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If you are interested in donations to charity--a thread on my just-published paper with Mark Wihelm
https://www.journals.uchicago.edu/doi/10.1086/713190#.YJQ-vXDvovA.twitter">https://www.journals.uchicago.edu/doi/10.10...
https://www.journals.uchicago.edu/doi/10.1086/713190#.YJQ-vXDvovA.twitter">https://www.journals.uchicago.edu/doi/10.10...
Two very common incentives when you donate are (a) tax-incentives (often a rebate), and (b) a match from a 3rd party. Both lower your price for getting $$$ to a charity.
Are matches and rebates the same? Basic theory says yes. But famous empirical work by @eckelcc and Grossman (and much follow up work) says no. Why the disconnect? No one knows.
To start in, we go back to the theory. We use a model where donors have different prefs for their own donation vs $$$ from a 3rd-party match (eg, they might get "warm glow" from former). Sounds obvious. But such models are really messy and hard to study.
We use a few tricks to make a model that is (a) tractable and (b) generates new insights about giving behavior. (See paper or DM for details on the tricks.)
If people get a "warm glow" from their own gift,
then the model says that matches and rebates *should* differ. But there& #39;s more.
then the model says that matches and rebates *should* differ. But there& #39;s more.
We show responses to matches are driven both by price elasticities and by warm glow. This means you cannot really "interpret" a match elasticity to learn about donor preferences. It is one number that combines several things.
But you can use a match and rebate together to test many standard models of giving. This leads us to part two of the paper...where we work with data.
We test models of giving using (a) a match offered in a high-stakes setting together with (b) a rebate from tax policy.
The sample is donors to a university. A subset are temporarily offered a match (up to $250k). Next, donors in Indiana get a tax credit (ie, rebate) for donations. The credit is capped at $400, so we do a bunching estimator for it.
These estimation methods are unusual for this literature and offer several technical advantages (see paper).
The match matters for donations:
And IN donors bunch at the $400 cap:
We find a match elasticity of -1.2 and a rebate elasticity of -0.3. These are close to many experimental estimates. But they differ from each other. They are also different from what the vanilla-flavored warm-glow model might predict.
Our model, which builds on warm glow, can accommodate these facts, however.
So top takeaways are: (1) rebates and matches are truly different; (2) a match response cannot be interpreted without a rebate response; and (3) if you combine them you& #39;re in business.
This is a long thread. (Thanks for reading.) The paper has a lot going on. Here are 6 final thoughts:
1. These results indicate strong external validity for papers estimating price elasticities of giving using students in labs.
2. We estimate a Hicksian price of giving--never seen that before.
3. The match we study is capped. Along with diff-diff, we can use buching for this elasticity too. We find a large elasticity; the largest bunching elasticity I& #39;ve ever seen. (Bunching is often dissed for finding small elasticities.) It matches the diff-diff estimate.
4. We develop 2 new (simple!) bunching estimators. Estimates are close to the normal method (but simpler!). We also implement a test of bunching close to what Blomquist-Newey propose. It doesn& #39;t change things.
5. I like tax-price-of-giving papers with big elasticities--I& #39;m no hater. *But*...in my view, in this literature of 1000+ papers, the papers using the best empirical methods typically get small elasticities.
6. Lots of work suggest matches are better than rebates for raising money to charities. True. But our model shows DONORS prefer rebates. Welfare analysis should consider both supply and demand.
