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Re: st: How to implement Wald estimator (for IV that is a ratio of coefficients)?


From   Stas Kolenikov <skolenik@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: How to implement Wald estimator (for IV that is a ratio of coefficients)?
Date   Fri, 9 Oct 2009 23:39:20 -0500

See if you can get your standard error via -nlcom- after -reg3-. I
would guess that's the most appropriate estimation method, and -nlcom-
is certainly the most appropriate method to deal with the
delta-method, Stata way.

On Fri, Oct 9, 2009 at 8:21 PM, Misha Spisok <misha.spisok@gmail.com> wrote:
> 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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>



-- 
Stas Kolenikov, also found at http://stas.kolenikov.name
Small print: I use this email account for mailing lists only.

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