Local Average Treatment Effect Research Articles

Local average treatment effects with binary outcomes.

Local average treatment effects with binary outcomes.

Inference in Experiments with Matched Pairs and Imperfect Compliance

This paper studies inference for the local average treatment effect in randomized controlled trials with imperfect compliance where treatment status is determined according to “matched pairs.” By “matched pairs,” we mean that units are sampled i.i.d. from the population of interest, paired according to observed, baseline covariates and finally, within each pair, one unit is selected at random for treatment. Under weak assumptions governing the quality of the pairings, we first derive the limit distribution of the usual Wald (i.e., two-stage least squares) estimator of the local average treatment effect. We show further that conventional heteroskedasticity-robust estimators of the Wald estimator’s limiting variance are generally conservative, in that their probability limits are (typically strictly) larger than the limiting variance. We therefore provide an alternative estimator of the limiting variance that is consistent. Finally, we consider the use of additional observed, baseline covariates not used in pairing units to increase the precision with which we can estimate the local average treatment effect. To this end, we derive the limiting behavior of a two-stage least squares estimator of the local average treatment effect which includes both the additional covariates in addition to pair fixed effects, and show that its limiting variance is always less than or equal to that of the Wald estimator. To complete our analysis, we provide a consistent estimator of this limiting variance. A simulation study confirms the practical relevance of our theoretical results. Finally, we apply our results to revisit a prominent experiment studying the effect of macroinsurance on microenterprise in Egypt.

Does Employing Skilled Immigrants Enhance Competitive Performance? Evidence from European Football Clubs

We investigate the effect of employing skilled immigrants on the competitive performance of organizations by studying European football (soccer) clubs in Germany, Italy, France, England, and Spain from 1990 to 2020. Microdata from this setting offers unusual transparency about players’ birthplaces and their contributions to organizational performance. Further, country-level rules govern how many immigrant players clubs can deploy. Using changes to these rules as the basis for instrumental variables, we find that the number of immigrant players in the club’s starting lineup has a positive local average treatment effect on the club’s performance. We show that this occurs for two related reasons. First, immigrants exhibit higher individual talent. Second, immigrants play a coordinating role that enables the organization to broaden the variety of on-field strategies and actions it uses to outperform rivals. The latter mechanism is novel to the literature. This paper was accepted by Olav Sorenson, organizations. Funding: F. Morales acknowledges research funding from Agencia Nacional de Investigación y Desarrollo, Chile (Fondecyt de Iniciación) [Grant 11200342]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2021.03356 .

Heterogeneous effects of Medicaid coverage on cardiovascular risk factors: secondary analysis of randomized controlled trial

ObjectivesTo investigate whether health insurance generated improvements in cardiovascular risk factors (blood pressure and hemoglobin A1c (HbA1c) levels) for identifiable subpopulations, and using machine learning to identify characteristics of people...

Causal interpretations of family GWAS in the presence of heterogeneous effects

Family-based genome-wide association studies (GWASs) are often claimed to provide an unbiased estimate of the average causal effects (or average treatment effects; ATEs) of alleles, on the basis of an analogy between the random transmission of alleles from parents to children and a randomized controlled trial. We show that this claim does not hold in general. Because Mendelian segregation only randomizes alleles among children of heterozygotes, the effects of alleles in the children of homozygotes are not observable. This feature will matter if an allele has different average effects in the children of homozygotes and heterozygotes, as can arise in the presence of gene-by-environment interactions, gene-by-gene interactions, or differences in linkage disequilibrium patterns. At a single locus, family-based GWAS can be thought of as providing an unbiased estimate of the average effect in the children of heterozygotes (i.e., a local average treatment effect; LATE). This interpretation does not extend to polygenic scores (PGSs), however, because different sets of SNPs are heterozygous in each family. Therefore, other than under specific conditions, the within-family regression slope of a PGS cannot be assumed to provide an unbiased estimate of the LATE for any subset or weighted average of families. In practice, the potential biases of a family-based GWAS are likely smaller than those that can arise from confounding in a standard, population-based GWAS, and so family studies remain important for the dissection of genetic contributions to phenotypic variation. Nonetheless, their causal interpretation is less straightforward than has been widely appreciated.

The Effect of Rent Control Status on Eviction Filing Rates: Causal Evidence From San Francisco

This paper presents causal evidence of a significant positive effect of rent control status on eviction filing rates in San Francisco, CA. Two datasets of eviction notices (n = 13,887) and property tax records (n = 1,978,687) are combined using a regression discontinuity design to estimate a local average treatment effect of ∼0.3% evictions per residential unit per year conditioned on positive rent control status. Compared to the baseline rate of eviction notices over this same time period, the findings suggest that for a given tenant, positive rent control status (i.e., living in a rent-controlled unit) increases the likelihood of eviction by approximately 127% per year. This finding is best understood not as an inherent characteristic of rent control policy in general, but rather as the result of specific state-wide laws, passed in the years following the adoption of rent control in San Francisco, which granted rent-controlled property owners an economic incentive to evict and the legal means to do so.

The long-term effects of job training on labor market and skills outcomes in Chile

Job training programs can be an effective policy for improving productivity and labor market outcomes in low- and middle-income countries. We report medium- and long-term impacts of a job training program for vulnerable workers in Chile on labor market and skill outcomes using experimental and administrative data. We estimate intention-to-treat effects, accounting for potential non-compliance by training providers in the assignment process, as well as local average treatment effects due to noncompliance with the assigned treatment status. Overall, the program shows limited effectiveness. While we find some positive impacts on labor income, the program fails to improve most labor outcomes. A detailed investigation of heterogenous effects by course-type, training provider and course quality, and gender reveals that the positive income effects are more likely to be realized for males and participants in courses that were offered by high-quality providers. Evidence on mechanisms indicates that the program's limited impact on labor outcomes could, at least partly, be due to its limited effect on workers’ skills.

Instrument-Based Estimation of Full Treatment Effects with Partial Compliers

Abstract The effect of the full treatment is a primary parameter of interest in policy evaluation, while often the effect of a subset of treatment is estimated. We partially identify the local average treatment effect of receiving full treatment (LAFTE) using an instrumental variable that may induce individuals into subsets of treatment (partial compliers). We show that partial compliers violate the standard exclusion restriction, necessary conditions on the absence of partial compliers are testable, and partial identification holds under a double exclusion restriction. We identify partial compliers in four applications and estimate informative bounds on the LAFTE in three of them.

NO DIFFERENCE IN SHORT-TERM REVISION RATE AND EARLY MORTALITY IN UNCEMENTED VERSUS CEMENTED TOTAL HIP ARTHROPLASTY: A REGRESSION DISCONTINUITY ANALYSIS IN THE DUTCH ARTHROPLASTY REGISTER DATA

Controversy persists over whether cemented or uncemented fixation is more effective in reducing revision and mortality risks following primary total hip arthroplasty (THA). Despite a shift towards uncemented THA in Europe, Australia, and the US, no consensus exists on superior outcomes. This ambiguity in evidence from randomized controlled trials (RCTs) and observational studies necessitates advanced research methodologies to derive more definitive conclusions.This study investigates the causal impact of THA fixation type on 2-year and 5-year revision rates, along with 90-day mortality, utilizing a regression discontinuity (RD) design in scenarios where fixation choice is guided by patient age.Employing data from the Dutch Arthroplasty Register, we conducted a cohort study on primary THAs for osteoarthritis from 2007 to 2019. A “fuzzy” RD design was executed to compute the Local Average Treatment Effect for subjects around the age-based selection threshold for fixation type. The main outcome of interest was the revision rate at 2 years post-operation.Analysis for the 2-year revision endpoint, covering any cause, included 2,344 females and 1,671 males across 5 hospitals each, with no significant variation in revision rates observed. For the 5-year mark, 1,058 females in 3 hospitals and 214 males in 1 hospital were examined, similarly showing no significant differences. Mortality within 90 days post-operation was also investigated in 5 female and 7 male cohorts, with 2,180 and 2,145 surgeries respectively, yielding no substantial disparities.In conclusion, the RD analysis revealed no notable differences in revision rates at 2 and 5 years or in early mortality based on the fixation method used in THA. These outcomes suggest that the age-based preference for THA fixation may not influence the revision or mortality risk, underscoring the value of RD design in deriving causal insights from observational data.

Reduced Cost Sharing and Medication Management Services for COPD

High out-of-pocket costs and improper use of maintenance inhalers contribute to poor outcomes among patients with chronic obstructive pulmonary disease (COPD). There is limited evidence for how addressing these barriers could improve adherence and affect COPD exacerbations, spending, or racial disparities in these outcomes. To examine the effect of a national program to reduce beneficiary cost sharing for COPD maintenance inhalers and provide medication management services that included education on proper technique for inhaler use. This randomized clinical trial included individuals with COPD. All individuals were enrolled in Medicare Advantage. Data were collected from January 2019 to December 2021, and data were analyzed from January 2023 to May 2024. Invitation to enroll in a program that reduced cost sharing for maintenance inhalers to $0 or $10 and provided medication management services. The random assignment of the invitation was used to estimate the effects of the invitation and program enrollment, overall and by race. Inhaler adherence measured as proportion of days covered (PDC), moderate-to-severe exacerbations, short-acting inhaler fills, total spending, and as an exploratory outcome, out-of-pocket spending. Of 19 113 included patients, 55.2% were female; 9.5% were Black, 81.1% were White, and 9.4% were another or unknown race; and the median (IQR) age was 74 (69-80) years. Program enrollment was higher in the invited group (29.4%) than the control group (5.1%). The PDC for maintenance inhalers was higher in the invited group than the control group (32.0% vs 28.4%; adjusted invitation effect, 3.8 percentage points; 95% CI, 3.1-4.5); the adjusted effect of the program (the local average treatment effect) was 15.5 percentage points (95% CI, 12.8-18.1), a 55% relative increase in adherence. Mean (SD) out-of-pocket spending for prescriptions was lower in the invited group ($619.5 [$863.1]) than the control group ($675.0 [$887.3]; adjusted invitation effect, -$49.5; 95% CI, -68.9 to -30.0; adjusted program effect, -$203.0; 95% CI, -282.8 to -123.2), but there was no statistically significant difference in exacerbations, short-acting inhaler fills, or total spending. Among Black individuals, the adjusted invitation effect on maintenance inhaler PDC was 5.5 percentage points (95% CI, 3.3-7.7), and the adjusted program effect was 19.5 percentage points (95% CI, 12.4-26.7). Among White individuals, the adjusted invitation effect was 3.7 percentage points (95% CI, 2.9-4.4), and the adjusted program effect was 15.1 percentage points (95% CI, 12.1-18.1). The difference between the invitation effects by race was not statistically significant (1.8 percentage points; 95% CI, -0.5 to 4.1; P = .13). Individuals in Medicare Advantage who received an invitation to enroll in a program that reduced cost sharing for maintenance inhalers and provided medication management services had higher inhaler adherence compared with the control group. The difference in the program's effect on inhaler adherence between Black and White individuals was substantial but not statistically significant. ClinicalTrials.gov Identifier: NCT05497999.

Consumption Feedback and Water Saving: A Field Intervention Evaluation in the Metropolitan Area of Milan

This paper investigates whether informative feedback on consumption can nudge water saving. We launched a five-month online information campaign which involved around 1,000 households located in the province of Milan (Italy) with a smart meter. A group of households received monthly reports via email on their per capita daily average water consumption, including a social comparison component. The Intention to Treat (ITT) analysis shows that, compared to a benchmark group, the units exposed to the intervention reduced their per capita water consumption by around 6% (25.8 liters per day or 6.8 gallons). Being able to observe the email opening rate, we find that the ITT effect is mainly driven by complying units. Through an Instrumental Variable approach, we estimated a Local Average Treatment Effect equal to 54.9 liters per day of water saving. A further Regression Discontinuity Design analysis shows that different feedback on consumption class size differentially affected water saving at the margin. We also found that the additional water saving increased with the number of monthly reports, though it did not persist two months after the campaign expired.

Estimation of the Local Conditional Tail Average Treatment Effect

The conditional tail average treatment effect (CTATE) is defined as a difference between the conditional tail expectations of potential outcomes, which can capture heterogeneity and deliver aggregated local information on treatment effects over different quantile levels and is closely related to the notion of second-order stochastic dominance and the Lorenz curve. These properties render it a valuable tool for policy evaluation. In this article, we study estimation of the CTATE locally for a group of compliers (local CTATE or LCTATE) under the two-sided noncompliance framework. We consider a semiparametric treatment effect framework under endogeneity for the LCTATE estimation using a newly introduced class of consistent loss functions jointly for the CTE and quantile. We establish the asymptotic theory of our proposed LCTATE estimator and provide an efficient algorithm for its implementation. We then apply the method to evaluate the effects of participating in programs under the Job Training Partnership Act in the United States.

Re: "Defining and identifying local average treatment effects".

Re: "Defining and identifying local average treatment effects".

Interpretable (not just posthoc-explainable) medical claims modeling for discharge placement to reduce preventable all-cause readmissions or death

We developed an inherently interpretable multilevel Bayesian framework for representing variation in regression coefficients that mimics the piecewise linearity of ReLU-activated deep neural networks. We used the framework to formulate a survival model for using medical claims to predict hospital readmission and death that focuses on discharge placement, adjusting for confounding in estimating causal local average treatment effects. We trained the model on a 5% sample of Medicare beneficiaries from 2008 and 2011, based on their 2009–2011 inpatient episodes (approximately 1.2 million), and then tested the model on 2012 episodes (approximately 400 thousand). The model scored an out-of-sample AUROC of approximately 0.75 on predicting all-cause readmissions—defined using official Centers for Medicare and Medicaid Services (CMS) methodology—or death within 30-days of discharge, being competitive against XGBoost and a Bayesian deep neural network, demonstrating that one need-not sacrifice interpretability for accuracy. Crucially, as a regression model, it provides what blackboxes cannot—its exact gold-standard global interpretation, explicitly defining how the model performs its internal “reasoning” for mapping the input data features to predictions. In doing so, we identify relative risk factors and quantify the effect of discharge placement. We also show that the posthoc explainer SHAP provides explanations that are inconsistent with the ground truth model reasoning that our model readily admits.

Abadie’s Kappa and Weighting Estimators of the Local Average Treatment Effect

Recent research has demonstrated the importance of flexibly controlling for covariates in instrumental variables estimation. In this article we study the finite sample and asymptotic properties of various weighting estimators of the local average treatment effect (LATE), motivated by Abadie’s kappa theorem and offering the requisite flexibility relative to standard practice. We argue that two of the estimators under consideration, which are weight normalized, are generally preferable. Several other estimators, which are unnormalized, do not satisfy the properties of scale invariance with respect to the natural logarithm and translation invariance, thereby exhibiting sensitivity to the units of measurement when estimating the LATE in logs and the centering of the outcome variable more generally. We also demonstrate that, when noncompliance is one sided, certain weighting estimators have the advantage of being based on a denominator that is strictly greater than zero by construction. This is the case for only one of the two normalized estimators, and we recommend this estimator for wider use. We illustrate our findings with a simulation study and three empirical applications, which clearly document the sensitivity of unnormalized estimators to how the outcome variable is coded. We implement the proposed estimators in the Stata package kappalate.

Multiple Discoveries in Causal Inference: LATE for the Party

Multiple discoveries in statistics may be more common than many readers realize. We tell a story of multiple discoveries in causal inference related to a quantity called the local average treatment effect (LATE). The development of LATE by Imbens and Angrist contributed greatly to their winning the 2021 Nobel Prize in Economics. We discuss how multiple investigators were either early or late for the “party” of intermediate and final discoveries involving LATE.

The interpretation of 2SLS with a continuous instrument: A weighted LATE representation

This note introduces a novel weighted local average treatment effect representation for the two-stages least-squares (2SLS) estimand in the continuous instrument with binary treatment case. Under standard conditions, we obtain weights that are nonnegative, integrate to unity, and assign larger values to instrument support points that deviate from their average. Our representation does not require instruments to be discretized nor relies on limiting arguments, such as those used in the definition of the marginal treatment effect (MTE). The pattern of the weights also has a clear interpretation. We believe these features of the representation to be useful for applied researchers when communicating their results. As a direct byproduct of our approach, we also obtain a representation of the 2SLS estimand as a weighted average of treatment effects among “marginal compliance” groups, without having to resort to the threshold-crossing representation underlying the MTE construction. The latter representation has an intuitive interpretation as well.

Defining and identifying local average treatment effects.

Defining and identifying local average treatment effects.

Improving Estimation Efficiency via Regression-Adjustment in Covariate-Adaptive Randomizations with Imperfect Compliance

Abstract We investigate how to improve efficiency using regression adjustments with covariates in covariate-adaptive randomizations (CARs) with imperfect subject compliance. Our regression-adjusted estimators, which are based on the doubly robust moment for local average treatment effects, are consistent and asymptotically normal even with heterogeneous probabilities of assignment and misspecified regression adjustments. We propose an optimal but potentially misspecified linear adjustment and its further improvement via a nonlinear adjustment, both of which lead to more efficient estimators than the one without adjustments. We also provide conditions for nonparametric and regularized adjustments to achieve the semiparametric efficiency bound under CARs.

A computational approach to identification of treatment effects for policy evaluation

For counterfactual policy evaluation, it is important to ensure that treatment parameters are relevant to policies in question. This is especially challenging under unobserved heterogeneity, as is well featured in the definition of the local average treatment effect (LATE). Being intrinsically local, the LATE is known to lack external validity in counterfactual environments. This paper investigates the possibility of extrapolating local treatment effects to different counterfactual settings when instrumental variables can be only binary. We propose a novel framework to systematically calculate sharp nonparametric bounds on various policy-relevant treatment parameters that are defined as weighted averages of the marginal treatment effect (MTE). Our framework is flexible enough to fully incorporate statistical independence (rather than mean independence) of instruments and a large menu of identifying assumptions beyond the shape restrictions on the MTE that have been considered in prior studies. We apply our method to understand the effects of medical insurance policies on the use of medical services.