How to instrument two variables in one regression?

[Maryia Donnachie]

Dear All,

I have the following panal data set: outcome and independent variable for n districts and t time periods.

I would like to test whether the efffect of the independent_variable on the outcome has significuntly changed after a certain event took place at a given time t=x therefore I run the following regression:

(1) acreg outcome independent_variable independent_variable#post_dummy, id(district_nr) time(period_t) spatial latitude(lat_el) longitude(lon_el) dist(100) pfe1(period_t) pfe2(district_nr)

However, due to reverse causality, I have to instrument the independent_variable. As an instrument I use an avarage value over T periods, i.e. I do not have separate observations for each of my t periods I only have one single value for each district.
Hence, the First Stage looks like

(2) independent_variable = instrument#Dummy_t0 instrument#Dummy_t1...instrument#Dummy_tT, id(district_nr) time(period_t) spatial latitude(lat_el) longitude(lon_el) dist(100) pfe1(period_t) pfe2(district_nr).


Is there any way to instrument both independent_variable and independent_variable#post_dummy at the same time in the regression (1)?

*outcome, independent variable and instrument are all continuous variables.

I would appreciate any suggestions.

Many thanks in advance.

Kind regards,
Maryia

[Joro Kolev]

I do not understand whether this is a question about the syntax of the user written -acreg-, or about IV regression.

If about the latter, as long as you have two or more instruments, you can of course instrument two endogenous regressors.

[Maryia Donnachie]

Dear Joro,

Thank you for your reply.

The question is about IV instrument. acereg includes the ivregress 2sls function in it.

The only instrument I have is described above.

My question is how to technically correctly instrument independent_variable and independent_variable#post_dummy at the same time.

just adding ...(independent_variable independent_variable#post_dummy =instrument#Dummy_t0 instrument#Dummy_t1...instrument#Dummy_tT instrument#Dummy_tx instrument#Dummy_tx+1 ...instrument#Dummy_tT) does not make much sense to me.

Thefore I would appreciate any suggestion w.r.t the possible technical implementation.

Many thanks,
Maryia

[Joro Kolev]

Dear Joro,

Thank you for your reply.

The question is about IV instrument. acereg includes the ivregress 2sls function in it.

The only instrument I have is described above.

My question is how to technically correctly instrument independent_variable and independent_variable#post_dummy at the same time.

just adding ...(independent_variable independent_variable#post_dummy =instrument#Dummy_t0 instrument#Dummy_t1...instrument#Dummy_tT instrument#Dummy_tx instrument#Dummy_tx+1 ...instrument#Dummy_tT) does not make much sense to me.

Thefore I would appreciate any suggestion w.r.t the possible technical implementation.

Many thanks,
Maryia

It might not make sense to you, but the way you show above, this is how it is done :P.

In Two Stage Least Squares each of the endogenous regressors is a linear function of all the instruments and all of the exogenous regressors.

[Maryia Donnachie]

In this case is it not better to just add (independent_variable independent_variable#post_dummy =instrument#Dummy_t0 instrument#Dummy_t1...instrument#Dummy_tT)?

as [instrument#Dummy_tx instrument#Dummy_tx+1 ...instrument#Dummy_tT] is a subset of [instrument#Dummy_t0 instrument#Dummy_t1...instrument#Dummy_tT], i.e. I would be adding it twice otherwise.

Many thanks!