Demand curves slope down but we'd still like to know how steeply they do slope down. Reading this article about Senior Citizen quality of life in New York City got me thinking.
Suppose an ambitious graduate student surveyed a representative sample of 64 year olds about their consumption and transportation choices. To make the problem simple, suppose that everyone in the sample works and doesn't plan to retire in the next couple of years. At age 65, you can start to qualify for the "Senior Discount" on public transit (here are some facts about the subsidy). So, the graduate student who can trace the same people over time as they age will have "exogenous price variation" in goods ranging from McDonalds' coffee to public transit and can study whether people purchase more public transit rides as the price falls (by conducting a before/after comparison).
Now, the discontinuity here is that age is increasing continuously but there is a negative "jump" in prices because of the start of the Senior Discount. I do realize that different senior discounts start at different ages but this can be accounted for.
The only confounding factor is if people retire at the same time that they qualify for the Senior Discount. In this case, we do not have an "all else equal" condition. A 65 year old who is retired now faces lower prices for coffee and public transit AND has more free time because she is not working. To keep this experiment simple, we would want to focus on people who do not retire at 65 and argue that we can abstract away from issues of "self-selection". So we could focus on people who don't work in their 60s and people who always work in their 60s and estimate the demand curves for these two subsets using the exogenous price variation brought about by the "Senior Discount".
Has this brilliant paper already been written? My quick google search suggests "no". Serious economists have asked what is the CPI inflation trends that seniors face (see this ). But, this economist is aggregating many different prices. I'm interested in using person level panel data to estimate how quantity consumed changes as price per unit exogenously falls. My regression would have person fixed effects and calendar year/month fixed effects and identify the price effect from the introduction of the Senior Discount.