Regression Discontinuity Design with Many Thresholds

Bertanha, Marinho

doi:10.2139/ssrn.2712957

Cited by 27 publications

(21 citation statements)

References 36 publications

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“…An extension of our methods to fuzzy RD designs is given in the Supporting Information Appendix . The methodological results discussed in this paper can also be used in other related RD settings, including multi‐running variable RD designs (e.g., Papay, Willett, & Murnane, ), geographic RD designs (e.g., Keele & Titiunik, ), and multi‐cutoff RD designs (e.g., Bertanha, ; Cattaneo et al., ). We do not discuss these extensions here to conserve space.…”

Section: Resultsmentioning

confidence: 97%

Comparing Inference Approaches for RD Designs: A Reexamination of the Effect of Head Start on Child Mortality

Cattaneo¹,

Titiunik²,

Vázquez-Baré³

2017

J. Pol. Anal. Manage.

132

145

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The regression discontinuity (RD) design is a popular quasi‐experimental design for causal inference and policy evaluation. The most common inference approaches in RD designs employ “flexible” parametric and nonparametric local polynomial methods, which rely on extrapolation and large‐sample approximations of conditional expectations using observations somewhat near the cutoff that determines treatment assignment. An alternative inference approach employs the idea of local randomization, where the very few units closest to the cutoff are regarded as randomly assigned to treatment and finite‐sample exact inference methods are used. In this paper, we contrast these approaches empirically by re‐analyzing the influential findings of Ludwig and Miller (), who studied the effect of Head Start assistance on child mortality employing parametric RD methods. We first review methods based on approximations of conditional expectations, which are relatively well developed in the literature, and then present new methods based on randomization inference. In particular, we extend the local randomization framework to allow for parametric adjustments of the potential outcomes; our extended framework substantially relaxes strong assumptions in prior literature and better resembles other RD inference methods. We compare all these methods formally, focusing on both estimands and inference properties. In addition, we develop new approaches for randomization‐based sensitivity analysis specifically tailored to RD designs. Applying all these methods to the Head Start data, we find that the original RD treatment effect reported in the literature is quite stable and robust, an empirical finding that enhances the credibility of the original result. All the empirical methods we discuss are readily available in general purpose software in R and Stata; we also provide the dataset and software code needed to replicate all our results.

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Section: Resultsmentioning

confidence: 97%

Comparing Inference Approaches for RD Designs: A Reexamination of the Effect of Head Start on Child Mortality

Cattaneo¹,

Titiunik²,

Vázquez-Baré³

2017

J. Pol. Anal. Manage.

132

145

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“…Consequently, around each cutoff, the municipalities are arbitrarily similar, with the only difference being their city-council sizes. q q q q q q q q q q qq q qq q qq q qq q qqq q q q q qq q q qq q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q qq qqq q q q q qq q q qqq q q q q qq q q q qq q q q q qq q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q qq q q qqq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq qq q q q q q qq q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q qq q q q q q q qq q q q q qq q q q q q q q q q q q qq q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q qqq q q q q q q q q qq q qq q q qq q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q qq q q q q qq q q q q qq q q q qq q q q q qq q q q q q q q q q q qq q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qqq q q q q q q q q q q q q qq q q q qq q qq q q q q q q q qq qq q q q q q q q q q q q q q q q q q qq q q q q q q q q q qq q q q q qq q q q q q q q q q q q qq q q qq q q q q q q q q q qq q qq q q q q q q q q q q q q q qq q q q q q q q q q q q q q q qq q q q q q q q q q q q For the second assumption, we know that running RDD in multiple thresholds may lead to inconsistent estimates when there is an imbalance in the running variable's distribution around the cutoffs (Bertanha 2017;Eggers et al 2018). For example, in our dataset, we have twelve discontinuities, and at each threshold we have a sharp increase of one councilor, from 9 to 21.…”

Section: Empirical Strategymentioning

confidence: 99%

Legislature Size and Welfare: Evidence from Brazil

Mignozzetti¹,

Cepaluni²

2019

Preprint

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What is the effect of legislature size on public service provision? While the literature relates legislature size to representation and government expenditure, its implications for welfare remain understudied. In this paper, we investigate the effects of legislature size on welfare, exploiting exogenous changes in city-council size in Brazil between 2005 and 2008. We show that adding a legislator improves education and health care. However, the results prove true for the services that are believed to be highly salient to voters and are easiest to claim credit for. In this sense, education quality and preventive health care remain unaffected while primary school enrollment and infant mortality significantly improve. To investigate the mechanism, we surveyed former councilors and analyzed 346,553 bills proposed by municipalities in the period. This analysis largely corroborates our findings, showing that politicians prefer to provide private and local public goods. This paper has implications for the design of legislative institutions.

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“…We largely follow the widely used Rubin Causal Model set up, extended to the fuzzy regression discontinuity design by Hahn, Todd, and Van Der Klaauw (2001), HTV from hereon. Recent theoretical contributions include Porter (2003), McCrary (2008), Imbens and Kalyanaraman (2012), Calonico, Cattaneo and Titiunik (2014abc), Dong (2014), Dong and Lewbel (2014), Bertanha (2014), and Gelman and Imbens (2014). Influential applications include Black (1999), Berk and Rauma (1983), Angrist andLavy (1999), Van Der Klaauw (2002), Jacob and Lefgren (2004), Battistin and Rettore (2008), Lee (2008), Lalive (2008), andMatsudaira (2008).…”

Section: Set Upmentioning

confidence: 99%