Critical Values for Cointegration Tests in Heterogeneous Panels with Multiple Regressors
| Author | Peter Pedroni |
| DOI | http://doi.org/10.1111/1468-0084.0610s1653 |
| Published date | 01 November 1999 |
| Date | 01 November 1999 |
CRITICAL VALUES FOR COINTEGRATION TESTS IN
HETEROGENEOUS PANELS WITH MULTIPLE
REGRESSORS
Peter Pedroni
I. INTRODUCTION
In this paper we describe a method for testing the null of no cointegration in
dynamic panels with multiple regressors and compute approximate critical
values for these tests. Methods for non-stationary panels, including panel
unit root and panel cointegration tests, have been gaining increased accep-
tance in recent empirical research. To date, however, tests for the null of no
cointegration in heterogeneous panels based on Pedroni (1995, 1997a) have
been limited to simple bivariate examples, in large part due to the lack of
critical values available for more complex multivariate regressions. The
purpose of this paper is to ®ll this gap by describing a method to implement
tests for the null of no cointegration for the case with multiple regressors
and to provide appropriate critical values for these cases. The tests allow for
considerable heterogeneity among individual members of the panel, includ-
ing heterogeneity in both the long-run cointegrating vectors as well as
heterogeneity in the dynamics associated with short-run deviations from
these cointegrating vectors.
1.1. Literature Review
Initial theoretical work on the non-stationary panel data focused on testing
for unit roots in univariate panels. Early examples include Quah (1994),
who studied the standard unit root null in panels with homogeneous
dynamics, and Levin and Lin (1993) who studied unit root tests in panels
with heterogeneous dynamics, ®xed effects, and individual-speci®c determi-
nistic trends. These tests take the autoregressive root to be common under
both the unit root null and the stationary alternative hypothesis. More
recently, Im, Pesaran and Shin (1997) and Maddala and Wu (1999) suggest
several panel unit root tests which also permit heterogeneity of the
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, SPECIAL ISSUE (1999)
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#Blackwell Publishers Ltd, 1999. Published by Blackwell Publishers, 108 Cowley Road, Oxford
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Acknowledgments: I thank Anindya Banerjee, David Canning and Peter Dunne for helpful
comments and I thank Terri Ziacik for valuable research assistance. A computer program which
implements these tests is available upon request from the author at ppedroni@indiana.edu
autoregressive root under the alternative hypothesis. Applications of panel
unit root methods have included Bernard and Jones (1996), Coakley and
Fuertes (1997), Evans and Karras (1996), Frankel and Rose (1996), Lee,
Pesaran and Smith (1997), MacDonald (1996), O'Connell (1998), Oh
(1996), Papell (1997), Wei and Parsley (1995), and Wu (1996).
However, many empirical questions involve multivariate relationships
and a researcher is interested to know whether or not a particular set of
variables is cointegrated. Consequently, Pedroni (1995, 1997a) studied the
properties of spurious regression, and tests for the null of no cointegration
in both homogeneous and heterogeneous panels. For the case with hetero-
geneous panels, Pedroni (1995, 1997a) provides asymptotic distributions for
test statistics that are appropriate for various cases with heterogeneous
dynamics, endogenous regressors, ®xed effects, and individual-speci®c
deterministic trends. Pedroni (1997a) includes tests that are appropriate both
for the case with common autoregressive roots under the alternative hypoth-
esis as well as tests that permit heterogeneity of the autoregressive root
under the alternative hypothesis in the spirit of Im et al. (1997).
Applications of the panel cointegration tests developed in Pedroni (1995,
1997a) for the case with heterogeneous cointegrating vectors have included,
among others, Butler and Dueker (1999), Canzoneri, Cumby and Diba
(1996), Chinn (1997), Chinn and Johnston (1996), Neusser and Kugler
(1998), Obstfeld and Taylor (1996), Ong and Maxim (1997), Pedroni
(1996b), and Taylor (1996). However, to date, these applications have been
limited to cases in which the cointegrating regressions involved a single
regressor. Many topics, on the other hand, involve applications in which
more than a single regressor is likely to be required. Therefore, the purpose
of this paper is to provide critical values that are appropriate for these
situations based on the heterogeneous panel cointegration statistics devel-
oped in Pedroni (1995, 1997a).
Finally, the panel cointegration tests in this paper should be distinguished
from those which are based on a maintained assumption of homogeneity of
the cointegrating vectors among individual members of the panel. In addition
to the heterogeneous case, Pedroni (1995, 1997a) also studied properties for
the special case of homogeneous cointegrating vectors. Speci®cally, Pedroni
(1995, 1997a) showed that for panels with homogeneous cointegrating
vectors, an interesting special result holds such that residual-based tests for
the null of no cointegration have distributions that are asymptotically equiva-
lent to raw panel unit root tests if and only if the regressors are exogenous.
Kao (1999) further studied the special case in which cointegrating vectors
are assumed to be homogeneous, but the asymptotic equivalency result is
violated because of the endogeneity of regressors. An example of the
application of these techniques for a test of the null of no cointegration in
panels that are assumed to be homogeneous is the paper by Kao, Chiang and
Chen (1999). By contrast, McCoskey and Kao (1999) examine the reversed
null hypothesis of cointegration in their study of urbanization.
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