Testing the Presence of Outliers in Regression Models

72 Pages Posted: 8 Aug 2018 Last revised: 15 Feb 2020

See all articles by Xiyu Jiao

Xiyu Jiao

University of Oxford - Department of Economics

Felix Pretis

University of Victoria, Department of Economics; University of Oxford - Institute for New Economic Thinking at the Oxford Martin School

Date Written: July 20, 2018

Abstract

Algorithms used to detect outliers in regression models have a positive probability of finding outliers even when the data generation process has no outliers. We propose two sets of tests for the overall presence of outliers based on the false-discovery rate of outliers. First, `simple' tests on whether the proportion (or number) of detected outliers deviates from its expected value. Second, `scaling' tests on whether the proportion (or number) of detected outliers decreases proportionally with the level of the cut-off used to detect outliers. The proposed tests can be uniformly applied to regressions regardless of whether the regressors are stationary, deterministically trending, unit root, or explosive processes. We show the versatility of the tests in a classic cross-sectional model of economic growth as well as a panel difference-in-differences model of CO2 emissions in response to the introduction of North America's first major carbon tax. Our tests show the presence of significant outliers in emissions in the un-taxed control group which results in an over-estimation of the emissions reductions in response to the carbon tax.

Keywords: misspecification, outlier detection, robust estimation, iterated 1-step Huber-skip M-estimator, indicator saturation

JEL Classification: C12, C52

Suggested Citation

Jiao, Xiyu and Pretis, Felix, Testing the Presence of Outliers in Regression Models (July 20, 2018). Available at SSRN: https://ssrn.com/abstract=3217213 or http://dx.doi.org/10.2139/ssrn.3217213

Xiyu Jiao

University of Oxford - Department of Economics ( email )

10 Manor Rd
Oxford, OX1 3UQ
United Kingdom

Felix Pretis (Contact Author)

University of Victoria, Department of Economics ( email )

3800 Finnerty Rd
Victoria, British Columbia V8P 5C2
Canada

University of Oxford - Institute for New Economic Thinking at the Oxford Martin School ( email )

Eagle House
Walton Well Road
Oxford, OX2 6ED
United Kingdom

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