Problem Set 4
ECO3121 - Fall 2023
December 4, 2023
Due 8am, 12/15/2023

Question 1

Suppose the researcher has data for Cropit and Xit; but he does not have data on Zit:

1. (8 points) Suppose the researcher knows that Zit = Zt during this period, i.e., Zit is the same for all land parcels but changes over time. Give an example for what Zt is modeling. Explain how the researcher should estimate with the data set he currently has.

2. (8 points) Suppose the researcher knows that Zit = Zi during this period, i.e., Zit is the same for all years but changes over land parcels. Give an example for what Zi is modeling. Explain how the researcher should estimate with the data set he currently has.

Question 2

regression. Let Yi 0 and Yi 1 denote the crop in location i before and after the attack. Let Di be a dummy variable that takes the value 1 if land parcel i is in Gansu province, 0 otherwise. We would like to estimate the treatment effect of the fertilizer usage on crop yield with the difference-in-difference estimator.

1. (6 points) Write down this difference-in-difference estimator as a function of {Yi 0 , Yi 1 , Di} for i = 1, ..., n.

2. (6 points) What is the key assumption for this estimator to be an unbiased estimator of the treatment effect?

Question 3

We are going to replicate a study conducted by Card and Krueger in 1994 that investigate the relationship between a rise in minimum wage and employment.

Economic theories have long suggested that increases in the minimum wage lead to a reduction in the employment for at least two reasons: Businesses are less likely to hire and will rather invest in other resources that are now cheaper because of wage increase. Higher salaries will induce businesses to raise their prices to compensate their greater costs; as prices increase, we expect fewer buyers, which will lead to lower demand and employment.

These theories have found mixed support but the discussion is still very much open within the policy world, as states discuss the opportunity to rise their minimum wage to help local populations to face increasing living costs. Discussions are currently occuring in New Jersey and Illinois to raise the minimum wage to 15$/hour (New york has successfully passed this same raise in 2018).

One of the first study looking at this policy problem was Card and Krueger’s. They applied a difference-in-difference the design to look at two groups of fast-food restaurants: fast-food restaurants in New Jersey where the minimum wage increased from 4.25$ to 5.05$ per hour (treatment group) AND fast-food restaurants in Pennsylvania where the minimum wage did not increase (control group). They collected employment data before and after the minimum wage was approved.

Table 1: Variable Description

1. Explain why comparing New Jersey vs. PA after the change in the minimum wage may not be a good estimation for the treatment effect. (1)

2. What is the regression model you’d like to estimate? (1 point)

3. What is the key assumption of the estimation method you use? (1 point)

4. The data is in the blackboard (bb) Assignment 4 file folder titled DID Example.csv, and the variables are defined as in Table 1. Run the regression model you proposed in 2. and report the regression results. (Please include control variables that you think necessary) (2 point)