```Title

Potential outcome parameter estimation

Syntax

poparms (treatvar gpsvars) (depvar cvars) [if] [in] [, options]

options                       Description
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quantiles(numlist)          estimate specified quantiles

vce(vcetype [, vceoptions]) vcetype may be bootstrap, analytic, or
none.
analytic is the default when quantiles() is
not specified.  bootstrap is the default
when quantiles() is specified.
vceoptions vary over vcetype and are
discussed below.

ipw                         use inverse-probability-weighted (IPW)
estimator instead of default
efficient-influence-function (EIF)
estimator

INCLUDE help shortdes-coeflegend

-------------------------------------------------------------------------
gpsvars and cvars may contain time-series operators; see fvvarlist.

Description

poparms estimates parameters of the potential-outcome distributions in
causal inference.

The estimators implemented in poparms were derived in Cattaneo(2010).
Cattaneo, Drukker, and Holland (2012) provides an introduction to this
command.

Options

quantiles() specifies the quantiles of the potential outcome
distributions that are to be estimated jointly with the means.  By
default, only the means are estimated.  By default, method
vce(bootstrap) is used when quantiles() is specified.  We strongly
recommend not using vce(analytic) when quantiles() is specified.

vce() specifies the method used to estimate the variance-covariance of
the estimator.

vce:(vcetype [, vceoptions])} specifies the vcetype and the type
specific options.

When specifying vce(bootstrap), the vceoption is reps(#) which
specifies the number of bootstrap repetitions which must be
integer that is at least 50.

With method analytic, the vceoptions are bwscale(#)),
bwidths(matname), and densities(matname).  These suboptions are
mutually exclusive.

By default, poparms uses an analytic estimator when only means are
estimated and it uses a bootstrap estimator when quantiles are
estimated.  We recommend not using the analytic method when
quantiles are specified because this method performed poorly in
Monte Carlo simulations.

With method bootstrap, you may change the number of repetitions
from the default 2000 by specifying vce(bootstrap , reps(#)).
The specified number of repetitions must an integer greater
than 49.

With method analytic, you may rescale the bandwidths used to
estimate the densities by specifying vce(analytic, bwscale(#)).
The specified number must be in the interval [.1, 10].

With method analytic, you may specify the bandwidths used to
estimate the densities by specifying vce(analytic,
bwidths(matname)), where matname specifies a Stata row vector
with the number of columns equal to the number of quantiles
times the number of treatment levels.

With method analytic, you may specify the densities used
vce(analytic, densities(matname)), where matname specifies a
Stata row vector with the number of columns equal to the number
of quantiles times the number of treatment levels.

ipw specifies that poparms use the IPW estimator instead of the default
EIF estimator.  The methods and differences are described in
Cattaneo, Drukker, and Holland (2012).

coeflegend; see [R] estimation options.

Examples

---------------------------------------------------------------------------
Setup
. use spmdata

Mean estimation
. poparms (w pindex eindex) (spmeasure pindex eindex)

Mean estimation with polynomial for conditional mean
. poparms (w pindex eindex) (spmeasure c.(pindex eindex)#c.(pindex
eindex))

Mean and quantile estimation with polynomial for conditional mean
This example limits the number of of bootstrap repetitions to 50 so
that the example runs relatively quickly.  We recommend using at
least the default of 2000 repetitions in practice.

. poparms (w pindex eindex) (spmeasure c.(pindex eindex)#c.(pindex
eindex)), quantiles(.25 .75) vce(bootstrap, reps(50))

Saved results

poparms saves the following in e():

Scalars
e(N)                number of observations
e(k)                number of variables in conditional mean
e(bwscale)          scale for bandwidths, if specified
e(reps)             number of requested bootstrap repetitions, if
specified}
e(bsreps)           number of successful bootstrap repetitions, if
specified}

Macros
e(cmd)              poparms
e(cmdline)          command as typed
e(depvar)           name of dependent variable
e(title)            title in estimation output
e(title2)           second title in estimation output
e(vce)              vcetype specified in vce()
e(vcetype)          title used to label Std. Err.
e(quantiles)        specified quantiles
e(properties)       b V or b if vce(none)
e(predict)          program used to implement predict

Matrices
e(b)                coefficient vector
e(V)                variance-covariance matrix of the estimators
e(V1)               outer product Psi functions used in variance

Functions
e(sample)           marks estimation sample

References

Cattaneo, M. D. 2010.  Efficient Semiparametric Estimation of
Multi-valued Treatment Effects under Ignorability. Journal of
Econometrics 155(2):  138-154.
http://www.sciencedirect.com/science/article/pii/S030440760900236X

Cattaneo, M. D., D. M. Drukker, and A. Holland. 2012.  Estimation of
multivalued treatment effects under conditional independence.
Working paper, University of Michigan, Department of Economics,
http://www-personal.umich.edu/~cattaneo/papers/Cattaneo-Drukker-Holla
> nd_2012_STATA.pdf.

Authors

Matias D. Cattaneo, University of Michigan, Ann Arbor, MI.
cattaneo@umich.edu.

David M. Drukker, StataCorp, College Station, TX.  ddrukker@stata.com.

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