Testing for Exogeneity in Cointegrated Panels

Date01 August 2015
Published date01 August 2015
©2014 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
doi: 10.1111/obes.12072
Testing for Exogeneity in Cointegrated Panels*
Lorenzo Trapani
Cass Business School, City University London, 106 Bunhill Row, London, EC1Y 8TZ, UK
(e-mail: l.trapani@city.ac.uk)
This paper proposes a test for the null that, in a cointegrated panel, the long-run correlation
between the regressors and the error term is different from zero. As is well known, in
such case the OLS estimator is T-consistent, whereas it is NT-consistent when there is
no endogeneity. Other estimators can be employed, such as the FM-OLS, that are NT-
consistent irrespective of whether exogeneityis present or not. Using the difference between
the former and the latter estimator, we construct a test statistic which diverges at a rate N
under the null of endogeneity, whilst it is bounded under the alternative of exogeneity,and
employ a randomization approach to carry out the test. Monte Carlo evidence shows that
the test has the correct size and good power.
I. Introduction
Consider the panel regression
yit =xit +eit (1)
where t=1,…, T,i=1,…, N, and equation (1) is a cointegrating equation for each i. In-
ference on equation (1) has been studied extensively. In a seminal contribution, Phillips and
Moon (1999) discuss both ordinary least squares (OLS) estimation, and estimation based
on the Fully Modified version of the OLS estimator (FM-OLS henceforth). The choice
between OLS and FM-OLS is driven by the presence or absence of long-run correlation
between xit and eit (Phillips and Moon, 1999; Pedroni, 2000). In the former case, it is
well known that the panel OLS estimator of is T-consistent, and it has a non-vanishing
bias. This is in contrast with the case of no endogeneity in equation (1), where the OLS
estimator is NT-consistent (Kao, 1999; Phillips and Moon, 1999).
Consequently, empirical applications that consider panel cointegration models like
equation (1) routinely employ estimation techniques that are designed to be robust to
the presence of endogeneity, i.e. that yield NT-consistent estimates irrespective of the
assumption of exogeneity holding or not. Many examples can be found e.g. in the context
of testing for PPP (see e.g. Pedroni, 2001; Carlsson, Lyhagen and ¨
Osterholm, 2007, and
*I am grateful to the Editor (Anyndia Banerjee) and two anonymous referees for extremely valuable comments.
The usual disclaimer applies.
JEL Classification numbers: C12, C23.
476 Bulletin
the references therein); in studies of employment growth and inflation (see e.g. Caporale
and ˇ
Skare, 2011); in the context of the Feldstein–Horioka puzzle (see e.g. Ho, 2002); and
in applications to the area of spillovers in R&D (Edmond, 2001). A frequently employed
estimator is the FM-OLS; however, such estimation technique can suffer from severe
problems in presence of movingaverage roots that are close to the unit circle (Ng and Perron,
2001), and in the case of small samples (see e.g. Breitung, 2005; Wagner and Hlouskova,
2010). Several other alternative techniques are available: examples include the Dynamic
OLS estimator, developed by Saikkonen (1991) for the single equation case and by Kao
and Chiang (2000) for panels; and Breitung’s (2005) two stage parametric methodology.
Wagner and Hlouskova (2010) assess the relative merits of various estimators through a
comprehensive simulation exercise. Whilst some techniques are found to dominate across
a wide variety of experiments, all estimators show poor performances when Tis small.
Hence, a test to find out whether long-run correlation between xit and eit is different from
zero or not can be useful in order to decide whether to use a standard OLS estimator, or
whether it is necessary to employ a different estimation technique.
The contribution of this paper is a test for the null hypothesis of endogeneity, i.e. for
the null hypothesis that the long-run correlation between xit and eit is not equal to zero
(so that OLS should not be employed). Under the alternative, there is exogeneity, and
therefore OLS can be employed. The test is based on using the difference (multiplied by
NT) between the OLS and the FM-OLS estimators. As pointed out above, whilst the
latter estimator is NT-consistent under both the null and the alternative hypothesis, the
former has different rates under the null and the alternative hypothesis.Thus, the proposed
test is similar, in spirit, to a Hausman test, in that it compares two estimators with different
properties accordingly as the null or the alternative hypothesis holds. However, the test
is not a Hausman test. Indeed, by construction, the difference between the two estimators
multiplied by NT is, heuristically, a test statistic that diverges under the null hypothesis
and it is bounded under the alternative. Given that the test statistic diverges under the null
hypothesis, wepropose a randomized testing procedure to car ry out the test (Pearson, 1950;
Corradi and Swanson, 2002, 2006; Bandi and Corradi, 2014). A related contribution to
this paper is an article by Gengenbach and Urbain (2011) see also the references therein),
where an LM-type test for weak exogeneity in cointegrated panels is proposed.
Other testing approaches can also be considered, e.g. by extendingtests available in the
time series literature (see Ericsson and Irons, 1994). Indeed, comparisons are only partly
possible, since other approaches are usually constructed to test for the null hypothesis of
exogeneity, whilst our test has exogeneity as the alternative hypothesis.The purpose of our
test also is slightly different, since one of its primary goals is to help choose between esti-
mation techniques – this is also reinforced by the way in whichthe null hypothesis is stated
in presence of heterogeneity (in the slopes or in the dynamics), as equation (24) illustrates.
Notwithstanding this, the literature has developed several approaches to verifywhether ex-
ogeneity is present or not. Usually, this is carried out by using some parametric model (e.g.
a VECM specification), and then by formulating the null hypothesis of exogeneity based
on such model – see e.g. the contributions by Gengenbach and Urbain (2011) and Moral-
Benito and Serven (2013; and the references therein). Such approaches are sensitive to the
correct specification of the VECM, and a less parametric testing approach such as the one
proposed in this paper could be advantageous. Similarly, one may think of constructing
©2014 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd

To continue reading

Request your trial

VLEX uses login cookies to provide you with a better browsing experience. If you click on 'Accept' or continue browsing this site we consider that you accept our cookie policy. ACCEPT