Anindya Banerjee and Martin Wagner 649relative toN, the size and power properties of panel tests are affected adversely.
The presence of moving average terms distorts the size of tests especially as the
moving average coefficientθin the processνi,t=εi,t+θεi,t− 1 tends to−1. This
is a feature of tests for unit roots that is also evident in the time series case (see
Molinas, 1986, or Schwert, 1989). Appropriate selection of the lag length in the
ADF regressions is an issue here, since one way to account for the moving aver-
age dynamics is by sufficiently expanding the order of the autoregressions. As
noted in a previous section, the impact of lag length selection, by various crite-
ria such as AIC or BIC, is found to be ambiguous – beneficial in some cases and
harmful in others. Evidence overall tends to suggest that, forθclose to zero,
smaller lag lengths than those selected by the BIC tend to lead to better per-
formance of the unit root tests, while the converse is true for values ofθclose
to−1.
13.2.2 Allowing for cross-sectional dependence
An important assumption underlying the so-called first-generation tests for unit
roots in panel data, discussed in the previous section, is that of cross-sectional
independence of the units of the panel. It is important, therefore, to assess the con-
sequences of making this assumption when applying these techniques to datasets
where it is not sustainable. As in our discussion of EK, in our view this appears to
be relevant for many of the datasets for which one would have occasion to use unit
root or cointegration tests in panels.
The motivation for the research presented next is to begin by analyzing, within
the framework of some simulation studies, the consequences of departures from
cross-sectional independence for the size and power properties of the first genera-
tion of commonly-used tests for unit roots in panels, and then to consider in detail
the second generation of unit root tests that have emerged to allow for dependence.
It is possible to generalize this framework to allow for structural breaks and we shall
return to this issue in a later section.
Some particular examples of cross-sectional dependence are presented here,
which we classify as short-run and long-run dependence according to the discus-
sion and definition given in Appendix B. We distinguish between these two forms
of dependence according to whether cross-unit cointegrating relationships, also
defined in Appendix B, are present in the panel or not. While there are many
ways of formulating dependence in panels, what is needed is the development
of a general framework to incorporate the different possibilities and analyze their
consequences. Appendix B contains a few simple observations.
13.2.2.1 Exemplifying the effects of cross-sectional dependence (O’Connell, 1998)
The study of O’Connell (1998) is a powerful demonstration of the oversizing of
the LLC tests in the presence of short-run dependence. His simulation results have
since been replicated and generalized, for example, by Hlouskova and Wagner
(2006) and Baltagi, Bresson and Pirotte (2007). In the latter paper, cross-sectional
dependence is derived from so-called spatial correlations. Describing some of this