# ECO 440/640 — Problem Set 7

## (Regression discontinuity)

## Due 11:59pm April 28, 2017

Your task is to determine whether spending time with cats makes people smile more.

### Setup

Get the cat happiness data (.RData, .csv). These data are fabricated, but they represent the prejudices of your instructor.

There are many places without animal shelters nearby, so we can imagine that someone who opens a cat shelter in one location might do so simply because there are few shelters there. This decision would then lower the cost to the townsfolk of interacting with cats. Thus we would imagine that the people living near the shelter would subsequently spend more of their time around cats.

The cat happiness data contains the following information:

`WeeksSinceCatShelter`

: the number of weeks since the cat shelter opened`CatHours`

: the average number of hours in the week spent with a cat by the people in the immediate neighborhood`Smiles`

: the average number of times per day the people in the immediate neighborhood smiled during the week`Rainbows`

: the number of rainbows visible during the week within 100 miles (yes, I know that rainbows do not have a distinct location, and that this entire concept is nonsense)

### Answering the question

- Explain why a regression discontinuity design might be useful in this case. What must be true for the RD estimates to be unbiased estimates of the causal effect of cats on smiling? Identify a potential source of bias.
- Graph the relevant data and comment on whether there is evidence for the hypothesis that cats make people smile.
- Write out the models you will estimate and explain why you are using those models. How specifically will you identify the effect of
*time with cats*on smiles rather than just the effect of being near a shelter (this involves instrumental variables estimation)? - Estimate the models, report the results, and test the hypothesis.
- Perform a
*set*of “non-parametric” estimates. Show the effect of the bandwidth size on the estimates.