is to control for individual-specific unobservable effects which may be correlated with other explanatory variables, e.g. latent ability in measuring returns to schooling in earnings equations or managerial ability in measuring returns to scale in firm cost functions. Using instrumental variables and the time-invariant characteristics of the latent variable, we derive: 1. (1) a test for the presence of this effect and for the over-identifying restriction we use; 2. (2) necessary and sufficient conditions for identification of all the parameters in the model; and 3. (3) the asymptotically efficient instrumental variables estimator and conditions under which it differs from the within-groups estimator. We calculate efficient estimates of a wage equation from the Michigan income dynamics data which indicate substantial differences from within-groups and Balestra-Nerlove estimates — particularly a significantly higher estimate of the returns to schooling.