econometrics3

This exercise is based on the paper \Does Prison Harden Inmates? A Discontinuity-based Approach" by Chen and Shapiro (just in case you are interested, you don't need to read it...). Convicted criminals are sentenced to prison-time, where prison sentences are in months. Prisoners with sentences of at least 2 years are put into high-security prisons. There are arguments that the harsh security protocols and the exposure to tough felons will actually increase recidivism of those who otherwise might have been rehabilitated. The probability of committing another crime after being released from prison depends on your previous prison sentence, and on whether you were in a high-security prison. In particular, let the probability of recidivism for low-security prison-inmates be given by Plow = 0:2 + 0:004  sentence and for high-security prison-inmates by Phigh = 0:2 + 0:006  sentence where sentence is in months. Note that Phigh for sentences of less than 2 years is hypothetical and so is Plow for sentences of two years or more. The distribution function of prison sentences is uniform between 0 and 10 years. (a) Describe how you would implement a regression discontinuity estimation. In particular, write down the equation that you would estimate, and write down the coecients that you would nd. (10 marks) (b) What is the \average treatment eect" of being in a high-security prison? (5 marks) (c) What is the eect you will get in a regression discontinuity design? Interpret this coecient. (5 marks) (d) Now assume Plow = 0:2 + 0:00005  sentence^2 and Phigh = 0:2 + 0:0001  sentence^2 What is the average treatment eect now? (10 marks)