On Testing Continuity and the Detection of Failures

65 Pages Posted: 1 Jul 2019

See all articles by Matthew Backus

Matthew Backus

Cornell University - Department of Economics

Sida Peng

Cornell University

Date Written: June 2019

Abstract

Estimation of discontinuities is pervasive in applied economics: from the study of sheepskin effects to prospect theory and “bunching” of reported income on tax returns, models that predict discontinuities in outcomes are uniquely attractive for empirical testing. However, existing empirical methods often rely on assumptions about the number of discontinuities, the type, the location, or the underlying functional form of the model. We develop a nonparametric approach to the study of arbitrary discontinuities — point discontinuities as well as jump discontinuities in the nth derivative, where n = 0,1,... — that does not require such assumptions. Our approach exploits the development of false discovery rate control methods for lasso regression as proposed by G’Sell et al. (2015). This framework affords us the ability to construct valid tests for both the null of continuity as well as the significance of any particular discontinuity without the computation of nonstandard distributions. We illustrate the method with a series of Monte Carlo examples and by replicating prior work detecting and measuring discontinuities, in particular Lee (2008), Card et al. (2008), Reinhart and Rogoff (2010), and Backus et al. (2018b).

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Suggested Citation

Backus, Matthew and Peng, Sida, On Testing Continuity and the Detection of Failures (June 2019). NBER Working Paper No. w26016. Available at SSRN: https://ssrn.com/abstract=3412690

Matthew Backus (Contact Author)

Cornell University - Department of Economics ( email )

414 Uris Hall
Ithaca, NY 14853-7601
United States

Sida Peng

Cornell University ( email )

Ithaca, NY 14853
United States

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