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ci :

  • yi2 yi1wi2 wi1ui2 ui1

or

Δyi Δwi  Δui.

If EΔwiΔui0, that is, the change in treatment status is uncorrelated with changes in the idiosyncratic errors, then OLS applied to (13) is consistent. If wi1 0 for all i, the OLS estimate is

  • ̂  Δȳtreat Δȳcontrol,

which is a DD estimate except that we different the means of the same units over time. With many time periods and arbitrary treatment patterns, we can use

yit t wit xitci uit, t 1, . . . , T,

18

(12)

(13)

(14)

(15)

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