Question

You are interested in the effect of private vs. social (statutory) health insurance on health in Germany.

a.   Can you interpret the mean health difference between individuals with a private and individuals with a statutory health insurance as a causal effect of purchasing private health insurance? Why or why not?

b.   Employees can only switch from statutory health insurance to private health insurance when their annual income is above the social security ceiling (in 2015, this was 54,900 Euro). You consider to exploit this discontinuity in a regression discontinuity framework. Please define D (treatment), T (threshold), X (running variable), and Y (outcome variable). Write down the first and second stage equation.

c.    Is this a sharp or a fuzzy RD design?

Answer 1

1. For the following differences between private and statutory health insurance, private insurance is mostly preferred.

• The cost of a private insurance is measured on your personal risk which is assessed by the state of your health and the health of your direct relatives at the time you sign up for the insurance and of course by your age. Note however, if you might have concealed information, your contract will be voided and you might even get sued for fraud. At the same time, with private insurance, you will have to pay many treatments yourself and can only send in the bills after you were treated. This requires some extra work and if your insurance determines that some treatment is not covered, you will not be refunded. This is problematic since some doctors try to convince privately insured "customers" to choose extra treatments / check-ups that are not medically meaningful just to earn money. Also, private insurances are not require to insure your kids for free. Furthermore, the fees of private insurance will raise with your age, especially during your retirement. Note that if your kids are born with some sort of health condition, private insurances are allowed to ask for up to twice the amount it would normally cost to insure a child.

• The public insurance is measured on your personal income. This means that during your retirement, where you do not earn money, you will usually pay less than with private insurance. Your state of health is not considered with this insurance. The fee is however capped at some given amount, such that you will not linearly pay more with increased income. Some doctors in Germany do not treat people with public insurance but those are few since most people choose public insurance. You will not have to pay your doctors a single Euro with public insurance since bills are covered automatically by your insurance. You will get a card for this purpose that you can show your doctor. However, some treatments that are popular in Germany, like for example osteopathy are not fully covered by the public insurance but only subsidized. With public insurance, your kids are insured for free until they leave high school / college. If your spouse does not work, s/he will also be insured with you.

Doctors are by law forbidden to prefer privately insured over publicly insured, once they decide to get a license for treating publicly insured patients, even though some doctors do of course discriminate. Be aware that once you sign up for a private insurance, you will not be able to sign up for a public insurance scheme unless your income decreases under a certain barrier for a given amount of time.

• Include nonlinear functions of the assignment variable in the equation, for example:

Yi = ˆ β0 + ˆ β1d + ˆ β2 (zi − zc ) + ˆ β3 (zi − zc )2 + ei

Where d is the treatment indicator and z is the assignment variable

• There are many such nonlinear functions, so selecting the correct one is crucial

One can also add interactions between treatment assignment (d) and the assignment variable (z), for example: Yi = ˆ β0 + ˆ β1di + ˆ β2 (zi − zc ) + ˆ β3xi(zi − zc ) + e

3. Prob. of treatment receipt must be discontinuous at cutoff. More of those receiving treatment should be on treatment side of cutoff than the other side. If all are, then “sharp” RD. Otherwise, “fuzzy” RD