Estimating panel VARs from macroeconomic data: Some Monte Carlo evidence and an application to OECD public spending shocks

Abstract

Listen

Translate article

This paper compares the performance of six widely applied techniques to estimate panel VARs from macroeconomic (large T ) data. We show that the bias of the popular least squares dummy variable estimator remains substantial even when the time dimension of the dataset is relatively large. Adopting a bias correction to the simple xed-e¤ects estimator is strongly recommended to obtain consistent estimates of the implied impulse response functions. Multivariate extensions of the GMM-type estimators usually applied for estimating single-equation dynamic panel data models perform reasonably well in terms of bias, but poorly in terms of root mean square error, in particular if the variance of the xed e¤ects is large relative to the variance of the innovations. To illustrate the methodological arguments we present an application in which we use annual OECD country data to estimate the e¤ects of changes in government consumption on aggregate output, private consumption, investment, and real wages. Keywords: Panel Vector Autoregressions, Simulation, Fiscal Policy E¤ects JEL classi cation: C13, C33, E62, E00 Address: TU Dortmund University, Department of Economics, Vogelpothsweg 87, D-44227 Dortmund, Germany. Email: falko.juessen@tu-dortmund.de Corresponding author. Address: TU Dortmund University, Department of Economics, Vogelpothsweg 87, D-44227 Dortmund, Germany. Email: ludger.linnemann@tu-dortmund.de Financial support by the Deutsche Forschungsgemeinschaft (SFB 823, ‘Statistical modelling of nonlinear dynamic processes’) is gratefully acknowledged. 1 Introduction Macroeconomists make extensive use of vector autoregressive models (VARs) to estimate the evolution and the interdependencies between multiple time series. Estimating VARs from panel data has generated interest, mainly because panel VARs allow one to control for unobserved heterogeneity and provide more precise estimates of the VAR coe¢ cients and thus the implied impulse response functions. Many macro studies have estimated panel VARs using existing techniques for singleequation dynamic panel data models, see Section 2 for a list of applications. In such models, it is well-known that the simple least squares dummy variable (LSDV) estimator is not consistent for a nite time dimension T even when the cross-sectional dimension N gets large, see e.g. Nickell (1981). Previous studies estimating macro panel VARs have typically followed one of two strategies to address this issue. The rst strategy is to use instrumental variables or generalized method of moments techniques. A second strategy is to adhere to the simple LSDV estimator, referring to the fact that its bias approaches zero if the time dimension of the panel dataset approaches in nity. Both strategies have their relative merits. The GMM techniques have been designed for the case of a large cross-sectional dimension relative to the time dimension. Since the number of cross-sectional units (e.g. countries) is often small in macro applications, GMM estimators may appear less suited for estimating macro panel VARs. Concerning the simple LSDV estimator, the critical question is whether the number of time periods encountered in macro studies is su¢ ciently large to make its bias unimportant from an economic point of view. In fact, the economic importance of the bias of the simple LSDV estimator has been a matter of debate in many studies estimating macro panel VARs (see Section 2 for a list of applications). Recent advances in the study of single-equation dynamic panel data models have opened up a third strategy to estimate panel VARs. Kiviet (1995), Hahn and Kuersteiner (2002), Bun and Kiviet (2003, 2006), Bun and Carree (2005, 2006), and Bruno (2005) have suggested bias-corrections to the simple LSDV estimator. In single-equation simulation studies, such bias-corrected estimators have often turned out to be more e¢ cient than GMM-type estimators.4 In this paper we examine the properties of various techniques to estimate panel vector autoregressive models. Throughout the paper, we have macroeconomic applications in mind, which means that we consider highly though not perfectly persistent time series and datasets having relatively small N and relatively large T . The estimation techniques we consider are representatives of the aforementioned three widely applied strategies to estimate macro panel VARs— simple xed-e¤ects procedures, bias-corrected xed e¤ects Panel VARs can also be estimated using Bayesian techniques (see e.g. Canova and Ciccarelli 2004 and Canova, Ciccarelli, and Ortega 2007) or likelihood-based procedures (see e.g. Binder, Hsiao, and Pesaran 2005, Yu, de Jong, and Lee 2008, and Mutl 2009).