Pooled Bewley Estimator of Long-Run Relationships in Dynamic Heterogenous Panels

Abstract

This paper, using the Bewley (1979) transformation of the autoregressive distributed lag model, proposes a pooled Bewley (PB) estimator of long-run coefficients for dynamic panels with heterogeneous short-run dynamics, in the same setting as the widely used Pooled Mean Group (PMG) estimator. The Bewley transform enables us to obtain an analytical closed form expression for the PB, which is not available when using the maximum likelihood approach. This lets us establish asymptotic normality of PB as n,T→∞ jointly, allowing for applications with n and T large and of the same order of magnitude, but excluding panels where T is short relative to n. In contrast, asymptotic distribution of PMG estimator was obtained for n fixed and T→∞. Allowing for both n and T large seems to be the more relevant empirical setting, as revealed by numerous applications of the PMG estimator in the literature. Dynamic panel estimators are biased when T is not sufficiently large. Three bias corrections (simulation based, split-panel jackknife and a combined procedure) are investigated using Monte Carlo experiments, of which the combined procedure works best in reducing bias. In contrast to PMG, PB does not weight by estimated variances, which can make it more robust in small samples, though less efficient asymptotically. The PB estimator is illustrated with an application to the aggregate consumption function estimated in the original PMG paper.