1. Chapter Three, Exercise 1 from the textbook

2. Chapter Three, Exercise 2 from the textbook (These two exercises were posted following)

3. Take any study that we have seen in class, which uses an instrumental variable. (a) Explain why the study had to use an instrumental variable (i.e. why a simple OLS would not have been enough to establish causation). (b) Explain how the study argues why the instrument is relevant and valid.

4. Take any study that we have seen in class, which uses a regression discontinuity design. (a) Explain why a simple OLS would not have been enough to establish causation. (b) Explain how the regression discontinuity design method helped in dealing with confounders in the context of this study.

5. You may have figured out that we can think of the method of randomization as an example of using the instrumental variables technique. Let us consider an example. Suppose we want to know the effect of missing classes on a student’s final score. (a) If we just ran an OLS regression of final score on having missed classes, what would be some confounders? Would we be able to control for all of them? (b) Now suppose we did the following randomization (which would be a terrible idea to do in practice): for each student, we flip a coin. If the coin lands heads, the student has to attend all classes. If the coin lands tails, the student may only attend 50% of the classes. Can we now use the coin toss resulting in heads as an instrument for attending classes? Would it be a relevant instrument? Would it be a valid instrument?

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