Highlights
Instructions
• You have until 11:59pm EST to complete this exam and submit your solutions on Canvas.
• There are six problems. Each problem is worth 10 points. Only 5 problems will count towards your score for the exam. The problem that receives the lowest score will not count. Thus, the exam is worth 50 points.
• To facilitate submission and grading, 6 separate “assignments” are created and opened on Canvas. So, you should prepare a separate solution for each problem you want to submit as a single file.
• Be mindful about potential technical difficulties and submit your solutions during the day as frequently as possible. Only the last submitted version before the deadline will be graded.
• If you plan to take pictures of your handwritten solutions, please use a scanning program/ap- plication to minimize the size of the file and to improve the readability of your text.
• If the question involves running code, submit both (1) a single pdf with your responses to the question and (2) an R file with the code. The pdf should include both your response to the questions as well as any output from the code that is used as a solution to the question. The code should be able to be run on any computer. Make sure your pdf submission is consistent with the submitted .R file. Any answer that you want to be graded has to be in the pdf file; the .R file will only be used to replicate your answers.
• Submissions received after the deadline (even one minute late!) will not be graded. Make sure that you submit your initial version at least two hours before the deadline. Do not delay until the last hour! You can always re-upload another version if necessary.
• To obtain full credit, make sure to explain and justify your answers. In the calculations, please keep at least two significant digits.
• The exam is open book. You may use any reference you want both offline and online, except for asking other people. You cannot share the exam problems or your solutions with anyone else; nor can you post them online. If you find an identical problem posted somewhere with a solution, you may just copy the solution. If it’s correct, you will receive full credit as long as you disclose the source properly.
• No clarifying questions are allowed during the exam! If you believe that a problem is am- biguous, state so explicitly, and use the most reasonable interpretation possible.
Problem 1 (10 points)
Your Uncle gave you a proprietary data set that records the wind direction and speed for any place in the United States for every half-an-hour period from January 1, 2010 to December 31, 2019. You want to use these data to construct an instrument that can answer an interesting economic question that involves causality. You need to describe your research project, including additional data you may want to use. Specifically:
1. Define the economic question you want to address. Make sure your question contains a question mark.
2. Define the unit of observation (i.e. if your data are cross-sectional, define i; if your data are a time series, define t, if your data are panel, define both i and t.)
3. Define the outcome variable yit. (This notation implies that your data are panel, but that does not need to be the case).
4. Define the key regressor of interest xit.
5. Define control variables wit.
6. Describe possible unobservable factors that will be picked up by uit.
7. Define the main estimated equation/model.
8. Explain why your regressor xit is likely to be endogenous.
9. Explain why your instrument zit is likely to be exogenous.
10. Explain why your instrument zit is likely to be relevant.
Problem 2 (10 points)
The following code in R was written to illustrate the phenomenon of weak instruments discussed in section 12.3. Unfortunately, the code has blanks ( ).
1. (6 points) Fill in the eight blanks so that the code achieves its intended purpose.
2. (1 points) Run your code and record the output.
3. (3 points) Briefly explain why the two numbers that your code generates illustrate the phenomenon of weak instruments.
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