In attempting to isolate the independent effect of FDI on CO

_{2} emissions, we rely on an empirical framework developed by

Kim and Baek (

2011) and

Pao and Tsai (

2011). The long-run form of the panel equation to be estimated is specified as follows:

where

c_{it} is CO

_{2} emissions in period

t for country

i;

y_{it} is real GDP per capita;

en_{it} is energy consumption;

fdi_{it} is FDI inflows;

u_{it} is the error term. In Equation (1), when the coefficient on

y_{it} is positive and the coefficient on

y_{it}^{2} is negative, the quadratic has a parabolic shape, thereby confirming the so-called

Environmental Kuznets curve (EKC) hypothesis: growth has a diminishing effect on CO

_{2} emissions after a certain (per capita) income turning point. The rise in energy consumption mainly driven by growth is likely to result in increasing CO

_{2} emissions; hence, the coefficient on

en_{it} is expected to be positive. Finally, if an increase in the inflow of FDI increases (decrease) CO

_{2} emissions by attracting more pollution intensive industries (adopting greener technologies), the coefficient on

fdi_{it} is expected to be positive (negative).

When estimating Equation (1) using the PMG estimator,

2 Pesaran et al. (

1999) recommend that the short-run dynamics among the variables for each country be incorporated into an error-correction modeling format. For this, by imposing one as the maximum lag length and using Akaike Information Criterion (AIC), the autogressive distributed lag (ARDL) (1, 1, 1, 1) equation is first determined as the most appropriate form for the analysis:

The error-correction modeling format is then specified as follows:

where

${\alpha}_{0i}={\mu}_{i}/(1-{\lambda}_{i})$;

${\alpha}_{1i}=({\delta}_{10i}+{\delta}_{11i})/(1-{\lambda}_{i})$;

${\alpha}_{2i}=({\delta}_{20i}+{\delta}_{21i})/(1-{\lambda}_{i})$;

${\phi}_{i}=-(1-{\lambda}_{i})$. In Equation (3),

α_{it} captures the long-run relationship between

c_{it} and its determinants, whereas δ

_{i1t} represents the short-run coefficients. Finally,

ϕ_{i} is the error-correction term and gauges how fast

c_{it} adjusts to the long-run equilibrium when a change in its determinants takes place.

It is worth mentioning that, when estimating dynamic (heterogeneous) panels, it is fairly common to see researchers apply alternative methods and then formally test for statistically significant differences in the selected estimators. In estimating Equation (3), therefore, we also employ the two alternative methods such as the mean group (MG) and dynamic fixed effect (DFE) estimators in addition to the PMG. The MG method does not impose homogeneity restrictions on the parameters across countries; hence, the estimates are the unweighted average of estimated coefficients in a single country (

Pesaran and Smith 1995). In the DFE method, on the other hand, the parameters of the short- and long-run (except for the intercepts) are assumed to be homogenous across countries. The PMG estimator restrains the long-run parameters to be homogenous while allowing other parameters to vary among countries; hence it is known as an intermediate estimator between the MG and DFE estimators. The Hausman test is generally used to identify the difference in the three methods.