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

 From Misha Spisok To statalist@hsphsun2.harvard.edu Subject Re: st: How to implement Wald estimator (for IV that is a ratio of coefficients)? Date Sat, 10 Oct 2009 12:44:29 -0700

```Stas,

Many thanks (большое спасибо), not just for solving this problem but
introducing me to another command in Stata.

Misha

On Fri, Oct 9, 2009 at 9:39 PM, Stas Kolenikov <skolenik@gmail.com> wrote:
> 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
>> *
>> *   For searches and help try:
>> *   http://www.stata.com/help.cgi?search
>> *   http://www.stata.com/support/statalist/faq
>> *   http://www.ats.ucla.edu/stat/stata/
>>
>
>
>
> --
> Stas Kolenikov, also found at http://stas.kolenikov.name
> Small print: I use this email account for mailing lists only.
>
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/
>

*
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```