Unit Averaging for Heterogeneous Panels

TL;DR

This paper introduces a unit averaging method for efficiently estimating unit-specific parameters in heterogeneous panel models, optimizing weights to minimize mean squared error.

Contribution

It proposes a novel weighted averaging procedure with derived optimal weights and analyzes its asymptotic properties under local heterogeneity.

Findings

The estimator minimizes mean squared error in heterogeneous panels.

Asymptotic distribution of the estimator is derived.

Application to forecasting unemployment rates demonstrates effectiveness.

Abstract

In this work we introduce a unit averaging procedure to efficiently recover unit-specific parameters in a heterogeneous panel model. The procedure consists in estimating the parameter of a given unit using a weighted average of all the unit-specific parameter estimators in the panel. The weights of the average are determined by minimizing an MSE criterion we derive. We analyze the properties of the resulting minimum MSE unit averaging estimator in a local heterogeneity framework inspired by the literature on frequentist model averaging, and we derive the local asymptotic distribution of the estimator and the corresponding weights. The benefits of the procedure are showcased with an application to forecasting unemployment rates for a panel of German regions.