Testing the Presence of Outliers to Assess Misspecification in Regression Models

52 Pages Posted: 8 Aug 2018  

Xiyu Jiao

University of Oxford - Department of Economics

Felix Pretis

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

Date Written: July 20, 2018

Abstract

The presence of outlying observations in a regression model can be indicative of model misspecification, consequently, it is important to check for possible outlier contamination. However, algorithms used to detect outliers have a positive probability of finding outliers even when, in fact, the data generation process has no outliers. Deriving distributional results on the expected retention rate of falsely discovered outliers, we propose two set of tests for the overall presence of outliers and thus model misspecification: first, tests on whether the observed proportion and number of detected outliers deviate from their expected values. Second, ‘scaling’ tests on whether the number of detected outliers decreases proportionally with the level of significance used to detect outliers. We derive the asymptotic distribution of the tests for the presence of outliers based on iterated 1-step Huber-skip M-estimators. The first set of tests has power against the number of outliers present, while the second set of tests has power against both outlier magnitude and number. In applications of the tests we consider a cross-sectional macroeconomic model of economic growth, and re-visit a set of previous studies using indicator saturation. The tests are valid for stationary as well as (stochastically) trending regressors and can readily be implemented using Autometrics in PcGive or the R-package gets.

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 to Assess Misspecification in Regression Models (July 20, 2018). Available at SSRN: https://ssrn.com/abstract=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, Department of Economics

Manor Road
Oxford, OX1 3UQ
United Kingdom

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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