A Heteroskedasticity Robust Breusch-Pagan Test for Contemporaneous Correlation in Dynamic Panel Data Models

TY - JOUR

T1 - A Heteroskedasticity Robust Breusch-Pagan Test for Contemporaneous Correlation in Dynamic Panel Data Models

AU - Halunga, Andreea

AU - Orme, Chris

AU - Yamagata, Takashi

N1 - © 2017, Elsevier B.V. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy.

PY - 2017/6/1

Y1 - 2017/6/1

N2 - This paper proposes a heteroskedasticity-robust Breusch–Pagan test of the null hypothesis of zero cross-section (or contemporaneous) correlation in linear panel data models, without necessarily assuming independence of the cross-sections. The procedure allows for either fixed, strictly exogenous and/or lagged dependent regressor variables, as well as quite general forms of both non-normality and heteroskedasticity in the error distribution. The asymptotic validity of the test procedure is predicated on the number of time series observations, T, being large relative to the number of cross-section units, N, in that: either (i) N is fixed as T→∞; or, (ii) N 2/T→0 as both T and N diverge, jointly, to infinity. Given this, it is not expected that asymptotic theory would necessarily provide an adequate guide to finite sample performance when T/N is “small”. Because of this we also propose, and establish asymptotic validity of, a number of wild bootstrap schemes designed to provide improved inference when T/N is small. Across a variety of experimental designs, a Monte Carlo study suggests that the predictions from asymptotic theory do, in fact, provide a good guide to the finite sample behaviour of the test when T is large relative to N. However, when T and N are of similar orders of magnitude, discrepancies between the nominal and empirical significance levels occur as predicted by the first-order asymptotic analysis. On the other hand, for all the experimental designs, the proposed wild bootstrap approximations do improve agreement between nominal and empirical significance levels, when T/N is small, with a recursive-design wild bootstrap scheme performing best, in general, and providing quite close agreement between the nominal and empirical significance levels of the test even when T and N are of similar size. Moreover, in comparison with the wild bootstrap “version” of the original Breusch–Pagan test (Godfrey and Yamagata, 2011) our experiments indicate that the corresponding version of the heteroskedasticity-robust Breusch–Pagan test appears reliable. As an illustration, the proposed tests are applied to a dynamic growth model for a panel of 20 OECD countries.

AB - This paper proposes a heteroskedasticity-robust Breusch–Pagan test of the null hypothesis of zero cross-section (or contemporaneous) correlation in linear panel data models, without necessarily assuming independence of the cross-sections. The procedure allows for either fixed, strictly exogenous and/or lagged dependent regressor variables, as well as quite general forms of both non-normality and heteroskedasticity in the error distribution. The asymptotic validity of the test procedure is predicated on the number of time series observations, T, being large relative to the number of cross-section units, N, in that: either (i) N is fixed as T→∞; or, (ii) N 2/T→0 as both T and N diverge, jointly, to infinity. Given this, it is not expected that asymptotic theory would necessarily provide an adequate guide to finite sample performance when T/N is “small”. Because of this we also propose, and establish asymptotic validity of, a number of wild bootstrap schemes designed to provide improved inference when T/N is small. Across a variety of experimental designs, a Monte Carlo study suggests that the predictions from asymptotic theory do, in fact, provide a good guide to the finite sample behaviour of the test when T is large relative to N. However, when T and N are of similar orders of magnitude, discrepancies between the nominal and empirical significance levels occur as predicted by the first-order asymptotic analysis. On the other hand, for all the experimental designs, the proposed wild bootstrap approximations do improve agreement between nominal and empirical significance levels, when T/N is small, with a recursive-design wild bootstrap scheme performing best, in general, and providing quite close agreement between the nominal and empirical significance levels of the test even when T and N are of similar size. Moreover, in comparison with the wild bootstrap “version” of the original Breusch–Pagan test (Godfrey and Yamagata, 2011) our experiments indicate that the corresponding version of the heteroskedasticity-robust Breusch–Pagan test appears reliable. As an illustration, the proposed tests are applied to a dynamic growth model for a panel of 20 OECD countries.

UR - http://www.scopus.com/inward/record.url?scp=85016180859&partnerID=8YFLogxK

U2 - 10.1016/j.jeconom.2016.12.005

DO - 10.1016/j.jeconom.2016.12.005

M3 - Article

VL - 198

SP - 209

EP - 230

JO - Journal of Econometrics

JF - Journal of Econometrics

SN - 0304-4076

IS - 2

ER -