This question extends the analysis of Exercise 7.10. Read the introduction to that exercise if you have not done so. Each city in the sample may have unique, unobservable characteristics that affect LNPRICE and LNUNITS. Following the discussion in Section 7.5.6, use the differenced data to control for these unobserved effects.

(a) Regress DLNPRICE and DLNUNITS on IZLAW. Compare the estimate of the treatment effect to those from the differences-in-differences regression of LNPRICE and LNUNITS on the explanatory variables D, the indicator variable for year 2000; IZLAW, and the interaction of D and IZLAW.

(b)^Explain, algebraically, why the outcome in

(a) occurs.

(c) To the regression in

(a) add the variable DLMEDHHINC. Interpret the estimate of this new variable, including its sign and significance. How does the addition affect the estimates of the treatment effect?