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Abstract Linear instrumental variable estimators, such as two-stage least squares (TSLS), are commonly interpreted as estimating non-negatively weighted averages of causal effects, referred to as local average treatment effects (LATEs). We examine whether the LATE interpretation actually applies to the types of TSLS specifications that are used in practice. We show that if the specification includes covariates—which most empirical work does—then the LATE interpretation does not apply in general. Instead, the TSLS estimator will, in general, reflect treatment effects for both compliers and always/never-takers, and some treatment effects for the always/never-takers will necessarily be negatively weighted. We show that the only specifications that have a LATE interpretation are “saturated” specifications that control for covariates nonparametrically, implying that such specifications are both sufficient and necessary for TSLS to have a LATE interpretation, at least without additional parametric assumptions. This result is concerning because, as we document, empirical researchers almost never control for covariates nonparametrically, and rarely discuss or justify parametric specifications of covariates. We apply our results to thirteen empirical studies and find strong evidence that the LATE interpretation of TSLS is far from accurate for the types of specifications actually used in practice. We offer concrete recommendations for practice motivated by our theoretical and empirical results. 

Abstract We show how to use randomized participation incentives to test and account for nonresponse bias in surveys. We first use data from a survey about labour market conditions, linked to full-population administrative data, to provide evidence of large differences in labour market outcomes between survey participants and nonparticipants, differences which would not be observable to an analyst who only has access to the survey data. These differences persist even after correcting for observable characteristics. We then use the randomized incentives in our survey to directly test for nonresponse bias and find evidence of substantial bias. Next, we apply a range of existing methods that account for nonresponse bias and find they produce bounds (or point estimates) that are either wide or far from the ground truth. We investigate the failure of these methods by taking a closer look at the determinants of participation, finding that the composition of participants changes in opposite directions in response to incentives and reminder emails. We develop a model of participation that allows for two dimensions of unobserved heterogeneity in the participation decision. Applying the model to our data produces bounds (or point estimates) that are narrower and closer to the ground truth than the other methods. Our results highlight the benefits of including randomized participation incentives in surveys. Both the testing procedure and the methods for bias adjustment may be attractive tools for researchers who are able to embed randomized incentives into their survey. 

We develop a new nonparametric approach for discrete choice and use it to analyze the demand for health insurance in the California Affordable Care Act marketplace. The model allows for endogenous prices and instrumental variables, while avoiding parametric functional form assumptions about the unobserved components of utility. We use the approach to estimate bounds on the effects of changing premiums or subsidies on coverage choices, consumer surplus, and government spending on subsidies. We find that a $10 decrease in monthly premium subsidies would cause a decline of between 1.8% and 6.7% in the proportion of subsidized adults with coverage. The reduction in total annual consumer surplus would be between $62 and $74 million, while the savings in yearly subsidy outlays would be between $207 and $602 million. We estimate the demand impacts of linking subsidies to age, finding that shifting subsidies from older to younger buyers would increase average consumer surplus, with potentially large impacts on enrollment. We also estimate the consumer surplus impact of removing the highly‐subsidized plans in the Silver metal tier, where we find that a nonparametric model is consistent with a wide range of possibilities. We find that comparable mixed logit models tend to yield price sensitivity estimates toward the lower end of the nonparametric bounds, while producing consumer surplus impacts that can be both higher and lower than the nonparametric bounds depending on the specification of random coefficients. 

This paper considers the problem of testing whether there exists a non‐negative solution to a possibly under‐determined system of linear equations with known coefficients. This hypothesis testing problem arises naturally in a number of settings, including random coefficient, treatment effect, and discrete choice models, as well as a class of linear programming problems. As a first contribution, we obtain a novel geometric characterization of the null hypothesis in terms of identified parameters satisfying an infinite set of inequality restrictions. Using this characterization, we devise a test that requires solving only linear programs for its implementation, and thus remains computationally feasible in the high‐dimensional applications that motivate our analysis. The asymptotic size of the proposed test is shown to equal at most the nominal level uniformly over a large class of distributions that permits the number of linear equations to grow with the sample size. 

Instrumental variable (IV) strategies are widely used to estimate causal effects in economics, political science, epidemiology, sociology, psychology, and other fields. When there is unobserved heterogeneity in causal effects, standard linear IV estimators only represent effects for complier subpopulations (Imbens and Angrist, 1994). Marginal treatment effect (MTE) methods (Heckman and Vytlacil, 1999, 2005) allow researchers to use additional assumptions to extrapolate beyond complier subpopulations. We discuss a flexible framework for MTE methods based on linear regression and the generalized method of moments. We show how to implement the framework using the ivmte package for R. 

We discuss the ivcrc command, which implements an instrumental-variables (IV) estimator for the linear correlated random-coefficients model. The correlated random-coefficients model is a natural generalization of the standard linear IV model that allows for endogenous, multivalued treatments and unobserved heterogeneity in treatment effects. The estimator implemented by ivcrc uses recent semiparametric identification results that allow for flexible functional forms and permit instruments that may be binary, discrete, or continuous. The ivcrc command also allows for the estimation of varying-coefficient regressions, which are closely related in structure to the proposed IV estimator. We illustrate the use of ivcrc by estimating the returns to education in the National Longitudinal Survey of Young Men.