2.) Suppose an employer announces a policy that offers a free gym membership to all their workers over 220 lbs in a bid to improve worker productivity. You decide to use a regression discontinuity approach to see if gym membership makes people more, or less productive at work.

a.) For this example define what is/are the: running variable, the outcome variable, the threshold. Describe in rough terms how you would estimate the treatment effect using a regression discontinuity design. Please draw a picture to complement your explanation.

b.) Explain how self-sorting or manipulation around the threshold could invalidate your attempt to get the causal relationship?

c.) Why wouldn't this be a problem if workers don't know the policy is coming until the moment they step on a scale at work?

d.) Suppose no one tells the workers, but you are suspicious that there might be a snitch in the workplace who told some of the workers. How could you check for evidence of self-sorting? Draw a picture where things look good, and a picture where things look kinda bad.

e.) What would be meant by the bandwidth in this specifc example?

f.) What's the key assumption made when doing an RD? What does it mean in this specifc

example?

g.) If all goes well we will uncover a local average treatment effect. What's local about the answer? What does average imply here?