Marginal effect for a recursive mutlivariate Probit

[Grazia Cecere]

Dear Statalist,

I compute the marginal effect of a recursive trivariate probit. To evaluate the program, i first estimate a recursive Bivariate probit using both command biprobit and mvprobit using Stata 14.1.

I would like to compute the marginal effect of P(Y1=1,Y2=1) or P(Y1=0,Y2=1)
After reading the Stata Journal article written by Cappellari/Jenkins 2003 and 2006 where they develop the mvprobit, I compute the marginal effect as follow :

 biprobit (Y1= Y2 X1 X2 i.X3 i.X4) (Y2 =  X1 X2 i.X3 i.X4)

 margins, dydx(*) predict(p11) force

1) I do not know if this method considers the endogeneity of the Y2.

2) I compute the margin my self using this program :

 mvprobit (Y1= Y2 X1 X2 X3 X4) (Y2 =  X1 X2 X3 X4)

scalar d22=sqrt(1 -(e(rho21))^2)
// Cholesky matrix

mat D=(1, 0 \e(rho21),d22)

I compute first for dummy variable, by compute the "predict" with X3=0 then "predict" with X3=1. I see the difference.

  local Dummy "Y2 X3 X4 "

foreach X of local Dummy {
        quietly{
        preserve
        gen double k1=1
        gen double k2=1
        replace `X'=0
        mvppred xb_ref, xb        
        mdraws, dr(700) neq(2) prefix(z) random seed(123456789) antithetics replace
        egen mv_ref= mvnp(xb_ref1 xb_ref2) , chol(D) draws(700) prefix(z) signs(k1 k2) adoonly
        replace `X'= 1
        mvppred xb_`X', xb 
        egen mv_`X'= mvnp(xb_`X'1 xb_`X'2) , chol(D) draws(700) prefix(z) signs(k1 k2) adoonly
        generate ME_`X'=mv_`X'-mv_ref 
        }
        sum ME_`X'
        restore
        }

Then I compute for Continuous variable by adding the (standard deviation)/1000 which is the method used by Cameron, A. Colin, and Pravin K. Trivedi (2010), Microeconometrics Using Stata, Revised Edition, Stata Press, College Station, TX USA (http://www.stata-press.com/books/mic...metrics-stata/)

 local Continuous "X1 X2"

mvppred xb_refc, xb
gen double k1=1
gen double k2=1
mdraws, dr(700) neq(2) prefix(z) random seed(123456789) antithetics replace
egen mv_ref= mvnp(xb_refc1 xb_refc2) , chol(D) draws(700) prefix(z) signs(k1 k2) adoonly

    foreach X of local Continuous {
    quietly{
    preserve
    sum `X'
    gen delta_`X'=r(sd)/1000
    replace `X'=`X' + delta_`X'
    mvppred xb_`X', xb
    egen mv_`X'= mvnp(xb_`X'1 xb_`X'2) , chol(D) draws(700) prefix(z) signs(k1 k2) adoonly
    gen ME_`X'=(mv_`X'- mv_ref)/delta_`X'
    }
    sum ME_`X'
    restore
}
drop xb_refc1 xb_refc2 mv_ref k1 k2
drop z1_1-z1_1400 z2_1-z2_1400

The coefficient of the margins written with my program are very different compared to the one estimated by default with the Stata margins command.

My last question, i would like also to compute the marginal effects after having estimate a recursive trivariate probit using the command mvprobit, i don't see why it will be an issue.

 mvprobit (Y1=  Y3 X1 X2 X3 X4) (Y2 = Y3 X1 X2 X3 X4) (Y3 =  X1 X2 X3 X4)

Thank you very much for your advice

Grazia

[Carlo Lazzaro]

Grazia:
sorry, wrong forum.
As per FAQ, please re-post your query on the General forrum. Thanks.