Question

7. Difference in difference analysis. Suppose we are interested in the effect of changing worker compensation laws, specifically, the effect of raising the cap on weekly earnings that are covered by workers' compensation. An increase in the cap would have no effect on low earners, but may have an effect on high earners (it would presumably make it less costly for a high earner to take more time off after an injury). Suppose we estimate the following log(durat)- 1.126+.0077 afchnge +256 highearn (0.031) 0447) +191 afchnge highearn 047) 069) -5,626, R-021 (i)Explain the effect of the policy (the coefficient on afchnge highearn, also known as the average treatment effect) (ii)Next, suppose we drop afchnge from the equation, and estimate the following logídurat)- 1.129+.253 highearn +.198 afchnge-highearn (0.022) (042) -5,626, R2-021. (052) Is it surprising that the estimate on the interaction is fairly close to the original? Explain. Next, suppose we drop highearn (but keep afchnge), and the result is logídurat)- 1.233 .100 afchnge +447 afchnge-highearn (0.023) (.040) n-5,626, R2-016. (050) (ii) Why is the coefficient on the interaction term now so much larger than before?

Answer 1

modenee dperdcnt varialie dura4 inderenden varvicLle ir afchange, highearsh tex (afchrye * high eorn) + aFchnge higheon)

al,、 in(neases. henv here effed is rorih'e equahan and ehmatr the followinj yer, here happen tha the eshmare on e

here afthnge deendpen nighenfr botih s aFharge) and

aftharge value m* derendu upon highearoh +-· is charged