2. DID in a regression Suppose we have two states (1' = 1,2) and for each states we have two data points, one before the policy change and one after....

Suppose we have two states () and for each states we have two data points, one before the policy change and one after.    

2. DID in a regression Suppose we have two states (1' = 1,2) and for each states we have two data points, one before thepolicy change and one after. Let 1? denote the time and t = 1 is the ”before" period and t = 2 is the"after” period. And the policy change is limited to State 1 (i = 1). 50 State 2 is the control or benchmark. Consider the following model3’” = Ci + dt +36ibi = 1,2,1: = 1,2 where Ci is a state specific intercept. y“ ivsvthe observation at time t for state i. For example, 3112 is the observation for state 1 in the "after"period. dt isa dummy variable that is 0 for the "before" period (t = 1), 1 for the "after” period (t = 2). 5i: = lixdt where Ii is an indicator that is 1 for state 1 (i = 1) and O for state 2 (i = 2). Show that )3 is the DID estimate of the causal effect of the policy change. (hint: write down each (of thefour) terms in the DID estimate in terms of Ci, (it, 36” and then simplify)