Should Children Do More Enrichment Activities? Leveraging Bunching to Correct for Endogeneity

Caetano, Carolina; Caetano, Gregorio; Nielsen, Eric

doi:10.17016/feds.2020.036

Cited by 6 publications

(4 citation statements)

References 34 publications

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“…In other applications (e.g. Caetano et al 2022a, Caetano et al 2022b, we see stability being achieved only beyond a certain number of clusters, thus indicating that the variation in Z is necessary, to a degree, in order to fully correct for endogeneity. baum 2020).…”

Section: Estimatementioning

confidence: 79%

“… Z] which we use in our application as well as in two other applications of our method: Caetano et al (2022a) and Caetano et al (2022b). Estimation remains feasible when the vector of controls Z is of high dimension, or when Z is too complex for the application of standard nonparametric estimation techniques, e.g.…”

Section: Discretization Of Z Through Clusteringmentioning

confidence: 99%

“…In addition, clusters may be used to relax the assumption of linearity in Z. For instance, Caetano et al (2022a) and Caetano et al (2022b) include cluster fixed effects in the corrected regression in order to allow control variables to enter the outcome equation more flexibly.…”

Section: Estimatementioning

confidence: 99%

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Correcting for Endogeneity in Models with Bunching

Caetano,

Nielsen

2023

Journal of Business & Economic Statistics

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In this online appendix, we provide additional details and extensions, including the following sections: A, which contains extensions of the approach into nonlinear and nonparametric models; B, a supplementary identification section that provides formal details of the claims made in the remarks from Section 2; C, a supplementary estimation section which contains technical assumptions and further discussion, as well as some additional results; D, which details the clustering discretization strategy; E, which discusses the implementation of the tests of the identification assumptions in our application and provides some additional technical details; F, an empirical Monte Carlo study; and G, where all the proofs are gathered. A Nonlinear/Nonparametric Model SpecificationsThis section presents some generalizations of the model in Section 2. Note that equation (3) can be relaxed both directly, in its linear structure, and in how flexibly one defines ⌘ in equation (2). We discuss several possible generalizations here, although these examples are by no means exhaustive. A.1 Linear Correlated Random CoefficientsWe relax linearity by allowing the treatment effect to be a known parametric function of X and Z. For example, suppose that = ↵ 0 X + Z 0 ↵ in equation ( 3). This is equivalent to Garen (1984) 's model (see, e.g., Chay and Greenstone 2005), except that we do not exclude Z from the structural equation, and we do not require that Z and ⌘ are independent. Then,is identified, then so are ↵ 0 and ↵, and thus we can identify the treatment effects. Our estimation results also cover this model (see Remark C.3 in Appendix C.1).Other models where = g 1 (X, Z; ↵ 1 ) for some function g 1 known up to the finite parameter vector ↵ 1 , may be identified analogously. If E[Y |X, Z] is linear in parameters, estimation is covered by the results in Section 4. Otherwise, this is a special case of the next model. A.2 Nonlinear Correlated Random EffectsDefine ⌘ as X ⇤ = h 1 (Z;  1 ) + h 2 (Z;  2 )⌘,

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Section: Estimatementioning

confidence: 79%

Section: Discretization Of Z Through Clusteringmentioning

confidence: 99%

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Correcting for Endogeneity in Models with Bunching

Caetano,

Nielsen

2023

Journal of Business & Economic Statistics

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“…Using bunching to estimate elasticities began with Saez (2010), Chetty et al (2011), and Kleven and Waseem (2013). Following these influential articles, bunching methods became a popular way to estimate elasticities in a variety of settings, such as electricity demand (Ito 2014), real estate taxes (Kopczuk and Munroe 2015), labor regulations (Garicano, Lelarge, and Van Reenan 2016), prescription drug insurance (Einav, Finkelstein, and Schrimpf 2017), marathon finishing times (Allen et al 2017), attribute-based regulations (Ito and Sallee 2018), education (Dee et al 2019; Caetano, Caetano, and Nielsen 2020a), minimum wage (Jales 2018; Cengiz et al 2019), and air-pollution data manipulation (Ghanem, Shen, and Zhang 2020), among others. Differences in mass point sizes across groups has been exploited as the first stage in a two-stage approach to control for endogeneity (Chetty, Friedman, and Saez 2013; Caetano 2015; Grossman and Khalil 2020).…”

Section: Introductionmentioning

confidence: 99%

Bunching estimation of elasticities using Stata

Bertanha

McCallum

Payne

et al. 2022

The Stata Journal: Promoting communications on statistics and S

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Typical censoring models have mass points at the upper or lower tails, or at both tails, of an otherwise continuous outcome distribution. In contrast, we consider a censoring model with a mass point in the interior of the outcome distribution. We refer to this mass point as “bunching” and use it to estimate model parameters. For example, economic theory suggests that, for increasing marginal income tax rates, many taxpayers will report income exactly at the threshold where the tax rate increases. This translates into a censoring model with bunching at the threshold. The size of this mass point of taxpayers can be used to estimate an elasticity parameter that summarizes taxpayers’ responses to taxes. In this article, we introduce the command bunching, which implements new nonparametric and semiparametric identification methods for estimating elasticities developed by Bertanha, McCallum, and Seegert (2021, Technical Report 2021-002, Board of Governors of the Federal Reserve System). These methods rely on weaker assumptions than what are currently made in the literature and result in meaningfully different estimates of the elasticity.

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