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st: Generating Murphy-Topel standard errors in Stata

From   "Breanna Pellegrini" <[email protected]>
To   <[email protected]>
Subject   st: Generating Murphy-Topel standard errors in Stata
Date   Wed, 14 Sep 2011 11:08:40 +1000

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" ( 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 Pellegrini
School of Economics, Finance and Marketing

RMIT University
379-405 Russell Street
Melbourne VIC 3000 Australia

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