A Conditional Approach to Panel Data Models with Common Shocks

Giovanni Forchini,Bin Peng

doi:10.3390/econometrics4010004

Giovanni Forchini, Bin Peng

Open Access

https://doi.org/10.3390/econometrics4010004

Copy DOI

Abstract

This paper studies the effects of common shocks on the OLS estimators of the slopes’ parameters in linear panel data models. The shocks are assumed to affect both the errors and some of the explanatory variables. In contrast to existing approaches, which rely on using results on martingale difference sequences, our method relies on conditional strong laws of large numbers and conditional central limit theorems for conditionally-heterogeneous random variables.

Highlights

The effects of common shocks, which may be macroeconomic, technological, institutional, political, environmental, health related, sociological, etc. (e.g., [1]), have been recently investigated by various authors, including, among others, [1,2,3,4,5,6]
Financial and political shocks are likely to be relevant when explaining the differences in individual countries’ exchange rate ratios in terms of their per capita GDP measured in purchasing power parity—the Balassa-Samuelson hypothesis (e.g., [8])
The approach that we suggest is based on two steps: 1. formulation of the assumptions concerning the unobservable and heterogeneous variables conditional on the sigma algebra capturing the common shocks; 2. application of conditional strong laws of large numbers and conditional central limit theorems to establish the limits of the estimator of interest conditional on the common shocks, from which the unconditional distribution can be obtained

Summary

Introduction

The effects of common shocks, which may be macroeconomic, technological, institutional, political, environmental, health related, sociological, etc. (e.g., [1]), have been recently investigated by various authors, including, among others, [1,2,3,4,5,6]. Kuersteiner and Prucha [14] have extended the work of Andrews [1] by deriving a stable central limit theorem for sample moments under weaker assumptions and have established limiting distributions of GMMand maximum likelihood estimators for general models in which unobservable factors may induce cross-sectional heterogeneity, but do not affect the regressors. Application of conditional strong laws of large numbers and conditional central limit theorems to establish the limits of the estimator of interest conditional on the common shocks, from which the unconditional distribution can be obtained

Homogeneous Slopes

Heterogeneous Slopes

A Fixed Effects Model

Conclusions