Use the data in PRISON.DTA to answer the following questions. Refer to Example 16.8. In the data set, variables beginning with “g” are growth rates from one year to the next, obtained as the changes in the natural log. For example, gcriv_it = log(criv_it) – log(crivi,_t–1). Variables beginning with “c” are changes in levels from one year to the next, for example, cunem_it = unem_it – unemi,_t–1.
(i) Estimate the equation

by OLS and verify that you obtain α̂₁ = – 0.181 (se = .048). The parameters e_t are to remind you to include year dummies for 1981 through 1993.
(ii) Estimate the reduced form equation for gprisit, where final1_it and final2_it are the instruments:

Verify that γ₁ and γ₂ are both negative. Are they each statistically significant? What is the F statistic for H₀: γ₁ = γ₂ = 0? (Remember again to put in a full set of year dummies.)
(iii) Obain the 2SLS estimates of the equation in part (i), using final1_it and final2_it as instruments for gprisit. Verify that you obtain α̂ = – 21.032 (se = .370).
(iv) If you have access to econometrics software that computes standard errors robust to heteroskedasticity and serial correlation, obtain them for the 2SLS estimate in part (iii). What happens to the standard error of α̂₁?
(v) Reestimate the reduced form in part (ii) using the differences, Δfinal1_it and Δfinal2_it, as the instruments. (You will lose 1980 in differencing the instruments.) Do Δfinal1_it and Δfinal2_it seem like sufficiently strong instruments for gprisit? In particular, do you prefer using the differences or levels as the IVS? Estimate the reduced form in part (ii) dropping 1980 to be sure that you reach your conclusion on instrument strength using the same set of data.

Transcribed Image Text:

gcriv = É, + a,8pris + Bigincpc + B2gpolpc + B;cag0_14 + B.cag15_17 + Bscag18_24 + B6cag25_34 + B;cunem, + Bscblack; + Bocmetron + Au