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  • Differences in coefficients estimated with CMP (ordinal probit specification) and eoprobit

    Dear Statalister,

    I am running the following triangular model using Stata 18.

    (hc + excluded variables) ->ret3 (+excluded variable)-> hirecando) -> + ret3 on fsk3.

    The triangular model has been implemented using the user written routine CMP in the following way:

    Code:
    cmp (fsk3 = ret3 hirecando $reg) (ret3 = i.hc_class wpsupp eidelay $reg) (hirecando = ret3 itprodimp itperfmon  skillch trski trflex supchek neverint $reg) [pweight= s5_wgt_final], ind( 5, 5, 5 ) vce(cluster country) difficult
    exclusion restrictions
    the equation for ret3 has the follwing variables entering only this equation: hc_class wpsupp eidelay
    the equation for hirecando has the follwing variables entering only this equation: itprodimp itperfmon skillch trski trflex supchek neverint

    except for the exclusion restrictions all the equations contain the same set of contorls

    In the last equation fsk is regressed on ret3 hirecando and the controls.

    All the three equations belonging to the triangular system have been modelled as ordinal probits, and they have been jointly estimated.

    The same triangular system has also been implemented using the extended regression suite of Stata

    Code:
    eoprobit fsk3 ret3 hirecando $reg [pweight= s5_wgt_final], endogenous(ret3 = i.hc_class wpsupp eidelay $reg, oprobit nomain) endogenous(hirecando = ret3 itprodimp itperfmon skillch trski trflex supchek neverint $reg, oprobit nomain) vce(cluster country) difficult
    the dendent variables are the same, the controls are the same, the exclusion restrictions are the same, the specification is the same (ordinal probit), yet the results are different. CMP uses a somewhat larger sample, 18,928 observations, while eoprobit uses 18,093 observations. I guess this difference could be traced back to the FIML (all usable observations for each equation) approach used in CMP. But it is a guess.

    For example, for the equation concerning the variable fsk I get the following results:

    CMP
    Robust
    Coefficient std. err. z P>z [95% conf. interval]
    fsk3
    ret3 .7808615 .1765825 4.42 0.000 .4347662 1.126957
    hirecando -.2332199 .1152787 -2.02 0.043 -.459162 -.0072779
    comorg_1 .0074937 .0123713 0.61 0.545 -.0167536 .0317411
    compprobs_1 .0245087 .0143221 1.71 0.087 -.0035621 .0525795
    contr_1 .053524 .0150753 3.55 0.000 .023977 .0830709

    eoprobit
    Robust
    Coefficient std. err. z P>z [95% conf. interval]
    fsk3
    ret3 1.046546 .2508465 4.17 0.000 .5548954 1.538196
    hirecando -.0236865 .3363055 -0.07 0.944 -.6828332 .6354602
    comorg_1 .0110178 .0102237 1.08 0.281 -.0090203 .031056
    compprobs_1 .0259533 .0144384 1.80 0.072 -.0023454 .0542521
    contr_1 .0374643 .0256565 1.46 0.144 -.0128216 .0877501


    The first two coefficients, those on ret3 and hirecando, are very different in the two specifications.

    The difference in sample size between the two commands may have caused some change.

    I assumed that both CMP and eoprobit would have implmented the same triangular system. I am missing something.

    Thank in advance for your help with this matter

    Kind regards

    Giovanni

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