Anindya Banerjee and Martin Wagner 707The final substantive section of our chapter is to apply some of the estimation
methods described in this section to the EKC analysis, building on our findings in
section 13.2.4.2.
13.3.5 The environmental Kuznets curve analysis continued
As indicated above, estimation of an equation of the form (13.17) using usual
cointegration methods is troublesome given the presence of nonlinear transforma-
tions of integrated regressors (GDP and its square). Regressions involving nonlinear
transformations of integrated regressors behave differently from the regressors usu-
ally considered and have been studied for the time series case in Chang, Park
and Phillips (2001) and Park and Phillips (1999, 2001). Hong and Wagner (2008a)
develop an FM-OLS estimator for nonlinear cointegrating relationships including
integer powers of integrated regressors as well as specification and cointegration
tests for this set-up. Hong and Wagner (2008b) derive first results for a simple panel
setting by considering a seemingly unrelated nonlinear cointegrating regressions
framework.
Ignoring the problems caused by nonlinear transformations, cross-sectional
dependencies and structural change, and applying the seven tests of Pedroni
(1999, 2004) leads to seemingly overwhelming support for cointegration (with
the detailed results available upon request). Again these findings are in line with
the Lyhagen result that in the presence of common non-stationary components
the unit root null hypothesis is over-rejected, which leads to seemingly strong
support for cointegration. Note that these findings are obtained both when using
the quadratic formulation (13.17) as well as the specification when only GDP is
included in the regression, with the latter specification being subject only to the
cross-sectional dependence and structural change problems.
Given the seemingly “strong evidence for cointegration,” the final step in panel
cointegration analysis is the estimation of relationship (13.17). In Table 13.10 we
present the results for sulphur dioxide emissions when applying the fully modified
OLS estimator discussed in detail in Phillips and Moon (1999), the dynamic OLS
estimator of Mark and Sul (2003) and the two-step estimator of Breitung (2005).
With the exception of the D-OLS estimator, seemingly strong evidence for the
prevalence of an EKC for sulphur dioxide appears, even with plausible turning
points with respect to income. Especially when applying fully modified estima-
tion the turning points are well within the sample. However, these findings should
be treated with some caution, given that the properties of the estimation meth-
ods in the presence of cross-sectional dependence and, in particular, of nonlinear
transformations of integrated regressors are far from fully worked out.
The finding of stationary de-factored GDP allows us to use standard econometric
methods to estimate equation (13.17) with de-factored observations. Table 13.11
shows the results from a variety of specifications, for example, one-way and
two-way fixed effects estimation and equations including the extracted factors
as additional regressors. For none of these specifications is there evidence for
an inverted U-shaped relationship, since the coefficients to income and squared
income are significantly positive.