Question 1 (25 points)
Answer the following questions. Be concise and to the point.
- Suppose you estimate the gender difference in returns to education using the following model:
where wage is the hourly wage, female is a gender dummy, which is =1 if the individual is female, and educ is the number of years of education. Provide an interpretation if and . [5 points]
- Someone asserts that expected wages are the same for men and women who have the same level of education. Referring to the model in part (a), what would be your null hypothesis to test this? How you would test it. [5 points]
- Suppose your estimation returns the following values for the model from part (a): , . Based on this, what is the expected wage differential between a man and a woman with 10 years of schooling?
- Suppose you find in addition that . What does it imply about the effect of 5 years more of education on the expected wage of a woman?
- Suppose we have estimated the following wage equation
Based on this, at what age would we expect the highest wage? [5 points]
Question 2 (25 points)
Consider the dataset ets_thres_final.dta. It contains emission figures (lnco2=log of CO2 emissions) for a sample of firms regulated by the European Emissions Trading System (EUETS) for the years from 2005 to 2017 although the firm identifiers have gone missing from the dataset. Note that an Emissions Trading System requires firms to buy permits for every unit of CO2 they emit. By restricting the total number of permits that are issued governments can control the total amount of emissions while allowing firms to trade permits freely so that they can be used with those businesses that find it hardest to reduce emissions. In the early days of the EU ETS (which started in 2005) permits where freely given to firms. This changed from 2013 onwards when permits where only given to certain firms and sectors that were deemed at risk from foreign competition. The variable free indicates those firms in the dataset. According to economic theory the method of permits allocation should have no effect on the eventual emissions by firms (Independence hypothesis). Firms that have been given free permits will have an incentive to reduce emissions as that frees up permits to sell within the permit market.
- Examine this hypothesis by running a regression of lnco2 on the free variable. Report what you find. [5 points]
- Provide an interpretation of the regression coefficient along with a discussion of the implications of your result. [5 points]
- The variable period is a categorical variable equal to 1 for observations from before 2013 and equal to 2 for observations from year 2013 onward. Convert it into a factor variable and run a regression of lnco2 on period. Provide an interpretation of the estimated coefficients [5 points]
- Would you say your results in part (a) provide a causal estimate of the effect of free permits? [5 points]
- With the data at hand can you propose and implement an alternative regression approach that might address any concerns raised in (d)? If yes, implement this regression and discuss its results. What does the result tell you about the Independence hypothesis discussed in the introduction. [5 points]
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