multivariate probit model using CMP code

[Qiuzhen Ren]

Dear Statalisters,

My research is to explore the impact of policy instruments on innovation. The data I used is cross-section data, including 7521 observations in EU 28 countries. One of the models I used is the multivariate probit model. Here, the y1-y5 are five dependent variables. All of them are dummy variables. For example, y1 = 1, if the firms undertake y1 innovation activity; otherwise, 0. Variable policy is the independent variable, Z is the covariates.

I take Prof. David Aristei's paper as reference which presents " The Maximum simulated likelihood estimation procedure is based on the Geweke-Hajivassiliou-Keane(GHK) multivariate normal simulator, with 200 random draws for each observation. Estimation has been carried out using the Stata CMP developed by Roodman" .

I run the cmp command with option ghkdraws(300), but the results do not contain the correlations (rho value) between the error terms across the five equations.

 local x " policy Z i.country "  // here, control the fixed effect at country level
cmp (y1=  `x') (y2 = `x') ( y3= `x')( y4=`x3')( y5=`x3'), ind(6 6 6 6 6)  ghkdraws(300) cluster(country) 
Fitting full model.
Likelihoods for 7521 observations involve cumulative normal distributions above dimension 2.
Using ghk2() to simulate them. Settings:
    Sequence type = halton
    Number of draws per observation = 300
    Include antithetic draws = no
    Scramble = no
    Prime bases = 2 3 5 7
Each observation gets different draws, so changing the order of observations in the data set would
>  change the results.

The STATA version I used is Stata 15. Could you help me to check and correct my STATA command. And how to estimate the marginal effect of multivariate probit model furtherly? Thank you.

Qiuzhen Ren

[David Roodman]

You should probably look at the section in the help file about mprobit models and the mprobit examples down at the bottom, and run them. There are two syntaxes. In the alternative-specific syntax, you need an extra pair of parentheses around those 8's. And you need alternative-specific regressors. It can be a problem if two choices have the same regressor set. In the other syntax, you would have a single 8, and single equation specification, and probably the iia option inside the equation.

[Qiuzhen Ren]

You should probably look at the section in the help file about mprobit models and the mprobit examples down at the bottom, and run them. There are two syntaxes. In the alternative-specific syntax, you need an extra pair of parentheses around those 8's. And you need alternative-specific regressors. It can be a problem if two choices have the same regressor set. In the other syntax, you would have a single 8, and single equation specification, and probably the iia option inside the equation.

@David Roodman Thanks for your help. It is very useful. I looked at the section and example of mprobit part. I found the problem. My case is not the alternative-specific, since the regressors are same for those five equations. I estimate 5-probit equation probit models. I should use the $cmp_probit(4) in the ind option rather than the $cmp_mprobit(6). After running the following command, I got the rho value . Thank you.

 
 cmp (y1=  `x') (y2 = `x') ( y3= `x')( y4=`x3')( y5=`x3'), indicators(4 4 4 4 4) ghkanti ghkdraws(200) ghktype(hammersley) nodrop structural technique(dfp nr) nrtolerance(1e-4) cluster(country)