13

Panel Methods to Test for Unit Roots

and Cointegration

Anindya Banerjee and Martin Wagner

Abstract
We provide an up-to-date analytical survey of methods which have been developed to deal with
estimation and inference in non-stationary panels. The chapter provides information not only on
the tools but also interprets the literature and highlights the important challenges that remain. We
discuss the difficulties involved in formulating hypotheses within a panel framework with unit roots
and cointegration. These issues include incorporating cross-sectional dependence and structural
breaks in the data. Both these features are widely prevalent in the panels and lead to complications
in estimation and inference. For example, factor models are a widely used class of methods used
to deal with dependence but constitute only one of several ways of formulating the problems
involved. We argue that the links between cointegration and factor models in panels need to be
considered adequately and the asymptotic theory put on a firmer footing in many respects. The
study of cross-sectional dependence, breaks, and multiple cointegrating vectors, all of which are
in their relative infancy, mark the way for productive research in the years ahead.

13.1 Introduction 633
13.1.1 An example: economic convergence in the sense of
Evans and Karras (1996) 634
13.2 Unit root analysis in non-stationary panels 640
13.2.1 Tests without cross-sectional dependence or structural breaks 643
13.2.1.1 Levin, Lin and Chu (2002) 643
13.2.1.2 Relaxing homogeneity – Im, Pesaran and Shin (2003) 645
13.2.1.3 Fisher tests – Maddala and Wu (1999) and Choi (2001) 647
13.2.1.4 Tests with stationarity as the null hypothesis 647
13.2.1.5 A summary of simulation evidence (Hlouskova and
Wagner, 2006) 648
13.2.2 Allowing for cross-sectional dependence 649
13.2.2.1 Exemplifying the effects of cross-sectional dependence
(O’Connell, 1998) 650
13.2.2.2 Cross-sectional dependence via approximate factor models –
Bai and Ng (2004) 653
13.2.2.3 Specializations of the Bai and Ng (2004) framework 657
13.2.2.4 Nonlinear instrumental variables unit root test – Chang
(2002) 662
13.2.2.5 Summary of section 13.2.2 662

632