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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)