Ivan A. Canay

This paper studies the properties of the wild bootstrap-based test proposed in Cameron et al. (2008) for testing hypotheses about the coeffcients in a linear regression model with clustered data.

This paper studies inference in randomized controlled trials with covariate-adaptive randomization when there are multiple treatments. More specically, we study in this setting inference about the average effect of one or more treatments relative to other treatments or a control.

This paper studies the properties of the wild bootstrap-based test proposed in Cameron et al. (2008) in settings with clustered data.

In the regression discontinuity design (RDD), it is common practice to assess the credibility of the design by testing the continuity of the density of the running variable at the cut-off, e.g., McCrary (2008). In this paper we propose a new test for continuity of a density at a point based on the so-called g-order statistics, and study its properties under a novel asymptotic framework.

This paper studies inference in randomized controlled trials with covariate-adaptive randomization when there are multiple treatments. More specifically, we study in this setting inference about the average effect of one or more treatments relative to other treatments or a control. As in Bugni et al. (2017), covariate-adaptive randomization refers to randomization schemes that first stratify according to baseline covariates and then assign treatment status so as to achieve "balance" within each stratum. In contrast to Bugni et al. (2017), however, we allow for the proportion of units being assigned to each of the treatments to vary across strata.

This paper studies inference for the average treatment effect in randomized controlled trials with covariate-adaptive randomization. Here, by covariate-adaptive randomization, we mean randomization schemes that first stratify according to baseline covariates and then assign treatment status so as to achieve "balance" within each stratum.

In the regression discontinuity design (RDD), it is common practice to asses the credibility of the design by testing whether the means of baseline covariates do not change at the cutoff(or threshold) of the running variable. This practice is partly motivated by the stronger im-plication derived by Lee (2008), who showed that under certain conditions the distribution of baseline covariates in the RDD must be continuous at the cutoff. We propose a permutation test based on the so-called induced ordered statistics for the null hypothesis of continuity of the distribution of baseline covariates at the cutoff; and introduce a novel asymptotic framework to analyze its properties. The asymptotic framework is intended to approximate a small sample phenomenon: even though the total number n of observations may be large, the number of effective observations local to the cutoff is often small. Thus, while traditional asymptotics in RDD require a growing number of observations local to the cutoff as n → ∞, our framework keeps the number q of observations local to the cutoff fixed as n → ∞. The new test is easy to implement, asymptotically valid under weak conditions, exhibits finite sample validity under stronger conditions than those needed for its asymptotic validity, and has favorable power properties relative to tests based on means. In a simulation study, we find that the new test controls size remarkably well across designs. We then use our test to evaluate the plausibility of the design in Lee (2008), a well-known application of the RDD to study incumbency advantage.

In the regression discontinuity design, it is common practice to asses the credibility of the design by testing whether the means of baseline covariates do not change at the cutoff (or threshold) of the running variable. This practice is partly motivated by the stronger implication derived by Lee (2008), who showed that under certain conditions the distribution of baseline covariates in the RDD must be continuous at the cutoff. We propose a permutation test based on the so-called induced ordered statistics for the null hypothesis of continuity of the distribution of baseline covariates at the cutoff; and introduce a novel asymptotic framework to analyze its properties. The asymptotic framework is intended to approximate a small sample phenomenon: even though the total number n of observations may be large, the number of effective observations local to the cutoff is often small. Thus, while traditional asymptotics in RDD require a growing number of observations local to the cutoff as n → ∞ , our framework keeps the number q of observations local to the cutoff fixed as n → ∞. The new test is easy to implement, asymptotically valid under weak conditions, exhibits finite sample validity under stronger conditions than those needed for its asymptotic validity, and has favorable power properties relative to tests based on means. In a simulation study, we find that the new test controls size remarkably well across designs. We then use our test to evaluate the validity of the design in Lee (2008), a well-known application of the RDD to study incumbency advantage.

This paper studies inference for the average treatment effect in randomized controlled trials with covariate-adaptive randomization. Here, by covariate-adaptive randomization, we mean randomization schemes that first stratify according to baseline covariates and then assign treatment status so as to achieve "balance" within each stratum. Such schemes include, for example, Efron's biased-coin design and stratied block randomization. When testing the null hypothesis that the average treatment effect equals a pre-specified value in such settings, we first show that the usual two-sample t-test is conservative in the sense that it has limiting rejection probability under the null hypothesis no greater than and typically strictly less than the nominal level. In a simulation study, we find that the rejection probability may in fact be dramatically less than the nominal level. We show further that these same conclusions remain true for a naïve permutation test, but that a modified version of the permutation test yields a test that is non-conservative in the sense that its limiting rejection probability under the null hypothesis equals the nominal level for a wide variety of randomization schemes. The modified version of the permutation test has the additional advantage that it has rejection probability exactly equal to the nominal level for some distributions satisfying the null hypothesis and some randomization schemes. Finally, we show that the usual t-test (on the coefficient on treatment assignment) in a linear regression of outcomes on treatment assignment and indicators for each of the strata yields a non-conservative test as well under even weaker assumptions on the randomization scheme. In a simulation study, we find that the non-conservative tests have substantially greater power than the usual two-sample t-test.

This paper surveys some of the recent literature on inference in partially identified models.

This paper introduces a bootstrap-based inference method for functions of the parameter vector in a moment (in)equality model.

This paper studies inference for the average treatment effect in randomized controlled trials with covariate-adaptive randomization.

This paper proposes an asymptotically valid permutation test for a testable implication of the identification assumption in the regression discontinuity design (RDD).

This paper studies the problem of specification testing in partially identified models defined by moment (in)equalities.

This paper introduces a bootstrap-based inference method for functions of the parameter vector in a moment (in)equality model.

This paper studies the problem of specification testing in partially identified models defined by a finite number of moment equalities and inequalities (i.e. (in)equalities).

This paper introduces a new hypothesis test for the null hypothesis H0 : f(θ) = y0, where f(
.) is a known function, y0 is a known constant, and θ is a parameter that is partially identied by a moment (in)equality model.

This paper examines three distinct hypothesis testing problems that arise in the context of identification of some nonparametric models with endogeneity.

This paper studies the problem of specification testing in partially indentified models defined by a finite number of moment equalities and inequalities (i.e., (in)equalities).

This paper examines three distinct hypothesis testing problems that arise in the context of identification of some nonparametric models with endogeneity.