Hello, Statalist!
In short, does -ivregress- (or -reg3-) include what I think is called
the Wald estimator? If so, how can I implement it for a problem like
the one below? I've searched for a command for the Wald estimator,
but can only find references to Wald _tests_.
I am considering a model similar to Ashenfelter and Greenstone (2004)
with two reduced-form equations, the estimates of which are used to
find an instrumental variable estimator in a third equation, the one
of primary interest.
My question is, how can I do this in Stata in one fell swoop?
The two equations are
F = lambda_F*VMT + PI_F*1(65mph limit in force) + epsilon
H = lambda_H*VMT + PI_H*1(65mph limit in force) + epsilon'
where 1(.) is an indicator variable which I'll call "65mph" below.
The equation of interest is
H = beta*VMT + theta*F + nu
The parameter of interest is theta. From the estimate of the reduced
form equations the IV for theta, theta_IV, is
theta_IV = (PI_H)/(PI_F)
Given estimates of PI_H and PI_F (as presented in the paper), one can
form the corresponding theta_IV. It seems that the authors use a
formula for the standard error of theta_IV like the following:
se_theta = theta_IV*sqrt((se_PI_H/PI_H)^2 + (se_PI_F/PI_F)^2)
I tried doing this in the following ways, but the results are not the
same. I wouldn't expect them to be, but I can't find a reference for
Wald estimator in Stata, so I thought I'd try it.
Method 1:
. reg F VMT 65mph
. reg H VMT 65mph
Calculate theta_IV from coefficients on 65mph in the above equations.
Method 2:
. ivregress 2sls H VMT (F 65mph)
Hope that theta_IV would be the coefficient on F.
Method 3:
. reg3 (F VMT 65mph) (H VMT F)
Hope that theta_IV would be the coefficient on F in the equation for H.
What is the correct way to get this ratio of coefficients (theta_IV =
(PI_H)/(PI_F)) and its standard error all at once in Stata?
Thanks,
Misha
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