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Problem set #1

Econ 705 (2nd half)

Due: Sunday, December 3, 2023

1. In this question, you will describe how you might evaluate a hypothetical policy using difference-in-differences methods.

Imagine that in 2004, 56 cities in southern US states enacted a regulation that required annual tests for contamination of residential drinking water. You are interested in studying the effects of this policy on cognitive development in children (measured using standardized test scores), which can be impaired by drinking water contaminated with lead.

You will be asked to think about some big picture choices in the research process and some econometric details. If at any point you need to make assumptions about what structure available data will need to have, state these assumptions, and proceed accordingly.

a. You would like to use difference-in-differences methods to evaluate the effects of the water testing policy on children’s test scores. The first step is to select a group of control cities. First, describe what properties these controls cities need to satisfy for the identifying assumption of the difference-in-differences strategy to hold. Second, briefly describe a process you might follow to look for control cities with this goal in mind.

b. Now imagine you have selected a group of control cities that have never enacted water testing policies. You would like to proceed with estimating the impact of the policy. Propose an estimating equation that you could use to estimate the program’s impacts using a difference-in-differences identification strategy. The equation should have an independent variable on the leti-hand side and explanatory variables, parameters, and a residual on the right-hand side. Be sure to define any variables that you use.

c. Now write a short set of instructions for a research assistant to follow to implement this estimator. You should describe to them the structure of the data that they are using, and how to construct any variables, in addition to describing the regression you would like them to run.

d. Next, you would like to estimate how treatment effects vary over time, with the idea being that prolonged exposure to clean water might have much larger benefits than exposure to clean water for just one year. Using the same set of control cities, propose an event study estimator to estimate the impact of the policy.

e. Provide additional instructions to the same research assistant describing how to implement this event study estimator. If they need to construct new variables, describe how they should go about doing this.

f. Now you would like to create a graph illustrating the event study estimates, following the style of the graph from Bailey and Goodman-Bacon (2015) that we looked at in class. Provide brief instructions for your research assistant to follow to create this graph. The graph should include both the point estimates of the time varying treatment effect and a 95% confidence interval.

g. A useful feature of the event study is that it lets us look at pretrends, and specifically to assess whether prior to enactment of the policy the treatment groups and the control groups exhibited outcomes that were moving in parallel. Briefly describe what patern would reflect a violation of the parallel-trends assumption, and draw an example of the event-study graph where the parallel trends assumption is violated in the pre-treatment years.

h. Now imagine that atier estimating the event study, you find that the control cities that you have chosen and the treated cities, are not on parallel trends in the years prior to treatment. You would like to use propensity score reweighting to improve the comparability of the control cities to the treated cities. There are 10 observable characteristics (X1 through X10) of cities that you would like to ensure are balanced between the treatment cities and a reweighted set of control cities. Provide a brief but complete description for a research assistant to follow to construct propensity score weights that will accomplish this, and to use the weights to estimate propensity score reweighted versions of the difference-in-differences estimator and the event study estimator that you proposed in earlier questions.