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# ARE 106 Quantitative Methods Problem Set 2

Part A

Please retrieve the data set “CO2 Country Panel 1990-2010.” It contains data on CO2 emissions, in kilotons; population, in millions; and gross national income (GNI), in millions of US dollars, for multiple countries and for two years: 1990 and 2010. (Your first homework used only the 2010 data.)

1. Using Shazam, please estimate a regression model of the following form:

Report your results in table or equation form.

1. Test, at the p=.05 significance level, the null hypothesis that:
1. Population has no effect on CO2 emissions
2. Income has no effect on CO2 emissions
1. What is the interpretation of b3 in this regression? Is it statistically significant at the p=.05 level? Why or why not?
2. Now propose a single model with which you can test whether: (a) the relationship between population and CO2 emissions is nonlinear; (b) the relationship between income and CO2 emissions is nonlinear; (c) the impacts of population and income on CO2 emissions are different in different years; and (d) the impact of population on CO2 emissions is different at higher than at lower income levels. What does your model look like?
3. Using Shazam, estimate the model you proposed in question 4. Report your findings on 4(a) through 4(d) in a table form.
4. Compare the R-squares from the regressions in (1) and (5). Based on this measure of fit, which of the two models do you think is better? Why?
5. Use your results to test the null hypotheses corresponding to each of 4(a) through 4(d).
6. Based on your findings, how would you explain the relationship between population and income, on one hand, and CO2 emissions, on the other, and how it has changed over time? In other words, what is the story these data tell?
7. Please construct a 95-percent confidence interval around your estimated effects of (a) population and (b) income on CO2 emissions.