scholarly journals Regression Discontinuity and Heteroskedasticity Robust Standard Errors: Evidence from a Fixed-Bandwidth Approximation

2018 ◽  
Author(s):  
Otávio Bartalotti
Keyword(s):  
Regression Discontinuity ◽  
Standard Errors ◽  
Robust Standard Errors

scholarly journals Regression Discontinuity and Heteroskedasticity Robust Standard Errors: Evidence from a Fixed-Bandwidth Approximation

2018 ◽  
Vol 8 (1) ◽  
Author(s):  
Otávio Bartalotti
Keyword(s):  
Bias Correction ◽  
Asymptotic Theory ◽  
Regression Discontinuity ◽  
Traditional Approach ◽  
Standard Errors ◽  
Test Coverage ◽  
Regression Discontinuity Designs ◽  
The Common ◽  
Theoretical Results ◽  
Robust Standard Errors

AbstractIn regression discontinuity designs (RD), for a given bandwidth, researchers can estimate standard errors based on different variance formulas obtained under different asymptotic frameworks. In the traditional approach the bandwidth shrinks to zero as sample size increases; alternatively, the bandwidth could be treated as fixed. The main theoretical results for RD rely on the former, while most applications in the literature treat the estimates as parametric, implementing the usual heteroskedasticity-robust standard errors. This paper develops the “fixed-bandwidth” alternative asymptotic theory for RD designs, which sheds light on the connection between both approaches. I provide alternative formulas (approximations) for the bias and variance of common RD estimators, and conditions under which both approximations are equivalent. Simulations document the improvements in test coverage that fixed-bandwidth approximations achieve relative to traditional approximations, especially when there is local heteroskedasticity. Feasible estimators of fixed-bandwidth standard errors are easy to implement and are akin to treating RD estimators aslocallyparametric, validating the common empirical practice of using heteroskedasticity-robust standard errors in RD settings. Bias mitigation approaches are discussed and a novel bootstrap higher-order bias correction procedure based on the fixed bandwidth asymptotics is suggested.

scholarly journals Regression Discontinuity Designs Using Covariates

2019 ◽  
Vol 101 (3) ◽  
pp. 442-451 ◽  
Author(s):  
Sebastian Calonico ◽  
Matias D. Cattaneo ◽  
Max H. Farrell ◽  
Rocío Titiunik
Keyword(s):  
Mean Squared Error ◽  
Regression Discontinuity ◽  
Standard Errors ◽  
Local Polynomial ◽  
Squared Error ◽  
Software Packages ◽  
Continuous Covariates ◽  
Regression Functions ◽  
Regression Discontinuity Designs ◽  
Robust Standard Errors

We study regression discontinuity designs when covariates are included in the estimation. We examine local polynomial estimators that include discrete or continuous covariates in an additive separable way, but without imposing any parametric restrictions on the underlying population regression functions. We recommend a covariate-adjustment approach that retains consistency under intuitive conditions and characterize the potential for estimation and inference improvements. We also present new covariate-adjusted mean-squared error expansions and robust bias-corrected inference procedures, with heteroskedasticity-consistent and cluster-robust standard errors. We provide an empirical illustration and an extensive simulation study. All methods are implemented in R and Stata software packages.

scholarly journals Understanding, Choosing, and Unifying Multilevel and Fixed Effect Approaches

2020 ◽  
pp. 1-20
Author(s):  
Chad Hazlett ◽  
Leonard Wainstein
Keyword(s):  
Random Effects ◽  
Fixed Effects ◽  
Multilevel Models ◽  
Standard Errors ◽  
Point Estimate ◽  
Fe Model ◽  
Grouped Data ◽  
Coefficient Estimates ◽  
Political Science Education ◽  
Robust Standard Errors

Abstract When working with grouped data, investigators may choose between “fixed effects” models (FE) with specialized (e.g., cluster-robust) standard errors, or “multilevel models” (MLMs) employing “random effects.” We review the claims given in published works regarding this choice, then clarify how these approaches work and compare by showing that: (i) random effects employed in MLMs are simply “regularized” fixed effects; (ii) unmodified MLMs are consequently susceptible to bias—but there is a longstanding remedy; and (iii) the “default” MLM standard errors rely on narrow assumptions that can lead to undercoverage in many settings. Our review of over 100 papers using MLM in political science, education, and sociology show that these “known” concerns have been widely ignored in practice. We describe how to debias MLM’s coefficient estimates, and provide an option to more flexibly estimate their standard errors. Most illuminating, once MLMs are adjusted in these two ways the point estimate and standard error for the target coefficient are exactly equal to those of the analogous FE model with cluster-robust standard errors. For investigators working with observational data and who are interested only in inference on the target coefficient, either approach is equally appropriate and preferable to uncorrected MLM.

scholarly journals The association between WASH, nutrition, and early childhood growth faltering in rural Cambodia: a cross-sectional risk factor analysis

2021 ◽  
Author(s):  
Amanda Justine Lai ◽  
Ramya Ambikapathi ◽  
Oliver Cumming ◽  
Krisna Seng ◽  
Irene Velez ◽  
...  
Keyword(s):  
Drinking Water ◽  
Regression Models ◽  
Water Source ◽  
Community Level ◽  
Standard Errors ◽  
Drinking Water Source ◽  
Household Level ◽  
Growth Outcomes ◽  
Growth Faltering ◽  
Robust Standard Errors

Background Inadequate nutrition in early life and exposure to sanitation-related enteric pathogens have been linked to poor growth outcomes in children. Despite rapid development in Cambodia, high prevalence of growth faltering and stunting persist among children. This study aimed to assess nutrition and WASH variables and their association with nutritional status of children under 24 months in rural Cambodia. Methods We conducted surveys in 491 villages across 55 rural communes in Cambodia in September 2016 to measure associations between child, household, and community-level risk factors for stunting and length-for-age z-score (LAZ). A primary survey measured child-level variables, including anthropometric measures and risk factors for growth faltering and stunting, for 4,036 children under 24 months of age from 3,877 households (approximately 8 households per village). A secondary survey of 5,341 households, including the same households from the primary survey and an additional 1,464 households (approximately 3 additional household per village) from the same villages, assessed village-level WASH variables to understand community water, sanitation, and hygiene (WASH) conditions that may influence child growth outcomes. For LAZ, we calculated bivariate and adjusted associations (as mean differences) with 95% confidence intervals using generalized estimating equations (GEEs) to fit linear regression models with robust standard errors. For stunting, we calculated unadjusted and adjusted prevalence ratios (PRs) with 95% confidence intervals using GEEs to fit Poisson regression models with robust standard errors. For all models assessing effects of household-level variables, we used GEEs to account for clustering at the village level. Findings After adjustment for potential confounders, presence of water and soap at a household's handwashing station was found to be significantly associated (p<0.05) with increased LAZ (adjusted mean difference in LAZ +0.10, 95% CI 0.03 to 0.16), and household use of an improved drinking water source was associated with less stunting in children compared to households that did not use an improved source of drinking water (aPR 0.81, 95% CI 0.66 to 0.98); breastfeeding and community-level access to an improved drinking water source were associated with a lower LAZ score (-0.16, 95% CI -0.27 to -0.05; -0.13, 95% CI -0.26 to 0.00). No other nutrition (i.e., dietary diversity, meal frequency) or sanitation variables (i.e., household's safe disposal of child stools, household-level sanitation, community-level sanitation) were measured to be associated with LAZ scores or stunting in children under 24 months of age.

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