EC 420, Fall 2009
Name and ID:
Show all work for each question, providing explanations wherever necessary. You may use the course textbook, but no notes. Total point value: 40
1. (5 points) Suppose we are interested in estimating the effect of the â€œCash for Clunkersâ€ (CFC) program on monthly sales of automobiles in the U.S., in billions of dollars (CARSALES). We estimate a distributed lag regression model with a two-order lag, where CFCt is a dummy variable that is equal to one if the program is in effect in month t and zero if not:
a. We estimate Î±0, Î±1, Î±2 and Î±3 to be 1.0, 0.4, -0.3 and 0.0, respectively. What is the estimated effect of ...view middle of the document...
You have a sample of 1000 people, and you know how much money they give to charity and whether they are a) Catholic, b) Protestant, c) Jewish, or d) some other religion. Everyone belongs to one and only one category.
a. Write down a regression model for the purpose (3 points)
OK, there are several different regression models that you could write out here. Here is an example of one: Charity_giving = Î²0 + Î²1Protestant + Î²2Catholic + Î²3Jewish + u
b. Write down the following null hypotheses in terms of the regression coefficients in (a), being as specific as possible (1 point each):
(i) Protestants and Catholics give the same amount to charity, on average.
If you wrote down the model in (a), then the answer is: H0: Î²1 = Î²2
(ii) Protestants, Catholics, and Jews give the same amount to charity, on average.
H0: Î²1 = Î²2= Î²3
(iii) People of all religions give the same amount to charity, on average.
H0: Î²1 = Î²2= Î²3 = 0
3. (6 points) Short answer and true or false.
a. True or false: as long as we have access to a valid instrumental variable Z, instrumental variables estimates of the slope of a regression are both unbiased and consistent. (2 points)
False. Even if we have access to a valid (or even a PERFECT) instrumental variable, an instrumental variables estimate of the slope is in general biased. It will be consistent, though.
b. You run a simple regression with one X variable and get an r-squared of 0.2. You decide to rerun the regression, adding another X variable so that you have two Xâ€™s in total. The r-squared does not change. What does that tell us about the slope on the variable that we added? (2 points)
It tells us that the additional variable doesnâ€™t explain any of the variation in Y, which means that its slope is zero.
c. You plan to estimate the following regression to estimate the effect of a variable X on Y:
Y = (0 + (1X + u
How would you change your specification if you believed that the effect of X on Y changed depending on the value of X? In other words, what would you do if you thought the relationship between X and the average of Y was a curve rather than a straight line (HINT: you would estimate a multiple regression â€“ write down what it would be)? (2 points)
You would be estimating a quadratic regression model:
Y = (0 + (1X + (2X2 +u
You could have also written down other examples of a regression with a nonlinear function of X, such as Y = (0 + (1X + (2log(X) +u
4. (14 points) A number of studies have tried to measure whether private high schools do a better job of educating students than public high schools by comparing the performance of students who go to private and public schools. For example, one study examined whether going to private high school affected the probability that a student attends college. In the sample, each student either went to a private or a public high...