### Part A (Theory)

(i) Solve one of questions 1–5 in Lecture 4 (PDF). (ii) Solve question 1 in Lecture 5.

### Part B. (Empirics)

(i) Solve question 6 from Lecture 4. (ii) Solve question 2 from Lecture 5 (PDF). You may consult the R code included (but do not copy it), it relies on the GMM package. If you are using Stata, there is a GMM command there with good documentation and there is also a bs command (no kidding) also called bstrap and bootstrap.

### Part C (Bonus and Make-up Problems)

Solve problem 5 in Lecture 4 or problems 3 or 4 or both in Lecture 5. For each one of the problems you solve correctly, we will increase the previous homework grades up by 2 brackets. For example, if you earned a check- on a homework question in one the previous or current homeworks, and you solve 1 bonus problem correctly, that check- gets converted to check+. If you did an okay job on 1 problem, we will bump you up one grade bracket (1 +) for trying. If you solve all 3 problems correctly, you can earn as much as 6 + increments to grades on the previous or current HWs.

Reminder: The best 3–4 performing students in the class will get prizes from Victor in the form of books! You can get either the Van der Vaart book on Asymptotic Statistics, the Imbens Rubin book on Causal Inference, or Pearl’s book on Causality.

Rules: Solutions should preferably be submitted as pdf documents prepared in latex and the code should be submitted as .zip file. Please provide detailed write-ups: explain theoretical foundations of your analysis and provide step-by-step explanation for your empirical analysis. Think that you are writing an empirical portion of your paper and you are trying to communicate the results to your colleagues and referees. You can work in groups to discuss the homework, but all the write-ups and all the coding should be individual.

#### Associated Files

R-code for BS Examples in Lecture 5 (R)