Problem Set 3

Assignment 3 Instructions 1. Create a single Rmd file to answer all the following questions, and make the output a PDF file. 2. Ensure that your name is on the top of your generated PDF file. 3. Make your document readable, with comments for the code, and titles for the output. This is especially important for cases where your answer may be incorrect -- you may still earn partial credit if your code is understandable. 4. Submit both the Rmd file and the rendered PDF file. Name the RMD file "firstname lastname.rmd’ and analogously for the PDF file. 5. Upload your files to Quercus no later than 17:00 PM EST on Oct 24, 2023. 6. Total points: 10. Marks for each question are listed in the square brackets. Question 1 We use the following model to study whether campaign expenditures affect election outcomes: voteA = By + [, log(expendA) + B, log(expendB) + u voteA is the percentage of the vote received by candidate A, and expendA and expendB are campaign expenditures by Candidates A and B. a. [0.5] How to interpret ;7 [0.5] Use data ‘votel’ to estimate the above multiple linear regression model. [0.5] State the assumptions required to guarantee that the estimation in b. for f; is unbiased. [0.5] Propose one omitted variable that can bias the OLS estimation of 5; in b. Explain why it would bias the estimation. [0.5] Is the omitted variable expected to bias the estimation of 8, in b. upward, downward, or unclear? Explain why. For the rest of the questions, we assume that Assumption MLR1-MLR6 hold. We aim to use the estimation results in b. to study if candidate A’s campaign expenditures affect her voting outcome or not. [1] State the null hypothesis and the alternative hypothesis. [1] We choose 1% as the significance level. Use the t-statistic for §; to conduct a two-tailed t-test. Is the null hypothesis stated in f. rejected or not? [1] Now we choose 10% as the significance level. Use the t-statistic for f; to conduct a two- tailed t-test. Is the null hypothesis stated in f. rejected or not?