Multiple Treatment Effects
version 1.1.0 09Mar2024 | Installation | Usage | Examples
This package implements contamination bias diagnostics in Stata using procedures from Goldsmith-Pinkham, Hull, and Kolesár (2024), based on R's multe package.
From Stata
local github "https://raw.githubusercontent.com"
cap noi net uninstall multe
net install multe, from(`github'/gphk-metrics/stata-multe/main/)You can also clone or download the code manually, e.g. to
stata-multe-main, and install from a local folder:
cap noi net uninstall multe
net install multe, from(`c(pwd)'/stata-multe-main)multe depvar [controls] [w=weight], treat(varname) [stratum(varname) options]
help multe
At least one of controls or stratum must be specified.
The examples here are copied from the vignette for the R package and adapted for Stata. The vignette also includes an overview of the methods used in this package.
See Fryer and Levitt (2013) for a description of the data. First, we fit a regression of test scores on a race dummy (the treatment of interest) and a few controls, using sampling weights.
use test/example_fryer_levitt.dta, clear
* Regress IQ at 24 months on race indicators and baseline controls
multe std_iq_24 i.age_24 female [w=W2C0], treat(race) stratum(SES_quintile)The function posts the estimates from the partly linear model (OLS with robust SE) and reports a table with alternative estimates free of contamination bias.
Partly Linear Model Estimates (full sample) Number of obs = 8,806
------------------------------------------------------------------------------
std_iq_24 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
race |
Black | -.2574154 .0281244 -9.15 0.000 -.3125383 -.2022925
Hispanic | -.2931465 .025962 -11.29 0.000 -.3440311 -.242262
Asian | -.262108 .034262 -7.65 0.000 -.3292603 -.1949557
Other | -.1563373 .0369127 -4.24 0.000 -.2286848 -.0839898
------------------------------------------------------------------------------
Alternative Estimates on Full Sample:
| PL OWN ATE EW CW
-------------+---------------------------------------------
Black | -.2574 -.2482 -.2655 -.255 -.2604
SE | .02812 .02906 .02983 .02888 .02925
Hispanic | -.2931 -.2829 -.2992 -.2862 -.2944
SE | .02596 .02673 .02988 .0268 .02792
Asian | -.2621 -.2609 -.2599 -.2611 -.2694
SE | .03426 .03432 .04177 .03433 .04751
Other | -.1563 -.1448 -.1503 -.1447 -.1522
SE | .03691 .03696 .03594 .03684 .03698
P-values for null hypothesis of no propensity score variation:
Wald test: 2.1e-188
LM test: 8.8e-197In particular, the package computes the following estimates in addition to the partly linear model (PL):
- OWN: The own treatment effect component of the PL estimator that subtracts an estimate of the contamination bias
- ATE: The unweighted average treatment effect, implemented using regression that includes interactions of covariates with the treatment indicators
- EW: Weighted ATE estimator based on easiest-to-estimate weighting (EW) scheme, implemented by running one-treatment-at-a-time regressions.
- CW: Weighted ATE estimator using easiest-to-estimate common weighting (CW) scheme, implemented using weighted regression.
For more precise definitions, see the methods section of the R vignette. Note any combination of estimates can be posted after multe has run:
. multe, est(ATE)
ATE Estimates (full sample) Number of obs = 8,806
------------------------------------------------------------------------------
std_iq_24 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
race |
Black | -.2655242 .0298285 -8.90 0.000 -.3239869 -.2070615
Hispanic | -.2992432 .0298811 -10.01 0.000 -.357809 -.2406774
Asian | -.2598644 .041769 -6.22 0.000 -.3417301 -.1779987
Other | -.1502789 .0359405 -4.18 0.000 -.220721 -.0798368
------------------------------------------------------------------------------In this example, the propensity score varies significantly with covariates, as indicated by the p-values of the Wald and LM tests. Including many controls may result in overlap failure, as the next example demonstrates:
. local controls i.age_24 female i.siblings i.family_structure
. multe std_iq_24 `controls' [w=W2C0], treat(race) stratum(SES_quintile)
(analytic weights assumed)
The following variables have no within-treatment variation
and are dropped from the overlap sample:
6.siblings
Partly Linear Model Estimates (full sample) Number of obs = 8,806
------------------------------------------------------------------------------
std_iq_24 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
race |
Black | -.2437653 .0307696 -7.92 0.000 -.3040726 -.183458
Hispanic | -.2928037 .0259029 -11.30 0.000 -.3435725 -.2420348
Asian | -.273888 .0341814 -8.01 0.000 -.3408823 -.2068938
Other | -.1519798 .0368914 -4.12 0.000 -.2242857 -.079674
------------------------------------------------------------------------------
Alternative Estimates on Full Sample:
| PL OWN ATE EW CW
-------------+---------------------------------------------
Black | -.2438 -.2043 -.2482 -.218 -.2415
SE | .03077 .03321 .03553 .03276 .03853
Hispanic | -.2928 -.2801 -.2878 -.285 -.3001
SE | .0259 .02671 .03 .02671 .02984
Asian | -.2739 -.2836 -.2742 -.2839 -.2863
SE | .03418 .0343 .04195 .03426 .04549
Other | -.152 -.1277 . -.1295 -.1452
SE | .03689 .03736 . .03713 .03817
P-values for null hypothesis of no propensity score variation:
Wald test: 1.3e-275
LM test: 2.2e-245
Alternativ Estimates on Overlap Sample:
| PL OWN ATE EW CW
-------------+---------------------------------------------
Black | -.2458 -.2062 -.2503 -.2199 -.2436
SE | .03074 .03318 .03532 .0327 .03824
Hispanic | -.2932 -.2809 -.288 -.2858 -.2987
SE | .02595 .02676 .03001 .02678 .02987
Asian | -.2741 -.2839 -.274 -.2841 -.2884
SE | .03417 .03429 .04187 .03426 .04563
Other | -.1511 -.127 -.1392 -.1289 -.1459
SE | .03688 .03735 .03618 .03711 .03853The issue is that no observations with 6 siblings have race equal to "Other":
. tab race if siblings == 6, mi
race | Freq. Percent Cum.
------------+-----------------------------------
White | 18 40.00 40.00
Black | 10 22.22 62.22
Hispanic | 12 26.67 88.89
Asian | 5 11.11 100.00
------------+-----------------------------------
Total | 45 100.00Thus, the ATE estimator comparing other to white is not identified. The package drops observations with 6 siblings from the sample to form an "overlap sample," where the all estimators are identified. The overlap sample drops all observations from strata that do not have all levels of the treatment as well as all control variables that do not have all levels of the treatment. In this example siblings is a control so the dummy for 6 siblings is dropped; however, if this happened for a level of SES_quintile then all the observations associated with that level would be dropped.
For a researcher who wants to check whether there is a significant difference between the PL estimator and the other estimators, e(diffmatrix) and e(overlapdiffmatrix) report the differences between the estimates in the full sample and the overlap sample, respectively, with the corresponding standard errors.
. matlist e(diffmatrix), format(%7.4g)
| OWN ATE EW CW
-------------+------------------------------------
Black | -.03947 .0044 -.02573 -.00229
SE | .01204 .0173 .01027 .0205
Hispanic | -.01269 -.00496 -.00783 .00725
SE | .00571 .01314 .00497 .01245
Asian | .00975 .00026 .01001 .01238
SE | .00487 .0246 .0048 .02814
Other | -.0243 . -.02246 -.00679
SE | .00738 . .00684 .01326
. matlist e(overlapdiffmatrix), format(%7.4g)
| OWN ATE EW CW
-------------+------------------------------------
Black | -.03958 .00453 -.02592 -.00218
SE | .01201 .01714 .01023 .02023
Hispanic | -.01229 -.00523 -.00738 .00554
SE | .00569 .01319 .00494 .01247
Asian | .00978 -8.7e-05 .01 .01433
SE | .00486 .02454 .0048 .0282
Other | -.02404 -.01189 -.02221 -.0052
SE | .00739 .01098 .00684 .01337We see statistically significant difference between the OWN and PL estimate (i.e. significant contamination bias) for all races, both in the full sample and in the overlap sample. Differences can also be posted after the main estimation:
. multe, est(OWN) diff
Own Treatment Effects Estimates (full sample) Number of obs = 8,806
------------------------------------------------------------------------------
std_iq_24 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
race |
Black | -.0394671 .0120418 -3.28 0.001 -.0630686 -.0158656
Hispanic | -.0126872 .0057131 -2.22 0.026 -.0238847 -.0014898
Asian | .009752 .0048651 2.00 0.045 .0002166 .0192874
Other | -.0242985 .0073833 -3.29 0.001 -.0387696 -.0098274
------------------------------------------------------------------------------
. multe, est(OWN) diff overlap
Own Treatment Effects Estimates (overlap sample)
Number of obs = 8,806
------------------------------------------------------------------------------
std_iq_24 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
race |
Black | -.0395843 .0120096 -3.30 0.001 -.0631227 -.0160458
Hispanic | -.01229 .0056924 -2.16 0.031 -.0234468 -.0011332
Asian | .009776 .0048602 2.01 0.044 .0002502 .0193019
Other | -.0240377 .0073857 -3.25 0.001 -.0385134 -.009562
------------------------------------------------------------------------------
The package also computes "oracle" standard errors, in addition to the usual
standard errors reported above. These can be accessed by adding the oracle
option to multe after the main estimation for ATE, EW, CW:
. multe, est(ATE) oracle
ATE Estimates (full sample) Number of obs = 8,806
------------------------------------------------------------------------------
| Oracle
std_iq_24 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
race |
Black | -.2481627 .0354964 -6.99 0.000 -.3177343 -.1785911
Hispanic | -.2878414 .0299246 -9.62 0.000 -.3464926 -.2291902
Asian | -.2741527 .0418856 -6.55 0.000 -.3562469 -.1920584
Other | 0 (omitted)
------------------------------------------------------------------------------These oracle standard errors don't account for estimation error in the
propensity score, in contrast to the default standard errors (note since ATE
was not identified for Other, Stata interprets it as an omitted category
for this estimator). Last, Specifying the cluster() argument allows for
computation of clustered standard errors:
. local controls i.age_24 female
. local options treat(race) stratum(SES_quintile)
. multe std_iq_24 `controls' [w=W2C0], `options' cluster(interviewer_ID_24)
(analytic weights assumed)
Partly Linear Model Estimates (full sample) Number of obs = 8,806
------------------------------------------------------------------------------
| Cluster
std_iq_24 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
race |
Black | -.2574154 .0411564 -6.25 0.000 -.3380804 -.1767504
Hispanic | -.2931465 .0440827 -6.65 0.000 -.379547 -.2067461
Asian | -.262108 .0521067 -5.03 0.000 -.3642353 -.1599807
Other | -.1563373 .0403717 -3.87 0.000 -.2354645 -.0772102
------------------------------------------------------------------------------
Alternative Estimates on Full Sample:
| PL OWN ATE EW CW
-------------+---------------------------------------------
Black | -.2574 -.2482 -.2655 -.255 -.2604
SE | .04116 .04248 .04099 .0422 .04199
Hispanic | -.2931 -.2829 -.2992 -.2862 -.2944
SE | .04408 .04541 .0495 .04572 .04738
Asian | -.2621 -.2609 -.2599 -.2611 -.2694
SE | .05211 .05234 .06194 .05232 .06755
Other | -.1563 -.1448 -.1503 -.1447 -.1522
SE | .04037 .04161 .04099 .04145 .04278
P-values for null hypothesis of no propensity score variation:
Wald test: 9.4e-133
LM test: 6.79e-07