Question

A researcher wants to investigate why some individuals released from prison on parole reoffend whereas others do not. As a starting point, the researcher considers the following probit model: Pr(??=1)=Φ(?0+?1??+?2ln??⁡+?3(??×ln??)), (2.1) where Φ denotes the standard normal cumulative distribution function, ln denotes the natural log and: ??=1 if paroled individual ? reoffends within three years of being paroled (0 otherwise); ??=1 if individual ? is male (0 otherwise); ?? is the number of years since individual ? was paroled. The above model was estimated using data on a sample of convicted individuals who were recently released from prison on parole, whose reoffending behavior was subsequently monitored. The (rounded) parameter estimates obtained (with standard errors in brackets) were ?̂0=0.00 (0.12), ?̂1=0.7 (0.02), ?̂2=−0.5 (0.07),⁡?̂3=−0.5 (0.10). (a) Robin Banks was paroled a year ago. What is his estimated probability of reoffending? (b) Emma Besler (everyone calls her ‘Em’) has an estimated probability of reoffending of 50%. How long ago was she paroled? (c) Based on a hypothesis test at the 5% significance level, could Em’s probability of reoffending be as high as 60%? (d) Estimate the number of years a man must be on parole to be equally likely to re-offend as a woman paroled 12 months ago.

Answer 1