Regression Discontinuity and Heteroskedasticity Robust Standard Errors: Evidence from a Fixed-Bandwidth Approximation
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The Department of Economic Science was founded in 1898 to teach economic theory as a truth of industrial life, and was very much concerned with applying economics to business and industry, particularly agriculture. Between 1910 and 1967 it showed the growing influence of other social studies, such as sociology, history, and political science. Today it encompasses the majors of Agricultural Business (preparing for agricultural finance and management), Business Economics, and Economics (for advanced studies in business or economics or for careers in financing, management, insurance, etc).
History
The Department of Economic Science was founded in 1898 under the Division of Industrial Science (later College of Liberal Arts and Sciences); it became co-directed by the Division of Agriculture in 1919. In 1910 it became the Department of Economics and Political Science. In 1913 it became the Department of Applied Economics and Social Science; in 1924 it became the Department of Economics, History, and Sociology; in 1931 it became the Department of Economics and Sociology. In 1967 it became the Department of Economics, and in 2007 it became co-directed by the Colleges of Agriculture and Life Sciences, Liberal Arts and Sciences, and Business.
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1898–present
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- Department of Economic Science (1898–1910)
- Department of Economics and Political Science (1910-1913)
- Department of Applied Economics and Social Science (1913–1924)
- Department of Economics, History and Sociology (1924–1931)
- Department of Economics and Sociology (1931–1967)
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- College of Agricultural and Life Sciences (parent college)
- College of Liberal Arts and Sciences (parent college)
- College of Business (parent college)
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Abstract
In 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 as locally parametric, 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.
Comments
This article is published as Bartalotti,O. Regression Discontinuity and Heteroskedasticity Robust Standard Errors: Evidence from a Fixed-Bandwidth Approximation. Journal of Econometric Methods, 2018; DOI: 10.1515/jem-2016-0007. Posted with permission.