Anindya Banerjee and Martin Wagner 675capita GDP and emissions, the use of a panel perspective may appear fruitful to
enhance the performance of unit root and cointegration tests. In any empirical
analysis of an EKC like (13.17), using panel unit root and cointegration techniques,
all the complications discussed above, such as cross-sectional dependence or struc-
tural changes in the deterministic component, may arise and have consequently
to be addressed. We turn to each of these problems below. Furthermore, the homo-
geneity restriction (that is,β 1 i=β 1 andβ 2 i =β 2 fori=1,...,N)needs to be
investigated, which we address in a later section in this chapter (having discussed
testing for cointegration and estimation of cointegrating vectors).
There is one additional problem that arises in an equation like (13.17): log per
capita GDP and its square are both present. However, at most one of the two
processes can be a unit root process, with the other process necessarily being a
nonlinear transformation thereof. We return to this issue and its implications later
when considering estimation of (13.17).
In our empirical application we consider sulphur dioxide (SO 2 )emissions using
a balanced panel of 97 countries over the period 1950–2000 (described in detail in
a table in Appendix A).
Let us start the discussion of the empirical results by looking at the results
obtained with the Bai and Ng (2004) methodology, summarized in Table 13.6.
For SO 2 two common factors are found and for GDP one common factor is found.
Depending upon the test chosen,MQc(m)orMQf(m), one or both common factors
in SO 2 are non-stationary and the ADF test on the single common factor in GDP
also does not lead to a rejection of the unit root null hypothesis. The GDP common
factor reflects the evolution of average worldwide GDP and also tracks the observed
slowdown of the mid 1970s quite well. The SO 2 common factors are less clearly
interpretable and are, furthermore, not cointegrated with the GDP common factor.
This implies that there is some long-run disconnect between per capita GDP and
per capita SO 2 emissions.
The idiosyncratic components for GDP (as tested byBNNandBNχ 2 )appear to be
stationary, since the unit root null hypothesis is rejected by both tests. This implies
that the deviations of the individual countries’ GDP from the common global factor
are stationary and that none of the countries’ GDP deviates permanently from the
single global stochastic trend.
For SO 2 emissions the null hypothesis of a unit root in the idiosyncratic com-
ponents is not rejected. This is consistent with large inter-country systemic and
technological differences in industry and energy production as well as differences
in environmental legislation.
The other, more restrictive, second-generation panel unit root tests, collected in
Table 13.7, provide very mixed results. The most relevant results from this table are
the Moon and Perron (2004) results, since the other results collected in this table
are for tests designed for panels without long-run cross-sectional dependencies.
In the specification with only fixed effects included, the unit root null hypoth-
esis is rejected for the idiosyncratic component for both GDP and SO 2 emissions,
whereas it is not rejected when both fixed effects and linear trends are included.