Search results1 – 10 of 274
Relative to the randomized controlled trial (RCT), the basic regression discontinuity (RD) design suffers from lower statistical power and lesser ability to generalize…
Relative to the randomized controlled trial (RCT), the basic regression discontinuity (RD) design suffers from lower statistical power and lesser ability to generalize causal estimates away from the treatment eligibility cutoff. This chapter seeks to mitigate these limitations by adding an untreated outcome comparison function that is measured along all or most of the assignment variable. When added to the usual treated and untreated outcomes observed in the basic RD, a comparative RD (CRD) design results. One version of CRD adds a pretest measure of the study outcome (CRD-Pre); another adds posttest outcomes from a nonequivalent comparison group (CRD-CG). We describe how these designs can be used to identify unbiased causal effects away from the cutoff under the assumption that a common, stable functional form describes how untreated outcomes vary with the assignment variable, both in the basic RD and in the added outcomes data (pretests or a comparison group’s posttest). We then create the two CRD designs using data from the National Head Start Impact Study, a large-scale RCT. For both designs, we find that all untreated outcome functions are parallel, which lends support to CRD’s identifying assumptions. Our results also indicate that CRD-Pre and CRD-CG both yield impact estimates at the cutoff that have a similarly small bias as, but are more precise than, the basic RD’s impact estimates. In addition, both CRD designs produce estimates of impacts away from the cutoff that have relatively little bias compared to estimates of the same parameter from the RCT design. This common finding appears to be driven by two different mechanisms. In this instance of CRD-CG, potential untreated outcomes were likely independent of the assignment variable from the start. This was not the case with CRD-Pre. However, fitting a model using the observed pretests and untreated posttests to account for the initial dependence generated an accurate prediction of the missing counterfactual. The result was an unbiased causal estimate away from the cutoff, conditional on this successful prediction of the untreated outcomes of the treated.
This chapter analyzes a geographic quasi-experiment embedded in a cluster-randomized experiment in Honduras. In the experiment, average treatment effects of conditional…
This chapter analyzes a geographic quasi-experiment embedded in a cluster-randomized experiment in Honduras. In the experiment, average treatment effects of conditional cash transfers on school enrollment and child labor were large – especially in the poorest experimental blocks – and could be generalized to a policy-relevant population given the original sample selection criteria. In contrast, the geographic quasi-experiment yielded point estimates that, for two of three dependent variables, were attenuated. A judicious policy analyst without access to the experimental results might have provided misleading advice based on the magnitude of point estimates. We assessed two main explanations for the difference in point estimates, related to external and internal validity.
We discuss the two most popular frameworks for identification, estimation and inference in regression discontinuity (RD) designs: the continuity-based framework, where the…
We discuss the two most popular frameworks for identification, estimation and inference in regression discontinuity (RD) designs: the continuity-based framework, where the conditional expectations of the potential outcomes are assumed to be continuous functions of the score at the cutoff, and the local randomization framework, where the treatment assignment is assumed to be as good as randomized in a neighborhood around the cutoff. Using various examples, we show that (i) assuming random assignment of the RD running variable in a neighborhood of the cutoff implies neither that the potential outcomes and the treatment are statistically independent, nor that the potential outcomes are unrelated to the running variable in this neighborhood; and (ii) assuming local independence between the potential outcomes and the treatment does not imply the exclusion restriction that the score affects the outcomes only through the treatment indicator. Our discussion highlights key distinctions between “locally randomized” RD designs and real experiments, including that statistical independence and random assignment are conceptually different in RD contexts, and that the RD treatment assignment rule places no restrictions on how the score and potential outcomes are related. Our findings imply that the methods for RD estimation, inference, and falsification used in practice will necessarily be different (both in formal properties and in interpretation) according to which of the two frameworks is invoked.
This chapter develops a novel bootstrap procedure to obtain robust bias-corrected confidence intervals in regression discontinuity (RD) designs. The procedure uses a wild…
This chapter develops a novel bootstrap procedure to obtain robust bias-corrected confidence intervals in regression discontinuity (RD) designs. The procedure uses a wild bootstrap from a second-order local polynomial to estimate the bias of the local linear RD estimator; the bias is then subtracted from the original estimator. The bias-corrected estimator is then bootstrapped itself to generate valid confidence intervals (CIs). The CIs generated by this procedure are valid under conditions similar to Calonico, Cattaneo, and Titiunik’s (2014) analytical correction – that is, when the bias of the naive RD estimator would otherwise prevent valid inference. This chapter also provides simulation evidence that our method is as accurate as the analytical corrections and we demonstrate its use through a reanalysis of Ludwig and Miller’s (2007) Head Start dataset.
The authors use laboratory experiments to test two self-assessment tax mechanisms for facilitating land assembly. One mechanism is incentive compatible with a complex tax…
The authors use laboratory experiments to test two self-assessment tax mechanisms for facilitating land assembly. One mechanism is incentive compatible with a complex tax function, while the other uses a flat tax rate to mitigate implementation concerns. Sellers publicly declare a price for their land. Overstating its true value is penalized by using the declared price to assess a property tax; understating its value is penalized by allowing developers to buy the property at the declared price. The authors find that both mechanisms increase the rate of land assembly and gains from trade relative to a control in which sellers’ price declarations have no effect on their taxes. However, these effects are statistically insignificant or transitory. The assembly rates in our self-assessment treatments are markedly higher than those of prior experimental studies in which the buyer faces bargaining frictions, such as costly delay or capital constraints.
There has been much discussion regarding the necessity of moving away from precise (rules-based) standards toward less precise (principles-based) standards. This study…
There has been much discussion regarding the necessity of moving away from precise (rules-based) standards toward less precise (principles-based) standards. This study examines the impact of the proposed shift by using a controlled experiment to evaluate the influence of rule precision and information ambiguity on reporting decisions in the presence of monetary incentives to report aggressively. Using motivated reasoning theory as a framework, we predict that the malleability inherent in both rule precision and information ambiguity amplify biased reasoning in a manner that is consistent with individuals’ pecuniary incentives. In contrast, consistent with research exploring ambiguity aversion we predict that high levels of ambiguity will actually attenuate aggressive reporting. Our results support these predictions. Specifically, we find an interactive effect between rule precision and information ambiguity on self-interested reporting decisions at moderate levels of ambiguity. However, consistent with ambiguity aversion, we find decreased self-interested reporting decisions at high levels of ambiguity relative to moderate ambiguity. This study should be of interest to preparers, auditors, and regulators who are interested in identifying situations which amplify and diminish aggressive reporting.
Identification in a regression discontinuity (RD) design hinges on the discontinuity in the probability of treatment when a covariate (assignment variable) exceeds a known…
Identification in a regression discontinuity (RD) design hinges on the discontinuity in the probability of treatment when a covariate (assignment variable) exceeds a known threshold. If the assignment variable is measured with error, however, the discontinuity in the relationship between the probability of treatment and the observed mismeasured assignment variable may disappear. Therefore, the presence of measurement error in the assignment variable poses a challenge to treatment effect identification. This chapter provides sufficient conditions to identify the RD treatment effect using the mismeasured assignment variable, the treatment status and the outcome variable. We prove identification separately for discrete and continuous assignment variables and study the properties of various estimation procedures. We illustrate the proposed methods in an empirical application, where we estimate Medicaid takeup and its crowdout effect on private health insurance coverage.
The purpose of this paper is to estimate the causal effect of vocational high school (VHS) education on employment likelihood relative to general high school (GHS…
The purpose of this paper is to estimate the causal effect of vocational high school (VHS) education on employment likelihood relative to general high school (GHS) education in Turkey using Census data.
To address non-random selection into high school types, the authors collect construction dates of the VHSs at the town level and use various measures of VHS availability in the town by the age of 13 as instrumental variables.
The first-stage estimates suggest that the availability of VHS does not affect the overall high school graduation rates, but generates a substitution from GHS to VHS. The OLS estimates yield the result that individuals with a VHS degree are around 5 percentage points more likely to be employed compared to those with a GHS degree. When the authors use measures of VHS availability as instruments, they still find positive and statistically significant effect of VHS degree on employment likelihood relative to GHS degree. However, once they include town-level controls or town fixed effects, IV estimates get much smaller and become statistically insignificant.
The authorsconclude that, although VHS construction generates a substitution from GHS to VHS education, this substitution is not transformed into increased employment rates in a statistically significant way.