Panel Data Unit Roots and Cointegration: An Overview
| Published date | 01 November 1999 |
| Author | Anindya Banerjee |
| DOI | http://doi.org/10.1111/1468-0084.0610s1607 |
| Date | 01 November 1999 |
PANEL DATA UNIT ROOTS AND COINTEGRATION:
AN OVERVIEW
Anindya Banerjee
I. INTRODUCTION
The analysis of unit roots and cointegration in panel data has been a fruitful
area of study in recent years, with Levin and Lin (1992, 1993) and Quah
(1994) being the seminal contributions in this ®eld. The investigation of
integrated series in a panel data context is based on two separate but richly
developed ®elds of econometric investigation, the ®rst being unit roots and
cointegration in time series and panel data econometrics the other. Both
literatures have been surveyed in rich detail. For unit roots and cointegration
in time series, Banerjee et al. (1993), Hamilton (1994) and Phillips and
Xiao (1998) are useful sources. The book by Baltagi (1995) and the edited
collection by Matyas and Sevestre (1996) are important references for the
literature on panel data econometrics. The several volumes of papers edited
by Maddala (1994) are also relevant in this regard.
The emphasis of the literature on unit roots and cointegration in panel
data has been the attempt to combine information from the time series
dimension with that obtained from the cross-sectional, in the hope that
inference about the existence of unit roots and cointegration can be made
more straightforward and precise by taking account of the cross-section
dimension, especially in environments in which the time series for the data
may not be very long but very similar data may be available across a cross-
section of units such as countries, regions, ®rms or industries.
The empirical motivations have therefore always been important. Further-
more, with increasingly larger quantities of panel data information becom-
ing available, the investing of effort in this area of research has seemed
worthwhile, given the well-known power de®ciencies of pure time series-
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, SPECIAL ISSUE (1999)
0305-9049
607
#Blackwell Publishers Ltd, 1999. Published by Blackwell Publishers, 108 Cowley Road, Oxford
OX4 1JF,UK and 350 Main Street, Malden, MA 02148, USA.
Paper prepared as editorial introduction for the special issue of the Oxford Bulletin of
Economics and Statistics. I am obliged to the contributors to this volume for their comments and
to Wallace Lo for valuable research assistance. A substantial part of the work for this paper and
for putting together the special issue was undertaken by me during March and April 1999 in the
Department of Economics at the University of Canterbury in Christchurch, New Zealand, under
the auspices of a Visiting Erskine Fellowship. The generosity of the Erskine Foundation and the
Department of Economics in Canterbury is gratefully acknowledged. In particular, I thank Robin
Harrison and Alfred Haug for their hospitality. I also thank the ESRC for funding this research
under grant L116251015.
based tests for unit roots and cointegration. Panel data techniques have been
used to investigate, for example, wages in unionized and non-unionized
industries (Breitung and Mayer (1994)), purchasing power parity (Bernard
and Jones (1996), Coakley and Fuertes (1997), Frankel and Rose (1996),
MacDonald (1996), O'Connell (1998), Oh (1996), Pedroni (1995, 1997a),
Papell (1997), Wu (1996)) and issues of convergence (Cechetti et al.
(1999), Evans and Karras (1996), Lee, Pesaran and Smith (1997), Pedroni
(1998)). The papers by Suzanne McCoskey and Chihwa Kao and by Chihwa
Kao, Min-Hsien Chiang and Bangtian Chen in this Special Issue look at
urbanization and international R&D spillovers respectively and are de-
scribed later in the introduction.
The literature that has emerged has liberally drawn many elements from
its parent literatures. The consideration of fully modi®ed estimation techni-
ques, to take account of endogeneity of the regressors and correlation and
heteroscedasticity properties of the residuals, on the one hand, and the use
of methods for ®xed or random effects estimation, developed in the
literature on panel data with stationary variables, on the other, are two
examples of where the clear links may be identi®ed. Yet, as in other
instances where a new literature comes to be seen to be signi®cant, the
aggregate has turned out to be greater than the sum of its par ts and the
theory and practice of integrated series in panel data have given rise to a set
of interesting and surprising results which are uniquely its own.
A few examples of the distinctive features will suf®ce to elaborate on the
point made in the previous paragraph. From the early papers which devel-
oped the asymptotic theory of unit root processes in time series (Phillips
(1987), Engle and Granger (1987)), many of the estimators and statistics of
interest have been shown to have limiting distributions which are compli-
cated functionals of Wiener processes. In direct contrast, the asymptotics of
non-stationary panels, starting with Levin and Lin, have led to demonstra-
tions of estimators having Gaussian distributions in the limit. These results
have been extended to allow for a wide degree of heterogeneity across the
units comprising the panel.
The limiting distributions have also required the development and use of
multivariate `panel' functional central limit theorems, since the limiting
behaviour has required consideration of processes indexed by not only time
but also by unit. The formal and general treatment of the asymptotic
behaviour of such double indexed integrated processes has begun only
recently (Phillips and Moon (1999a)), although various aspects had been
implicitly employed in the earlier literature. It has become clear that several
approaches are possible and the limit of the processes may depend on the
assumptions made about the manner in which N(the units) and Ttend to
in®nity. For example, one may ®x Nand let the other index pass to in®nity
and subsequently allow Nto tend to in®nity. This is denoted by Phillips and
Moon (1999a) as (N,T!1)seq. Alternatively Nand Tmay be allowed to
pass to in®nity at a controlled rate of the type TT(N). A third possibility
608 BULLETIN
#Blackwell Publishers 1999
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