Dear Stata list members,

I want to analyze a model using Lewbel's (2012) method of internal instruments for identification, because I am not aware of valid external instruments.

Let Y1 and Y2 be the endogenous variables and X a set of strictly exogenous variables.

Y1it = \alpha1 + Xit'\beta1 + Y2it\gamma1 + u1it
Y2it = \alpha2 + Xit'\beta2 + Y1it\gamma2 + u2it

I roughly understand the intuition behind Lewbels method (where heteroskedasticity in the errors is used to construct internal instruments) but I am not sure

(1) if I can apply it in a context of repeated measures : Assume that I have repeated measures of Y1, Y2 and X, with some of the X not varying over time.
Can I ignore the panel structure of the data for identification when the elements of X are strictly exogeneous? Is it sufficient if I only invoke the cluster(id) option to account for the panel structure of the data when standard errors are computed?

(2) how I instruct Stata to estimate parameters of a set of fully simultaneous equations, instead of a single equation model with an endogenous RHS variable, or is the method independent of the (true) value of \gamma2?
Will the following commandline produce the estimate of \gamma1 irrespective of \gamma2 equalling zero or not?
Code:


ivreg2h Y1 X (Y2=), cluster(id)




And the following commandline will produce the estimate of \gamma2 in the the system of simultaneous equations?




Code:




ivreg2h Y2 X (Y1=), cluster(id)



Thank you very much for your kind help!



Susanne