**3. Empirical results and discussion**

#### **3.1 Pre-tests discussion**

Before estimating the PSTR model, I performed a homogeneity test in which the income per capita is a transition variable (q). The results of this test (**Table 3** of Appendix) indicate whether a PSTR model can assess the effect of income on environmental pollution. The three statistics (LR, LMF, and LRT – the Wald, Fisher, and Likelihood ratio test statistics) indicate that the hypothesis of a homogeneous effect of income on environmental pollution is rejected. Furthermore, LM, LMF, and LRT p-values are smaller for the exponential model meaning that it is favored over the logistic one.

Considering these results, income influences environmental degradation in different ways. The test of remaining regimes (**Table 4** of Appendix) concludes on the existence of a two-threshold level of income. The LM and LMF statistics of these two tests are statistically significant at 1% and 5% levels, which indicate a rejection of the null hypothesis and the acceptance of at least two transition functions. **Table 5** of the Appendix complements the previous finding by indicating that three extreme regimes (m = 2) are enough to capture the nonlinearity of the income-pollution nexus based on the modulating effect of the income level. The optimal number of location parameters is given by the Akaike and Schwartz criterion and their values are also shown.

**Table 6** of the Appendix gives thresholds of income per capita for 34 OECD economies. The threshold of income remains quite similar among different specifications ranging from 9.29 to 10.71. Because data are in natural logarithms, the exact value of the threshold is computed by applying an exponential function to the constant C. This transformation gives us the level of income per head around which income exerts a negative or a positive effect on the CO2 emissions. Hence, the threshold of income ranges between about 10 774\$ and 44968\$.

For the advanced economies, the threshold of 25245\$ means that below this level of income, each group of countries will have higher levels of pollution. Conversely, it is only above this high threshold that these countries can improve the environmental degradation. Therefore, less income means more environmental pollution for these

economies. An examination of the possibility of each country having more income based on the estimated threshold value of PSTR 1 and PSTR 2 (25245\$ and 26132\$ in the first regime) found that about a third of the advanced-economies countries (13) can respond to this threshold. These countries are Turkey and the new EU members. The rest of OECD countries have income per head superior to 25000\$.
