Guido W. Imbens

Identification of Causal Effects Using Instrumental Variables

Abstract We outline a framework for causal inference in settings where assignment to a binary treatment is ignorable, but compliance with the assignment is not perfect so that the receipt of treatment is nonignorable. To address the problems associated with comparing subjects by the ignorable assignment—an “intention-to-treat analysis”—we make use of instrumental variables, which have long been used by economists in the context of regression models with constant treatment effects. We show that the instrumental variables (IV) estimand can be embedded within the Rubin Causal Model (RCM) and that under some simple and easily interpretable assumptions, the IV estimand is the average causal effect for a subgroup of units, the compliers. Without these assumptions, the IV estimand is simply the ratio of intention-to-treat causal estimands with no interpretation as an average causal effect. The advantages of embedding the IV approach in the RCM are that it clarifies the nature of critical assumptions needed for a...

Identification and Estimation of Local Average Treatment Effects

We investigate conditions sufficient for identification of average treatment effects using instrumental variables. First we show that the existence of valid instruments is not sufficient to identify any meaningful average treatment effect. We then establish that the combination of an instrument and a condition on the relation between the instrument and the participation status is sufficient for identification of a local average treatment effect for those who can be induced to change their participation status by changing the value of the instrument. Finally we derive the probability limit of the standard IV estimator under these conditions. It is seen to be a weighted average of local average treatment effects.

Two-Stage Least Squares Estimation of Average Causal Effects in Models with Variable Treatment Intensity

Abstract Two-stage least squares (TSLS) is widely used in econometrics to estimate parameters in systems of linear simultaneous equations and to solve problems of omitted-variables bias in single-equation estimation. We show here that TSLS can also be used to estimate the average causal effect of variable treatments such as drug dosage, hours of exam preparation, cigarette smoking, and years of schooling. The average causal effect in which we are interested is a conditional expectation of the difference between the outcomes of the treated and what these outcomes would have been in the absence of treatment. Given mild regularity assumptions, the probability limit of TSLS is a weighted average of per-unit average causal effects along the length of an appropriately defined causal response function. The weighting function is illustrated in an empirical example based on the relationship between schooling and earnings.

Estimation of causal effects using propensity score weighting: An application to data on right heart catheterization

We consider methods for estimating causal effects of treatments when treatment assignment is unconfounded with outcomes conditional on a possibly large set of covariates. Robins and Rotnitzky (1995) suggested combining regression adjustment with weighting based on the propensity score (Rosenbaum and Rubin, 1983). We adopt this approach, allowing for a flexible specification of both the propensity score and the regression function. We apply these methods to data on the effects of right heart catheterization (RHC) studied in Connors et al (1996), and we find that our estimator gives stable estimates over a wide range of values for the two parameters governing the selection of variables.

On the Failure of the Bootstrap for Matching Estimators

Matching estimators are widely used in empirical economics for the evaluation of programs or treatments. Researchers using matching methods often apply the bootstrap to calculate the standard errors. However, no formal justification has been provided for the use of the bootstrap in this setting. In this article, we show that the standard bootstrap is, in general, not valid for matching estimators, even in the simple case with a single continuous covariate where the estimator is root-N consistent and asymptotically normally distributed with zero asymptotic bias. Valid inferential methods in this setting are the analytic asymptotic variance estimator of Abadie and Imbens (2006a) as well as certain modifications of the standard bootstrap, like the subsampling methods in Politis and Romano (1994).

Bias-Corrected Matching Estimators for Average Treatment Effects

In Abadie and Imbens (2006), it was shown that simple nearest-neighbor matching estimators include a conditional bias term that converges to zero at a rate that may be slower than N1/2. As a result, matching estimators are not N1/2-consistent in general. In this article, we propose a bias correction that renders matching estimators N1/2-consistent and asymptotically normal. To demonstrate the methods proposed in this article, we apply them to the National Supported Work (NSW) data, originally analyzed in Lalonde (1986). We also carry out a small simulation study based on the NSW example. In this simulation study, a simple implementation of the bias-corrected matching estimator performs well compared to both simple matching estimators and to regression estimators in terms of bias, root-mean-squared-error, and coverage rates. Software to compute the estimators proposed in this article is available on the authors’ web pages (http://www.economics.harvard.edu/faculty/imbens/software.html) and documented in Abadie et al. (2003).

Instrumental Variables Estimates Of The Effect Of Subsidized Training On The Quantiles Of Trainee Earnings

This paper reports estimates of the effects of JTPA training programs on the distribution of earnings. The estimation uses a new instrumental variable (IV) method that measures program impacts on quantiles. The quantile treatment effects (QTE) estimator reduces to quantile regression when selection for treatment is exogenously determined. QTE can be computed as the solution to a convex linear programming problem, although this requires first-step estimation of a nuisance function. We develop distribution theory for the case where the first step is estimated nonparametrically. For women, the empirical results show that the JTPA program had the largest proportional impact at low quantiles. Perhaps surprisingly, however, JTPA training raised the quantiles of earnings for men only in the upper half of the trainee earnings distribution.

Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity

This paper is about identification and estimation in a triangular nonparametric structural model with instrumental variables and non-additive errors. Identification and estimation is based on a control function consisting of the conditional distribution function of the endogenous variable given the instruments. We allow for a structural disturbance of arbitrary, unknown dimension while identifying interesting structural effects, such as quantile and average effects. We consider a two-step approach to estimation. We find that the convergence rate for the second-step structural estimator depends on the strength of the instrument.

Estimating outcome distributions for compliers in instrumental variables models

In Imbens and Ingrist (1994), Angrist, Imbens and Rubin (1996) and Imbens and Rubin (1997), assumptions have been outlined under which instrumental variables estimands can be given a causal interpretation as a local average treatment effect without requiring functional form or constant treatment effect assumptions. We extend these results by showing that under these assumptions one can estimate more from the data than the average causal effect for the subpopulation of compliers; one can, in principle, estimate the entire marginal distribution of the outcome under different treatments for this subpopulation. These distributions might be useful for a policy maker who wishes to take into account not only differences in average of earnings when contemplating the merits of one job training programme vs. another. We also show that the standard instrumental variables estimator implicitly estimates these underlying outcome distributions without imposing the required nonnegativity on these implicit density estimates, and that imposing non-negativity can substantially alter the estimates of the local average treatment effect. We illustrate these points by presenting an analysis of the returns to a high school education using quarter of birth as an instrument. We show that the standard instrumental variables estimates implicitly estimate the outcome distributions to be negative over a substantial range, and that the estimates of the local average treatment effect change considerably when we impose nonnegativity in any of a variety of ways.

The Interpretation of Instrumental Variables Estimators in Simultaneous Equations Models with an Application to the Demand for Fish

In markets where prices are determined by the intersection of supply and demand curves, standard identification results require the presence of instruments that shift one curve but not the other. These results are typically presented in the context of linear models with fixed coefficients and additive residuals. The first contribution of this paper is an investigation of the consequences of relaxing both the linearity and the additivity assumption for the interpretation of linear instrumental variables estimators. Without these assumptions, the standard linear instrumental variables estimator identifies a weighted average of the derivative of the behavioural relationship of interest. A second contribution is the formulation of critical identifying assumptions in terms of demand and supply at different prices and instruments, rather than in terms of functional-form specific residuals. Our approach to the simultaneous equations problem and the average-derivative interpretation of instrumental variables estimates is illustrated by estimating the demand for fresh whiting at the Fulton fish market. Strong and credible instruments for identification of this demand function are available in the form of weather conditions at sea.