Suppose your conducting a randomized experiment to measure the causal effect of a new weight-loss drug called W8-B-Gon

This is an open-book exam. You may refer to whatever books, notes, etc. you deem helpful, but you may not collude or seek the help of others in any way. The work you submit must be your own.

 

There are three questions, each with multiple parts. You should answer all of them. There are a total of 100 points, and you have 24 hours to complete the exam. Good luck, and remember: econometrics is fun!

 

1. Suppose you're conducting a randomized experiment to measure the causal effect of a new weight-loss drug called W8-B-Gon. You randomly assign subjects to treatment and control groups, measure their pre-treatment weight, provide the treatment group with a six-month supply of W8-B-Gon and the control group with a placebo, and then measure their weight again at the conclusion of the six- month trial. Let 𝑦i indicate the change in subject 𝑖's weight over the course of the trial, and let 𝑇i = 1 if subject 𝑖 was part of the treatment group and zero otherwise.

 

At the conclusion of the trial, you learn that some members of your treatment group didn't follow the rules of your experiment, and sold their W8-B-Gon on the black market instead of taking the treatment. Even worse, some members of your control group bought W8-B-Gon on the black market and ended up taking the treatment! Luckily, your cousin knows someone who knows someone, and is able to find out which of your subjects actually completed the W8-B-Gon treatment, and which ones did not. From this information, you create a new variable, 𝑃i = 1 if subject 𝑖 completed the W8-B-Gon treatment, and zero otherwise.

 

a. [10 points] Suppose you estimate the regression 𝑦i = 𝛼 + 𝜓 𝑃i + 𝜂i via OLS, where 𝜂i is an error term. Does the OLS estimator 𝜓, provide a good estimate of the causal effect of W8-B- Gon on weight loss? Explain.

 

b. [10 points] Suppose you estimate the regression 𝑦i = 𝛼 + 𝜙𝑇i + 𝜈i via OLS instead, where 𝜈i is an error term. Does the OLS estimator 𝜙, provide a good estimate of the causal effect of W8-B- Gon on weight loss? Explain.

 

c. [10 points] Is there another way to use these data to obtain a good estimate of the causal effect of W8-B-Gon on weight loss? Explain.

 

2. The government of Canada recently announced a massive wage subsidy that will be paid to some Canadian employers. Employers that qualify for the subsidy will be paid up to 75 percent of each employee's wage (to a maximum of $847 per employee per week), for up to 12 weeks between March 15 and June 6 2020. To qualify for the subsidy in a given month, employers must experience a 30% year-over-year decline in monthly revenue.

 

Suppose you have data on a sample of 10,000 Canadian firms. Your data include each firm 𝑖’s total revenue in 2018, 2019, 2020, and 2021 (𝑅2#$%, 𝑅2#$&, 𝑅2#2#, 𝑅2#2$), their employment in each of those years (𝐸2#$%, 𝐸2#$&, 𝐸2#2#, 𝐸2#2$), the year-over-year percentage change in their monthly

revenue between March 15 and June 6 2020 (𝑄𝑅i), the province where each firm is located (𝑃i), the industry in which they operate (𝐼i), and a random lottery number 𝐿i assigned to each firm, where 1 ≤ 𝐿i ≤ 10.

 

a. [10 points] Is it possible to estimate the causal effect of the wage subsidy on a firm's total revenue for the year 2021 using these data? If yes, clearly explain how. What causal effect are you estimating, what assumptions does your method require, and how would you ensure that you are making valid inferences about the causal effect? If it’s not possible to measure the causal effect of the wage subsidy program, explain why not.

 

b. [10 points] Now suppose that the government is unable to keep their promise to subsidize all firms that experience a 30% decline in revenue. Instead, only some of the firms that experience a 30% decline will receive the subsidy, and the remaining firms will not. Unfortunately, you are unable to observe what factors are used to determine which of the firms experiencing a 30% decline receive the subsidy, and which ones do not. Is it possible to estimate the causal effect of the wage subsidy on a firm's total revenue for the year 2021? If yes, clearly explain how. What causal effect are you estimating, what assumptions does your method require, and how would you ensure that you are making valid inferences about the causal effect? If it’s not possible to measure the causal effect of the wage subsidy program, explain why not.

 

c. [10 points] Now suppose that in response to intense political pressure, the government eliminates the qualifying requirement that employers must experience a 30% decline in revenue. Instead, all firms that operate in a subset of industries that are deemed to have been most harmed (“harmed industries”) will receive the subsidy, and firms in all other industries (“unharmed industries”) will not. Is it possible to estimate the causal effect of the wage subsidy on a firm's total revenue for the year 2021? If yes, clearly explain how. What causal effect are you estimating, what assumptions does your method require, and how would you ensure that you are making valid inferences about the causal effect? If it’s not possible to measure the causal effect of the wage subsidy program, explain why not.

 

d. [10 points] Now suppose that for equity reasons, all firms with 𝐿i > 5 will receive the subsidy. Is it possible to estimate the causal effect of the wage subsidy on a firm's total revenue for the year 2021? If yes, clearly explain how. What causal effect are you estimating, what assumptions does your method require, and how would you ensure that you are making valid inferences about the causal effect? If it’s not possible to measure the causal effect of the wage subsidy program, explain why not.

 

e. [5 points] Which of the methods that you proposed in parts (a)-(d) do you prefer, and why?