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help for inteff3                                               (Version 1.2.0)
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Compute partial effects in a probit or logit model with a triple dummy variable
>  interaction term

inteff3 [if] [in], [average at(numlist) me(newlist) se(newlist) post
varx1() varx2() varx3() varx1x2() varx1x3() varx2x3()
varx1x2x3()
pex1() pex2() pex3() pex1x2() pex1x3() pex2x3() pex1x2x3()
sx1() sx2() sx3() sx1x2() sx1x3() sx2x3() sx1x2x3()]

inteff3 is 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.

Description

Norton 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, inteff3 computes 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. inteff3 uses 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.

average               rather 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 options pex1() -
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
options sx1() - sx1x2x3() have to be combined with the
option average.

post                  When post is specified, inteff3 will post the vector of
partial effects and the diagonal elements of the
variance-covariance matrix to e().  Important: inteff3
only computes the variances of the partial effects needed
for simple tests on the partial effects.  inteff3 does
not compute the the covariances. The covariances are
posted in e(V) as zero, which are not the true
covariances!
The option post overwrites 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)

Authors

Thomas 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

References

Gruber, J. and J. Poterba (1994): Tax Incentives and the Decision to Purchase
Health Insurance:  Evidence from the Self-Employed, The Quarterly Journal of
Economics, 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

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