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Compute partial effects in a probit or logit model with a triple dummy variable> interaction term

inteff3[if] [in], [averageat(numlist)me(newlist)se(newlist)postvarx1()varx2()varx3()varx1x2()varx1x3()varx2x3()varx1x2x3()pex1()pex2()pex3()pex1x2()pex1x3()pex2x3()pex1x2x3()sx1()sx2()sx3()sx1x2()sx1x3()sx2x3()sx1x2x3()]

inteff3is for use after a probit or logit model has been estimated. The model must include the three single dummies, all double interactions and the triple interaction term.

DescriptionNorton et al. (2004) have derived the formulae for partial effects of interaction terms of two variables in logit and probit models, implemented in the module inteff.

In the same logic,

inteff3computes partial effects in a probit or logit model with a triple dummy variable interaction term. The default is to compute the partial effects at means.The model may be applied when the effect of a binary regressor on a binary dependent variable is allowed to vary over combinations of two sub-groups. For example, one may be interested in the way a university degree and the presence of children affect the gender difference in labour market participation. To this effect, one may run a probit model of labour market participation including dummies for female, university degree and presence of children, as well as their pairwise and triple interaction terms.

A difference-in-difference-in-differences estimator with a binary dependent variable (see for example Gruber and Poterba 1994) may also seem to be a suitable application. However, Puhani (2008) argues that the treatment effect in non-linear difference-in-differences models is not given by the interaction effect à la Ai and Norton (2003). In fact, computing the interaction effect à la Ai and Norton (2003) would not ensure that the difference-in-differences treatment effect is bounded between 0 and 1.

See Cornelissen and Sonderhof (2009) for the formulae of the partial effects of the interaction terms in the probit model with triple dummy variable interactions.

inteff3uses the delta method to compute the standard errors of the partial effects and partly relies on the built-in Stata functions nlcom and predictnl for this purpose.

Options

varx1() -varx1x2x3() can be used to specify the variable names of the the three single dummies (x1, x2, x3), all double interactions (x1*x2, x1*x3, x2*x3) and the triple interaction term (x1*x2*x3). By default, inteff3 assumes (and checks) that they are given by the first seven regressors in the following order: x1 x2 x3 x1*x2 x1*x3 x2*x3 x1*x2*x3.averagerather than computing the partial effect at certain values (e.g. means), the effect is computed for each observation and then averaged over all observations. The default is to compute the partial effects at means.

at(numlist) specifies that partial effects are to be computed at the values passed in this option. The first three values are those for the three dummy variables followed by the values for the control variables (excluding the double and triple dummy interactions). The default is to compute the partial effects at means.

pex1() -pex1x2x3() specifiy names of new variables, in which the respective partial effects are to be stored. These optionspex1() -pex1x2x3() have to be combined with the option average.

sx1() -sx1x2x3() specifiy names of new variables, in which the standard errors of the partial effects are to be stored. These optionssx1() -sx1x2x3() have to be combined with the option average.

postWhen post is specified,inteff3will post the vector of partial effects and the diagonal elements of the variance-covariance matrix to e(). Important:inteff3only computes the variances of the partial effects needed for simple tests on the partial effects.inteff3does not compute the the covariances. The covariances are posted in e(V) aszero, which are not the true covariances! The optionpostoverwrites the saved estimates of the preceding probit model, and inteff3 cannot be recalled unless another probit model is estimated.

Examples. probit y x1 x2 x3 x1x2 x1x3 x2x3 x1x2x3 z1 z2 z3 z4 . inteff3

. probit y x1 x2 x3 x1x2 x1x3 x2x3 x1x2x3 z1 z2 z3 z4 . inteff3, average pex1x2x3(pe) sx1x2x3(se)

. probit y x1 x2 x3 x1x2 x1x3 x2x3 x1x2x3 z1 z2 z3 z4 . inteff3, at(0.5 0 1 1.2 -0.3 1 0.7 1)

AuthorsThomas Cornelissen, CReAM, Department of Economics, University College > London, UK. t.cornelissen@ucl.ac.uk

Katja Sonderhof, Leibniz Universität Hannover, Germany sonderhof@aoek.uni-hannover.de

ReferencesGruber, J. and J. Poterba (1994): Tax Incentives and the Decision to Purchase Health Insurance: Evidence from the Self-Employed,

The Quarterly Journal ofEconomics, Vol. 109, No. 3, pp. 701-733.Norton, E. C., H. Wang and C. Ai (2004): Computing interaction effects and standard errors in logit and probit models,

The Stata Joumal, 4(2), 154-167.Cornelissen and Sonderhof (2009): Partial effects in probit and logit models with a triple dummy variable interaction term, Leibniz Universität Hannover Discussion Paper No. 386 (revised version).

Puhani, P. (2008): The Treatment Effect, the Cross Difference, and the Interaction Term in Nonlinear “Difference-in-Differences” Models, IZA Discussion Paper No. 3478.

Also see