Stata Command: robustate

Stata Command: robustate.ado

Under the limited overlap, the naive inverse propensity score estimation method suffers from large variances (if not a lack of the consistency or the asymptotic normality). This command executes estimation and inference for the average treatment effect (ATE) robustly against the limited overlap based on the method of Sasaki and Ura (2022). The Stata output displayed below shows both the standard inverse propensity score weighted estimate (NAIVE_ATE) and our proposed robust estimate (ROBUST_ATE) of the average treatment effects of catheterization on the 30-day survival.

Installation:

. ssc install robustate

Usage:

. use "catheterization_small.dta"

. robustate outcome treat age alb1 amihx aps1 bili1 ca_meta ca_yes card cardiohx cat1_chf cat1_cirr cat1_colon cat1_coma cat1_copd cat1_lung cat1_mosfmal cat1_mosfsep cat2_cirr cat2_colon cat2_coma cat2_lung cat2_mosfmal cat2_mosfsep chfhx chrpulhx crea1 das2d3pc dementhx

Help:

. help robustate

Reference: Sasaki, Y & T. Ura (2022) Estimation and Inference for Moments of Ratios with Robustness against Large Trimming Bias. Econometric Theory, 38 (1), pp. 66-112. Paper.

Download the manuscript and package forthcoming in The Stata Journal

Frequently Asked Questions:

Q1. How does the "robustate" command compare with the existing IPW estimator such as the "teffects ipw" command?

  • A. "teffects ipw" tends to produce larger standard errors than "robustate". If the overlap is severely limited (i.e., if the tail index of the inverse propensity score is above 0.5), then the standard error for "teffects ipw" is not guaranteed to exist while that of "robustate" still exists.

Q2. How does the "robustate" command compare with the IPW estimation with trimming/truncating small propensity scores?

  • A. Trimmed and truncated estimators are biased for the average treatment effects (ATE), while the "robustate" estimator is de-biased and its standard error accounts for the effects of the de-biasing.

Q3. How does the "robustate" command compare with the matching estimators such as "teffects pamatch" and "teffects nnmatch" commands?

  • A. The matching estimators tend to be biased for the average treatment effects (ATE) when the overlap is limited, while the "robustate" estimator being de-biased consistently estimates the ATE and its standard error accounts for the effects of the de-biasing.

Q4. How does the "robustate" command compare with the overlap weighting approaches?

  • A. The "robustate" estimates the average treatment effects (ATE), while the overlap weighting approaches estimate only weighted averages of treatment effects and hence in general fail to estimate the ATE.

Title
 robustate -- Executes estimation and inference for the average treatment effect (ATE) robustly against the limited overlap.
Syntax
 robustate outcome treatment controls [if] [in] [, probit h(real) k(real)]

Description
 robustate executes estimation and inference for the average treatment effect (ATE) robustly against the limited overlap based on Sasaki and Ura (2021) -- Section 7. Under the limited overlap, the naive inverse propensity score estimation method suffers from large variances (if not a lack of the consistency or the asymptotic normality). Hence, it is a common practice to trim observations whose propensity scores are close to 0 or 1, but such a practice biases the estimator of the ATE. This command, robustate, corrects the bias from the trimming and computes a valid standard error accounting for the bias correction. The command accepts an outcome variable, a binary treatment variable, and a list of control variables. It returns both the naive inverse propensity score weighted estimate and the robust inverse propensity score weighted estimate. The robust estimator in general yields a smaller standard error than the naive estimator.
Options
 probit sets an indicator for the method of estimating the propensity score. Not calling this option leads to the logit propensity score estimation by default. Calling this option leads to the probit propensity score estimation.
 h(real) sets the trimming threshold. The default value is h(0.1). It has to be a real number in (0,1). Larger values induce larger biases of the naive estimator.
 k(real) sets the sieve dimension for bias correction. The default value is k(4). It has to be an integer which is no smaller than 4.
Example
 Average treatment effect of catheterization on 30-day survival.
 . use "catheterization_small.dta" . robustate outcome treat controls
 where the controls in the last command line above includes: age, alb1, amihx, aps1, bili1, ca_meta, ca_yes, card, cardiohx, cat1_chf, cat1_cirr, cat1_colon, cat1_coma, cat1_copd, cat1_lung, cat1_mosfmal, cat1_mosfsep, cat2_cirr, lon, cat2_coma, cat2_lung, cat2_mosfmal, cat2_mosfsep, chfhx, chrpulhx, crea1, das2d3pc, and dementhx
Stored results
 robustate stores the following in e():
 Scalars e(N) observations e(h) trimming threshold e(k) order of orthonormal basis
 Macros e(pscore) logit or probit e(cmd) robustate e(properties) b V
 Matrices e(b) coefficient vector e(V) variance-covariance matrix of the estimators
 Functions e(sample) marks estimation sample
Reference
 Sasaki, Y. and T. Ura 2022. Estimation and Inference for Moments of Ratios with Robustness against Large Trimming Bias. Econometric Theory, 38 (1), pp. 66-112. Link to Paper.
Authors
 Yuya Sasaki, Vanderbilt University, Nashville, TN.
 Takuya Ura, University of California, Davis, CA.