Problems - Ch2

Create the following simulated data.

1. x ~ U[0,1] (uniformly distributed)

2. w ~ U[0,1] + d*x, where d = 3 (uniformly distributed between 0 and 1 + the effect of x)

3. e ~ N(0,1) (normally distributed with a variance of 1)

4. y = a + b*x + c*w + e, where a = 1, b = 0, c = -3

5. N = 50 (50 data points)

6. Run ordinary least squares on the relationship between y and x (y as a function of x). Present the estimates of b. Discuss why it is or is not close to the true value.

7. Draw the causal diagrams representing this data generating process.

8. Run ordinary least squares on the relationship between y and all of x and w. Present the estimates of b. Discuss why the it is or is not close to the true value.

9. Can you show that b must be equal to zero? Show your test.

Download the data for Mortgage Lending in Boston. Available here: HMDA data (Google Sheets)

1. Create variables for mortgage denials, race, income, credit worthiness.

2. Run ordinary least squares on the relationship between mortgage denials and race. Does this provide evidence that banks are acting illegally?

3. Using ordinary least squares can you show that there is evidence that banks are illegally denying mortgages based on race? Or that there is evidence that banks are behaving legally? Explain your method. Explain the concerns with your analysis.

Download the data for Using Geographic Variation in College Proximity to Estimate Returns to Schooling by David Card (http://www.nber.org/papers/w4483). The data is available here: http://davidcard.berkeley.edu/data_sets.html. Also available here: Google Sheets

1. Replicate Table 2 of the paper (to the extent you can with the data). Note that you need to read the paper carefully to determine the definitions of the variables.

2. How should we interpret the estimates for row (1) Education and (2) Experience?

3. What concerns should we have about these estimates for determining the value of a policy that subsidizes college?

4. Using matrix algebra create a bootstrapped estimates of column (1) of Table 2. Explain why the standard errors are the same or different from the ones presented in the paper.