I have a problem in a linear regression analogue to the difference-in-
difference method. The regression runs as the following.
Here, TZ=T*Z is the interaction term, T is the time dummy (=1 after
the policy change), and Z are the continuous endogenous treatments, X
are exogenous variables.
The instruments for Z is W and V. TW and TV are considered as
instruments for T*Z.
I am think about the following procedure:
1) predict Z from W, V, TW, TV, T, and X, denoted as Z'
2) let TZ'=T*Z'.
3) run regression of Y on Z', TZ', T, and X.
However, it seems that I cannot implement the procedure by ivreg2.
"ivreg2 Y T X (TZ Z=W V TW TV)" is doing the following procedure:
1) predict TZ from W, V, TW, TV,T, and X, denoted as (TZ)'
2) predict Z from W, V, TW, TV, T, and X, denoted as Z'
3) run regression of Y on Z', (TZ)', T, and X.
Can anyone tell me which procedure is better? Is there a
command/syntax to implement the first procedure and adjust the
standard errors at the same time.
Thank you in advance.
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