help for drlate

Title

drlate -- Doubly robust estimation of the local average treatment effect (LATE) and the local average treatment effect on the treated (LATT)

Syntax

drlate
(ovar [omvarlist] [, omodel])
(tvar [tmvarlist] [, tmodel])
(iv [ivvarlist] [, ivmodel])
[if] [in]
[weight]
[, options]

ovar is an outcome variable.

omvarlist specifies the covariates in the outcome model.

tvar is a treatment variable.

tmvarlist specifies the covariates in the treatment model.

iv is a binary instrumental variable.

ivvarlist specifies the covariates in the instrument propensity score model.

omvarlist, tmvarlist, and ivvarlist may contain
factor variables; see fvvarlists.

omodel

Outcome model
linear linear regression; the default

logit logistic regression; ovar must be 0/1

poisson Poisson regression; ovar must be non-negative

tmodel

Treatment model
logit logistic regression; tvar must be 0/1; the default

linear linear regression

poisson Poisson regression; tvar must be non-negative

ivmodel

Instrument propensity score model
logit logistic regression estimated by maximum likelihood (MLE); the default

cbps logistic regression estimated by covariate balancing (CBPS),
as in Imai and Ratkovic (2014); not available with latt

ipt logistic regression estimated by inverse probability tilting (IPT),
as in Egel et al. (2008) and Graham et al. (2012, 2016)

options

Estimand
late estimate the local average treatment effect (LATE); the default

latt estimate the local average treatment effect on the treated (LATT)

Estimator
method(string) string may be ipwra (default), ipw,
aipw, or ra; see Methods below

nrm use normalized moment conditions (only relevant for ipw and aipw); the default

unnrm use unnormalized moment conditions (only relevant for ipw and aipw)

SE/Robust
vce(vcetype) vcetype may be robust (default) or
cluster clustvar

GMM options
iterate(#) perform maximum of # iterations

technique(string) optimization technique; gn (default),
nr, dfp, and bfgs are allowed

Overlap
pstolerance(#) set tolerance for the overlap assumption;
default is 1e-5; drlate exits with an error if any estimated
instrument propensity score is below # or above 1−#

osample(newvar) create indicator variable newvar equal
to 1 for observations that violate the overlap assumption

pweights are allowed; see weight.

Description

drlate estimates the local average treatment effect (LATE) and the local
average treatment effect on the treated (LATT) using observational data.
The command accommodates a binary instrument, a continuous, binary, or count
treatment, and a continuous, binary, or count outcome.
All standard errors are computed jointly for the instrument propensity score,
the outcome regression, the treatment regression, and the causal estimand,
using Stata's gmm command with iterate(0) (one-step GMM with
analytical starting values), yielding valid inference.

This is a companion software package for Słoczyński, Uysal, and Wooldridge (2022).
Please cite this paper if you use drlate in your work.

Methods

The estimator is selected via method(). All methods jointly estimate the
causal parameter and all nuisance models in a single GMM system, so that
standard errors correctly account for estimation uncertainty in each stage.

ipwra (default) selects inverse-probability-weighted regression adjustment
(IPWRA). The outcome and treatment models are fitted with IPW weights derived
from the instrument propensity score, and the causal parameter is identified from
the implied regression predictions. IPWRA weights are always normalized.
This method is doubly robust: the estimator is consistent if either the instrument
propensity score model or the outcome/treatment regression models are
correctly specified.

ipw selects inverse probability weighting (IPW). This method does not feature
an explicit outcome or treatment regression. omvarlist and tmvarlist should
not be specified with method(ipw).

aipw selects augmented inverse probability weighting (AIPW). The outcome and
treatment models are fitted without IPW weights, and an IPW-based augmentation
term is added to the moment conditions. This method is also doubly robust.

ra selects regression adjustment (RA). No instrument propensity score is
estimated. The outcome and treatment models are fitted separately for both instrument
values, and predictions are averaged. Standard errors are computed by GMM.
ivvarlist should not be specified with method(ra).

Normalization

For method(ipw) and method(aipw), the user may choose between
normalized (nrm) and unnormalized (unnrm) moment conditions.
Normalized estimators ensure that the IPW weights sum to one within each
instrument group.

For method(ipwra) and method(ra), normalization is not necessary
and the nrm/unnrm options have no effect.

When ipt is selected for ivmodel, the IPT weights are ex-ante normalized,
so normalized and unnormalized estimators coincide; drlate automatically
sets normalization to nrm in this case.

Overlap

drlate checks the overlap assumption after estimating the instrument
propensity score. It exits with an error if any in-sample estimated propensity
score falls outside the interval [pstolerance, 1−pstolerance].
The default tolerance is 1e-5. Use osample(newvar) to save an indicator
of violating observations for inspection before re-running on a restricted
sample.

Examples

Load data and prepare variables:

. use https://people.brandeis.edu/~tslocz/sipp.dta, clear

. drop if kwage==. | educ==. | rsncode==999

. generate double lwage = ln(kwage)

LATE with default settings (IPWRA, logit instrument propensity score and treatment models,
linear outcome model):

. drlate (lwage age_5) (nvstat age_5) (rsncode age_5)

LATE with IPT instrument propensity score:

. drlate (lwage age_5) (nvstat age_5) (rsncode age_5, ipt)

LATT with IPT instrument propensity score:

. drlate (lwage age_5) (nvstat age_5) (rsncode age_5, ipt), latt

LATE with IPW estimator:

. drlate (lwage) (nvstat) (rsncode age_5), method(ipw)

LATE with AIPW estimator, unnormalized:

. drlate (lwage age_5) (nvstat age_5) (rsncode age_5), method(aipw) unnrm

LATE with regression adjustment:

. drlate (lwage age_5) (nvstat age_5) (rsncode), method(ra)

LATE with regression adjustment, including Poisson regression for the original wage variable:

. drlate (kwage age_5, poisson) (nvstat age_5) (rsncode), method(ra)

Stored results

drlate stores the following in e():

Scalars

e(N) number of observations

e(N_clust) number of clusters (if vce(cluster) is specified)

e(dmeanz1) mean of treatment variable among observations with Z=1

e(dmeanz0) mean of treatment variable among observations with Z=0

Macros

e(cmd) drlate

e(cmdline) command as typed

e(yvar) name of outcome variable

e(tvar) name of treatment variable

e(zvar) name of instrumental variable

e(ymodelvars) covariates in outcome equation

e(tmodelvars) covariates in treatment equation

e(zmodelvars) covariates in instrument equation

e(omodel) model for outcome equation

e(tmodel) model for treatment equation

e(zmodel) model for instrument propensity score

e(method) estimator used (ipwra, ipw, aipw, or ra)

e(stat) estimand (late or latt)

e(statnorm) normalization (nrm or unnrm)

e(vce) vcetype specified in vce()

e(vcetype) title used to label standard errors

e(ifcond) if condition used in estimation

e(properties) b V

Matrices

e(b) coefficient vector; columns are the causal estimate,
the numerator, and the denominator

e(V) variance-covariance matrix

Functions

e(sample) marks estimation sample

The column labeled LATE: D on Y (or LATT: D on Y) in e(b)
contains the causal estimate. The columns labeled ATE: Z on Y and
ATE: Z on D (or ATT: Z on Y and ATT: Z on D) contain the
estimated intent-to-treat (ITT) effect and first-stage compliance probability,
respectively, from which the causal estimate is formed as their ratio.

References

Egel, Daniel, Bryan S. Graham, and Cristine Campos de Xavier Pinto
(2008). "Inverse Probability Tilting and Missing Data Problems."
NBER Working Paper No. 13981.

Graham, Bryan S., Cristine Campos de Xavier Pinto, and Daniel Egel
(2012). "Inverse Probability Tilting for Moment Condition Models with
Missing Data." Review of Economic Studies 79(3), 1053–1079.

Graham, Bryan S., Cristine Campos de Xavier Pinto, and Daniel Egel
(2016). "Efficient Estimation of Data Combination Models by the Method
of Auxiliary-to-Study Tilting (AST)."
Journal of Business & Economic Statistics 34(2), 288–301.

Imai, Kosuke, and Marc Ratkovic (2014). "Covariate Balancing Propensity
Score." Journal of the Royal Statistical Society, Series B 76(1),
243–263.

Słoczyński, Tymon, S. Derya Uysal, and Jeffrey M. Wooldridge
(2022). "Doubly Robust Estimation of Local Average Treatment Effects
Using Inverse Probability Weighted Regression Adjustment."
Available at https://doi.org/10.48550/arXiv.2208.01300.

Authors

S. Derya Uysal, LMU Munich

Email: derya.uysal@econ.lmu.de

Tymon Słoczyński, Brandeis University

Email: tslocz@brandeis.edu

Jeffrey M. Wooldridge, Michigan State University

Email: wooldri1@msu.edu