Marginal effects after IVprobit is same as the IVprobit regression coefficient

[Ketan Reddy]

Dear Statalist Users,

I am hoping for some insight into the issue that I am facing.

I am using IVPROBIT command in stata and the coefficients of the regression are exactly same as that of the marginal effects.

https://www.stata.com/statalist/arch.../msg00405.html - this thread contains the issue I am facing.

I am using the following commands

ivprobit gs age foreign group tfp (xliq=l.xlq_mean) , vce(cluster id)

margins, dydx(_all) post

Could someone provide me insight into as to why the marginal effects are similar to the coefficients of IVprobit. I am using Stata 15.

[Andrew Musau]

Richard Williams already explained in the thread that you reference that the default for ivprobit is -predict(xb)- to obtain linear predictions. Note that this applies to probit and logit, i.e., the linear prediction will coincide with the estimated coefficients in these models. The only difference is that the default for probit and logit is -predict(pr)-, the probabilities.

. webuse lbw, clear
(Hosmer & Lemeshow data)

. probit low age smoke i.race

Iteration 0:   log likelihood =   -117.336  
Iteration 1:   log likelihood = -109.26071  
Iteration 2:   log likelihood = -109.21408  
Iteration 3:   log likelihood = -109.21408  

Probit regression                               Number of obs     =        189
                                                LR chi2(4)        =      16.24
                                                Prob > chi2       =     0.0027
Log likelihood = -109.21408                     Pseudo R2         =     0.0692

------------------------------------------------------------------------------
         low |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |  -.0218726   .0201108    -1.09   0.277    -.0612891    .0175439
       smoke |   .6758233   .2210635     3.06   0.002     .2425469      1.1091
             |
        race |
      black  |   .6183845   .2994882     2.06   0.039     .0313984    1.205371
      other  |   .6455825   .2401702     2.69   0.007     .1748575    1.116308
             |
       _cons |  -.6062843   .5187651    -1.17   0.243    -1.623045    .4104765
------------------------------------------------------------------------------

. margins, dydx(*) pr(xb)

Average marginal effects                        Number of obs     =        189
Model VCE    : OIM

Expression   : Linear prediction, predict(xb)
dy/dx w.r.t. : age smoke 2.race 3.race

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |  -.0218726   .0201108    -1.09   0.277    -.0612891    .0175439
       smoke |   .6758233   .2210635     3.06   0.002     .2425469      1.1091
             |
        race |
      black  |   .6183845   .2994882     2.06   0.039     .0313984    1.205371
      other  |   .6455825   .2401702     2.69   0.007     .1748575    1.116308
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.