arXiv subjects

Guido Imbens

Publications and source records attributed to Guido Imbens.

At least 37 records · Page 2Linked to original sources

arXiv2025

Using Experiments to Correct for Selection in Observational Studies

Researchers increasingly have access to two types of data: (i) large observational datasets where treatment (e.g., class size) is not randomized but several primary outcomes (e.g., graduation rates) and secondary outcomes (e.g., test scores) are observed and (ii) experimental data in which treatment is randomized but only secondary outcomes are observed. We develop a new method to estimate treatment effects on primary outcomes in such settings. We use the difference between the secondary outcome and its predicted value based on the experimental treatment effect to measure selection bias in the observational data. Controlling for this estimate of selection bias yields an unbiased estimate of the treatment effect on the primary outcome under a new assumption that we term latent unconfoundedness, which requires that the same confounders affect the primary and secondary outcomes. Latent unconfoundedness weakens the assumptions underlying commonly used surrogate estimators. We apply our estimator to identify the effect of third grade class size on students outcomes. Estimated impacts on test scores using OLS regressions in observational school district data have the opposite sign of estimates from the Tennessee STAR experiment. In contrast, selection-corrected estimates in the observational data replicate the experimental estimates. Our estimator reveals that reducing class sizes by 25% increases high school graduation rates by 0.7 percentage points. Controlling for observables does not change the OLS estimates, demonstrating that experimental selection correction can remove biases that cannot be addressed with standard controls.

stat.ME↗

arXiv2025

Comparing Experimental and Nonexperimental Methods: What Lessons Have We Learned Four Decades After LaLonde (1986)?

In 1986, Robert LaLonde published an article comparing nonexperimental estimates to experimental benchmarks (LaLonde 1986). He concluded that the nonexperimental methods at the time could not systematically replicate experimental benchmarks, casting doubt on their credibility. Following LaLonde's critical assessment, there have been significant methodological advances and practical changes, including (i) an emphasis on the unconfoundedness assumption separated from functional form considerations, (ii) a focus on the importance of overlap in covariate distributions, (iii) the introduction of propensity score-based methods leading to doubly robust estimators, (iv) methods for estimating and exploiting treatment effect heterogeneity, and (v) a greater emphasis on validation exercises to bolster research credibility. To demonstrate the practical lessons from these advances, we reexamine the LaLonde data. We show that modern methods, when applied in contexts with sufficient covariate overlap, yield robust estimates for the adjusted differences between the treatment and control groups. However, this does not imply that these estimates are causally interpretable. To assess their credibility, validation exercises (such as placebo tests) are essential, whereas goodness-of-fit tests alone are inadequate. Our findings highlight the importance of closely examining the assignment process, carefully inspecting overlap, and conducting validation exercises when analyzing causal effects with nonexperimental data.

econ.EM↗

arXiv2025

Using Multiple Outcomes to Adjust Standard Errors for Spatial Correlation

Empirical research in economics often examines the behavior of agents located in a geographic space. In such cases, statistical inference is complicated by the interdependence of economic outcomes across locations. A common approach to account for this dependence is to cluster standard errors based on a predefined geographic partition. A second strategy is to model dependence in terms of the distance between units. Dependence, however, does not necessarily stop at borders and is typically not determined by distance alone. This paper introduces a method that leverages observations of multiple outcomes to adjust standard errors for cross-sectional dependence. Specifically, a researcher, while interested in a particular outcome variable, often observes dozens of other variables for the same units. We show that these outcomes can be used to estimate dependence under the assumption that the cross-sectional correlation structure is shared across outcomes. We develop a procedure, which we call Thresholding Multiple Outcomes (TMO), that uses this estimate to adjust standard errors in a given regression setting. We show that adjustments of this form can lead to sizable reductions in the bias of standard errors in calibrated U.S. county-level regressions. Re-analyzing nine recent papers, we find that the proposed correction can make a substantial difference in practice.

econ.EM↗

arXiv2025

Identification of Average Treatment Effects in Nonparametric Panel Models

This paper studies identification of average treatment effects in a panel data setting. It introduces a novel nonparametric factor model and proves identification of average treatment effects. The identification proof is based on the introduction of a consistent estimator. Underlying the proof is a result that there is a consistent estimator for the expected outcome in the absence of the treatment for each unit and time period; this result can be applied more broadly, for example in problems of decompositions of group-level differences in outcomes, such as the much-studied gender wage gap.

econ.EM↗

arXiv2024

Computationally Efficient Estimation of Large Probit Models

Probit models are useful for modeling correlated discrete responses in many disciplines, including consumer choice data in economics and marketing. However, the Gaussian latent variable feature of probit models coupled with identification constraints pose significant computational challenges for its estimation and inference, especially when the dimension of the discrete response variable is large. In this paper, we propose a computationally efficient Expectation-Maximization (EM) algorithm for estimating large probit models. Our work is distinct from existing methods in two important aspects. First, instead of simulation or sampling methods, we apply and customize expectation propagation (EP), a deterministic method originally proposed for approximate Bayesian inference, to estimate moments of the truncated multivariate normal (TMVN) in the E (expectation) step. Second, we take advantage of a symmetric identification condition to transform the constrained optimization problem in the M (maximization) step into a one-dimensional problem, which is solved efficiently using Newton's method instead of off-the-shelf solvers. Our method enables the analysis of correlated choice data in the presence of more than 100 alternatives, which is a reasonable size in modern applications, such as online shopping and booking platforms, but has been difficult in practice with probit models. We apply our probit estimation method to study ordering effects in hotel search results on Expedia's online booking platform.

stat.ME↗

arXiv2024

Long-term Causal Inference Under Persistent Confounding via Data Combination

We study the identification and estimation of long-term treatment effects when both experimental and observational data are available. Since the long-term outcome is observed only after a long delay, it is not measured in the experimental data, but only recorded in the observational data. However, both types of data include observations of some short-term outcomes. In this paper, we uniquely tackle the challenge of persistent unmeasured confounders, i.e., some unmeasured confounders that can simultaneously affect the treatment, short-term outcomes and the long-term outcome, noting that they invalidate identification strategies in previous literature. To address this challenge, we exploit the sequential structure of multiple short-term outcomes, and develop three novel identification strategies for the average long-term treatment effect. We further propose three corresponding estimators and prove their asymptotic consistency and asymptotic normality. We finally apply our methods to estimate the effect of a job training program on long-term employment using semi-synthetic data. We numerically show that our proposals outperform existing methods that fail to handle persistent confounders.

stat.ME↗

arXiv2024

Estimating Treatment Effects using Multiple Surrogates: The Role of the Surrogate Score and the Surrogate Index

Estimating the long-term effects of treatments is of interest in many fields. A common challenge in estimating such treatment effects is that long-term outcomes are unobserved in the time frame needed to make policy decisions. One approach to overcome this missing data problem is to analyze treatments effects on an intermediate outcome, often called a statistical surrogate, if it satisfies the condition that treatment and outcome are independent conditional on the statistical surrogate. The validity of the surrogacy condition is often controversial. Here we exploit that fact that in modern datasets, researchers often observe a large number, possibly hundreds or thousands, of intermediate outcomes, thought to lie on or close to the causal chain between the treatment and the long-term outcome of interest. Even if none of the individual proxies satisfies the statistical surrogacy criterion by itself, using multiple proxies can be useful in causal inference. We focus primarily on a setting with two samples, an experimental sample containing data about the treatment indicator and the surrogates and an observational sample containing information about the surrogates and the primary outcome. We state assumptions under which the average treatment effect be identified and estimated with a high-dimensional vector of proxies that collectively satisfy the surrogacy assumption, and derive the bias from violations of the surrogacy assumption, and show that even if the primary outcome is also observed in the experimental sample, there is still information to be gained from using surrogates.

stat.ME↗

arXiv2024

Causal Models for Longitudinal and Panel Data: A Survey

In this survey we discuss the recent causal panel data literature. This recent literature has focused on credibly estimating causal effects of binary interventions in settings with longitudinal data, emphasizing practical advice for empirical researchers. It pays particular attention to heterogeneity in the causal effects, often in situations where few units are treated and with particular structures on the assignment pattern. The literature has extended earlier work on difference-in-differences or two-way-fixed-effect estimators. It has more generally incorporated factor models or interactive fixed effects. It has also developed novel methods using synthetic control approaches.

econ.EM↗

arXiv2024

Semiparametric Estimation of Treatment Effects in Observational Studies with Heterogeneous Partial Interference

In many observational studies in social science and medicine, subjects or units are connected, and one unit's treatment and attributes may affect another's treatment and outcome, violating the stable unit treatment value assumption (SUTVA) and resulting in interference. To enable feasible estimation and inference, many previous works assume exchangeability of interfering units (neighbors). However, in many applications with distinctive units, interference is heterogeneous and needs to be modeled explicitly. In this paper, we focus on the partial interference setting, and only restrict units to be exchangeable conditional on observable characteristics. Under this framework, we propose generalized augmented inverse propensity weighted (AIPW) estimators for general causal estimands that include heterogeneous direct and spillover effects. We show that they are semiparametric efficient and robust to heterogeneous interference as well as model misspecifications. We apply our methods to the Add Health dataset to study the direct effects of alcohol consumption on academic performance and the spillover effects of parental incarceration on adolescent well-being.

stat.ME↗

arXiv2023

Double and Single Descent in Causal Inference with an Application to High-Dimensional Synthetic Control

Motivated by a recent literature on the double-descent phenomenon in machine learning, we consider highly over-parameterized models in causal inference, including synthetic control with many control units. In such models, there may be so many free parameters that the model fits the training data perfectly. We first investigate high-dimensional linear regression for imputing wage data and estimating average treatment effects, where we find that models with many more covariates than sample size can outperform simple ones. We then document the performance of high-dimensional synthetic control estimators with many control units. We find that adding control units can help improve imputation performance even beyond the point where the pre-treatment fit is perfect. We provide a unified theoretical perspective on the performance of these high-dimensional models. Specifically, we show that more complex models can be interpreted as model-averaging estimators over simpler ones, which we link to an improvement in average performance. This perspective yields concrete insights into the use of synthetic control when control units are many relative to the number of pre-treatment periods.

econ.EM↗

arXiv2023

Optimal Experimental Design for Staggered Rollouts

In this paper, we study the design and analysis of experiments conducted on a set of units over multiple time periods where the starting time of the treatment may vary by unit. The design problem involves selecting an initial treatment time for each unit in order to most precisely estimate both the instantaneous and cumulative effects of the treatment. We first consider non-adaptive experiments, where all treatment assignment decisions are made prior to the start of the experiment. For this case, we show that the optimization problem is generally NP-hard, and we propose a near-optimal solution. Under this solution, the fraction entering treatment each period is initially low, then high, and finally low again. Next, we study an adaptive experimental design problem, where both the decision to continue the experiment and treatment assignment decisions are updated after each period's data is collected. For the adaptive case, we propose a new algorithm, the Precision-Guided Adaptive Experiment (PGAE) algorithm, that addresses the challenges at both the design stage and at the stage of estimating treatment effects, ensuring valid post-experiment inference accounting for the adaptive nature of the design. Using realistic settings, we demonstrate that our proposed solutions can reduce the opportunity cost of the experiments by over 50%, compared to static design benchmarks.

econ.EM↗

arXiv2023

Fixed Effects and the Generalized Mundlak Estimator

We develop a new approach for estimating average treatment effects in observational studies with unobserved group-level heterogeneity. We consider a general model with group-level unconfoundedness and provide conditions under which aggregate balancing statistics -- group-level averages of functions of treatments and covariates -- are sufficient to eliminate differences between groups. Building on these results, we reinterpret commonly used linear fixed-effect regression estimators by writing them in the Mundlak form as linear regression estimators without fixed effects but including group averages. We use this representation to develop Generalized Mundlak Estimators (GMEs) that capture group differences through group averages of (functions of) the unit-level variables and adjust for these group differences in flexible and robust ways in the spirit of the modern causal literature.

econ.EM↗

arXiv2023

A Design-Based Perspective on Synthetic Control Methods

Since their introduction in Abadie and Gardeazabal (2003), Synthetic Control (SC) methods have quickly become one of the leading methods for estimating causal effects in observational studies in settings with panel data. Formal discussions often motivate SC methods by the assumption that the potential outcomes were generated by a factor model. Here we study SC methods from a design-based perspective, assuming a model for the selection of the treated unit(s) and period(s). We show that the standard SC estimator is generally biased under random assignment. We propose a Modified Unbiased Synthetic Control (MUSC) estimator that guarantees unbiasedness under random assignment and derive its exact, randomization-based, finite-sample variance. We also propose an unbiased estimator for this variance. We document in settings with real data that under random assignment, SC-type estimators can have root mean-squared errors that are substantially lower than that of other common estimators. We show that such an improvement is weakly guaranteed if the treated period is similar to the other periods, for example, if the treated period was randomly selected. While our results only directly apply in settings where treatment is assigned randomly, we believe that they can complement model-based approaches even for observational studies.

econ.EM↗

arXiv2023

Synthetic Difference In Differences Estimation

In this paper, we describe a computational implementation of the Synthetic difference-in-differences (SDID) estimator of Arkhangelsky et al. (2021) for Stata. Synthetic difference-in-differences can be used in a wide class of circumstances where treatment effects on some particular policy or event are desired, and repeated observations on treated and untreated units are available over time. We lay out the theory underlying SDID, both when there is a single treatment adoption date and when adoption is staggered over time, and discuss estimation and inference in each of these cases. We introduce the sdid command which implements these methods in Stata, and provide a number of examples of use, discussing estimation, inference, and visualization of results.

econ.EM↗

arXiv2022

When Should You Adjust Standard Errors for Clustering?

In empirical work it is common to estimate parameters of models and report associated standard errors that account for "clustering" of units, where clusters are defined by factors such as geography. Clustering adjustments are typically motivated by the concern that unobserved components of outcomes for units within clusters are correlated. However, this motivation does not provide guidance about questions such as: (i) Why should we adjust standard errors for clustering in some situations but not others? How can we justify the common practice of clustering in observational studies but not randomized experiments, or clustering by state but not by gender? (ii) Why is conventional clustering a potentially conservative "all-or-nothing" adjustment, and are there alternative methods that respond to data and are less conservative? (iii) In what settings does the choice of whether and how to cluster make a difference? We address these questions using a framework of sampling and design inference. We argue that clustering can be needed to address sampling issues if sampling follows a two stage process where in the first stage, a subset of clusters are sampled from a population of clusters, and in the second stage, units are sampled from the sampled clusters. Then, clustered standard errors account for the existence of clusters in the population that we do not see in the sample. Clustering can be needed to account for design issues if treatment assignment is correlated with membership in a cluster. We propose new variance estimators to deal with intermediate settings where conventional cluster standard errors are unnecessarily conservative and robust standard errors are too small.

math.ST↗

arXiv2022

Matrix Completion Methods for Causal Panel Data Models

In this paper we study methods for estimating causal effects in settings with panel data, where some units are exposed to a treatment during some periods and the goal is estimating counterfactual (untreated) outcomes for the treated unit/period combinations. We propose a class of matrix completion estimators that uses the observed elements of the matrix of control outcomes corresponding to untreated unit/periods to impute the "missing" elements of the control outcome matrix, corresponding to treated units/periods. This leads to a matrix that well-approximates the original (incomplete) matrix, but has lower complexity according to the nuclear norm for matrices. We generalize results from the matrix completion literature by allowing the patterns of missing data to have a time series dependency structure that is common in social science applications. We present novel insights concerning the connections between the matrix completion literature, the literature on interactive fixed effects models and the literatures on program evaluation under unconfoundedness and synthetic control methods. We show that all these estimators can be viewed as focusing on the same objective function. They differ solely in the way they deal with identification, in some cases solely through regularization (our proposed nuclear norm matrix completion estimator) and in other cases primarily through imposing hard restrictions (the unconfoundedness and synthetic control approaches). The proposed method outperforms unconfoundedness-based or synthetic control estimators in simulations based on real data.

math.ST↗

arXiv2021

Covariate Balancing Sensitivity Analysis for Extrapolating Randomized Trials across Locations

The ability to generalize experimental results from randomized control trials (RCTs) across locations is crucial for informing policy decisions in targeted regions. Such generalization is often hindered by the lack of identifiability due to unmeasured effect modifiers that compromise direct transport of treatment effect estimates from one location to another. We build upon sensitivity analysis in observational studies and propose an optimization procedure that allows us to get bounds on the treatment effects in targeted regions. Furthermore, we construct more informative bounds by balancing on the moments of covariates. In simulation experiments, we show that the covariate balancing approach is promising in getting sharper identification intervals.

econ.EM↗

arXiv2021

Synthetic Design: An Optimization Approach to Experimental Design with Synthetic Controls

We investigate the optimal design of experimental studies that have pre-treatment outcome data available. The average treatment effect is estimated as the difference between the weighted average outcomes of the treated and control units. A number of commonly used approaches fit this formulation, including the difference-in-means estimator and a variety of synthetic-control techniques. We propose several methods for choosing the set of treated units in conjunction with the weights. Observing the NP-hardness of the problem, we introduce a mixed-integer programming formulation which selects both the treatment and control sets and unit weightings. We prove that these proposed approaches lead to qualitatively different experimental units being selected for treatment. We use simulations based on publicly available data from the US Bureau of Labor Statistics that show improvements in terms of mean squared error and statistical power when compared to simple and commonly used alternatives such as randomized trials.

stat.ME↗