Palgrave Handbook of Econometrics: Applied Econometrics

Anindya Banerjee and Martin Wagner 677

Table 13.8 Results of the tests of Bai and Carrion-i-

Silvestre (2007) for unit roots in non-stationary panels

with common factors and structural breaks

GDP SO 2

Z and p-value tests

Z −1.38 5.59

BCN 0.51 −1.01

BCχ 2 210.14 174.02

Simplified Z and p-value tests

Z 0.63 9.10

BCN −1.12 −2.10

BCχ 2 177.70 152.61

Number of breaks 44 39

Notes: The number of factors is chosen according to the informa-

tion criterion BIC 3. The test results reported allow for at most one

break in both the intercept and linear trend. The critical value

(at the 5% nominal level) is given by –1.645 for theZtest, by

1.645 for theBCNtest and by 227.50 for theBCχ 2 test. Number

of breaks indicates the number of countries in which a break has

been detected. Also see notes to Table 13.5.

(a) Homogeneity or heterogeneity of the roots under the null and alternative
hypotheses.
(b) Deciding upon testing strategy – pooled (LLC) versus group mean methods
(IPS), for example, governed largely by the form of the alternative hypothesis
adopted.
(c) The need to allow for dependence; based upon the definition presented in
Appendix B, we distinguish short-run and long-run dependence, with the latter
being related to cross-unit cointegrating relationships and, hence, in a sense
made precise in Appendix B, the prevalence of joint common trends across
cross-section members. Up to now the most popular model to allow for cross-
sectional dependencies is the approximate factor model of Bai and Ng (2004),
whose cross-unit cointegration implications are also discussed in Appendix B.
For very special cases, short-run cross-sectional dependence can be handled by
resorting to relatively simple corrections such as the feasible GLS procedure of
O’Connell (1998), which, however, can only be used if the time dimension of
the panel exceeds the cross-section dimension.
(d) The construction of the statistics themselves, involving mean and variance
corrections to center and standardize the densities of the statistics derived from
the individual units.
(e) The startling features of Gaussianity in the limit for many of these statistics,
based on constructing statistics that are a weighted aggregate of the individual
unit-by-unit statistics. If these units are taken to be independent, under appro-
priate assumptions (that, for example, ensure the existence of the required