RE: st: Generating Murphy-Topel standard errors in Stata

[Cameron McIntosh <cnm100@hotmail.com>]

Hi Breanna,

I think that a lot of hassle could be saved by estimating this model in -gllamm-, using numerical integration. You could estimate the whole path model (X--->Z---Y; X--->Y) with both the probit and linear links simultaneously rather than in piecemeal fashion, and correct the standard errors for clustering at the same time. I don't know how you would get a consistent estimator of the asymptotic covariance matrix of the parameter estimates by combining the Murphy-Topel and Taylor linearization methods for the clustered case. This would need to be studied. Maybe it has, I don't know, but I think just avoiding that issue with -gllamm- would be the most prudent strategy. Anyway, the model might take a little while to converge in -gllamm-... but my guess is that it would probably not be prohibitively long because you have no latent variables.
http://www.gllamm.org/  ;

My two cents,

Cam

> From: breanna.pellegrini@rmit.edu.au
> Date: Wed, 14 Sep 2011 11:08:40 +1000
> To: statalist@hsphsun2.harvard.edu
> Subject: st: Generating Murphy-Topel standard errors in Stata
> 
> Dear Statalist,
>  
> I have a two-step estimation setup where the first stage is modelled using a binary probit specification. I then use the predicted values from the first stage model as an explanatory regressor in the second stage. The second stage is estimated using a linear regression model. Since I have included a generated regressor in the second stage, the standard errors from the second stage model will need to be adjusted using the Murphy-Topel variance estimator.
>  
> The Stata Journal paper by Hole (2006) titled "Calculating Murphy-Topel variance estimates in Stata: A simplified procedure" (http://www.stata-journal.com/sjpdf.html?articlenum=st0114) provides Stata code for calculating the Murphy-Topel standard errors for a two-step model with a logit model in the first stage and then a Poisson model in the second stage. Additional code changes are also suggested for a number of variations to the model specification at both stages of estimation.
>  
> I have been able to adapt the code from Hole (2006) for my particular model setup and the code runs fine and Murphy-Topel standard errors are produced. However, specific code amendments for the situation of having a linear regression model in the second stage were not discussed in the Hole (2006) paper. So I am a little unsure as to whether I have properly amended my code for the setup of a probit model in the first stage and a linear regression model in the second stage. In particular:
> 
> 1) When calculating the score for the second stage linear regression model can I directly use the second stage code used in Hole (2006, pp. 523) and simply replace "poisson" with "regress"?
>  
> 2) Would I need to also adjust the C-matrix and R-matrix calculations to take into account the residual variance parameter in the linear regression model? Hole (2006) discusses how to account for the auxiliary (dispersion) parameter if a negative binomial model is estimated in the second stage, but how would this be done in a linear regression setup?
>  
> 3) In both stages of my estimation I am also using clustered standard errors to allow for intra-group correlation between twenty different regional sites. Are there any further code adjustments I would need to make to calculate the Murphy-Topel estimates in this case?
>  
>  
> Any guidance from those who may have previous experience in dealing with and coding the Murphy-Topel variance estimates would be greatly appreciated.
>  
>  
> Kind regards,
> Breanna
> 
> 
>  
>  
>  
> 
> Breanna Pellegrini
> School of Economics, Finance and Marketing
> 
> RMIT University
> 379-405 Russell Street
> Melbourne VIC 3000 Australia
> 
> Tel     +61 3 9925 0944
> Fax    +61 3 9925 5986
> 
> 
> 
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