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  • An interaction with categorical and endogenous variables in CMP setting

    Dear all,

    I am trying to measure how the impact of an exogenous indicator variable varies across three different categories, where the assignment of observations into these categories may be endogenous. I consider using CMP (Roodman, 2011) with a code below:

    Code:
    cmp ( Y = I1 I2 A I1_A I2_A $x i.cbsa) (I = Z1 Z2 Z1sq Z2sq Z1Z2 $x, iia), nolrtest ind($cmp_cont $cmp_mprobit) tech(dfp nr) nonrtol vce(robust) ghkdraws(7) difficult
    , where I1 =1 if the observation falls into the second category, 0 otherwise. I2=1 if the observation falls into the third category, 0 othewise.
    A is the exogenous indicator variable of interest.
    I1_A = I1*A, and I2_A = I2*A
    I is a categorical variable with values of {0, 1, 2}.
    Z1 and Z2 are instruments. Z1sq= Z1*Z1, Z2sq = Z2*Z2, and Z1Z2 = Z1*Z2.

    I am wondering whether the model above is valid. Or, do I need to add extra equations with the interaction terms as dependent variables? In other words, do I need to use a code like below?

    Code:
    cmp ( Y = I1 I2 A I1_A I2_A $x i.cbsa) (I1_A = Z1 Z2 Z1sq Z2sq Z1Z2 $x) (I2_A = Z1 Z2 Z1sq Z2sq Z1Z2 $x) (I = Z1 Z2 Z1sq Z2sq Z1Z2 $x, iia), nolrtest ind($cmp_cont $cmp_probit $cmp_probit $cmp_mprobit) tech(dfp nr) nonrtol vce(robust) ghkdraws(7) difficult
    Thank you for your advice in advance.

    Best regards,
    Hong
    Last edited by Hong Lee; 17 Feb 2020, 12:22. Reason: endogenous interaction with categorical variables, CMP,
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