Getting Kinky on Valentine's Day

We all know and love regression discontinuity (RD) designs. We use these to estimate the impact of a policy by comparing outcomes for people just below and just above a policy cutoff. Look here for some RD porn. Well now, there's a "kinkier" version of this becoming more and more popular: the regression kink design (RKD). A really nice description is available here, but let me quote the basic idea:

"The regression discontinuity design exploits a jump or discontinuity in the likelihood of being treated at some threshold point. In the RKD design, there is instead a change in slope at the likelihood of being treated at a kink point, resulting in a discontinuity in the first-derivative of the assignment function...For example, Simonsen et al. (2015) use a kink in the Danish government’s prescription drug reimbursement schedule: the subsidy is based on the total prescription costs the individual has paid during the year – there is 0% subsidy for the first 500 DKK in expenses, then 50% subsidy once you have paid 500 up until you have paid 1200, then 75% subsidy, and eventually an 80% subsidy for expenses above 2800 DKK. The result is that the share of the price paid out of pocket kinks as shown in Figure 1:


Figure 1: Y-axis is the share of the price paid out of pocket. It falls as one approaches 500 DKK since if you have spent 480 and buy something for 50, you get 0% subsidy on 20 DKK and then 50% subsidy on the 30 DKK that is expenditure past the threshold."


I have seen this strategy used for estimating the impact of unemployment insurance payments in the US as well. I'm sure there are many other public policies that can be analyzed using RKD. In honor of Valentine's Day, I suggest you go off to find them!  ;)