Problems - Ch4

Download the data for Tying Odysseus to the Mast (Google Sheets - dta file). Think of the treatment assignment as an instrument.

1. Does the treatment assignment satisfy the assumptions of an instrumental variables?

2. Calculate the IV estimator of the ATE and the LATE.

3. Calculate the Manski bounds of the ATE. Determine the natural bounds, bounds with level-set restrictions and bounds with a monotonicity assumption. Explain your assumptions.

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: Data (Google Sheets)

1. Split the observations into two groups:

   1. Received 12 or few years of education prior to 1976

   2. Received 13 or more years of education prior to 1976

2. For the two groups in (a) calculate the proportion in each group and average log wages in 1976.

3. If we are interested in the average treatment effect of receiving 13 or more years of education, why can’t we simply use the difference between the two averages calculated in (b). Under what assumption would that be appropriate?

4. Using the minimum and maximum values for the log wages in 1976 in the data, determine the bounds on the average treatment effect (discussed in (c)) under the following assumptions:

   1. No (additional) assumptions

   2. Revealed preference (individuals choose the education level that gives them the highest expected income)

   3. Monotonicity (attending college leads to higher income than only attending high school).

A policy maker wants to introduce a scheme where each person aged 17 to 24 gets $3,000 per year to attend a 4-year college full-time for a maximum of 4 years. Write a brief (one paragraph) summary of the research on the economic benefit of such a policy based on Card (1993) and your own analysis of the data.