The Environmental Kuznets Curve (EKC) measures the relationship between environmental degradation and a country's income per capita. Environmental degradation may change with income because of changes in industrial activities as income grows and changes in the level of environmental regulation that countries enact as they become richer. We want to estimate the EKC and allow for the possibility of a non-linear relationship. We estimate the following regression using data on each country's air particulate pollution concentration in micrograms per cubic meter [PMl-) and gross domestic product per capita GDP: and the total population of each country (populationi): PM: = 13., + lGDPiHRzGDPE + apopulationi + gt. a. It is hypothesized that the EKC should have an inverted U-shape. At low levels of income, economic development leads to more environmental degradation as countries prioritize growth over environmental protection. As income reaches a certain threshold, the rate of environmental degradation slows. Beyond this threshold, as income continues to increase, environmental degradation begins to decrease, suggesting that economic growth leads to environmental improvement as rich countries add more environmental regulations and protections. If the above hypothesis is true, what would you expect for the signs of 1 and 32? b. What if, instead, we ran the following regression by taking the natural log of both the PM and GDP_variables: ln(PM1) 2 0 + 31 ln(GDPi) + zpopulationi + e; Coefcient Estimate Standard Error p-value constant 1.2 0.5 0.0000]. ln(GDP) 2.2 4.4 0.6182 population 0.002 0.001 0.0482 Interpret the estimate of 31 for this regression. c. Interpret the estimate of g for the regression in part b. d. According to the table in part b. Which coefficients are statistically significant at the 5% confidence level