Testing for Coefficient Distortion due to Outliers with an Application to the Economic Impacts of Climate Change

78 Pages Posted: 2 Sep 2021 Last revised: 27 Jul 2022

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

Moritz Schwarz

Smith School of Enterprise and the Environment, University of Oxford; Climate Econometrics, Institute for New Economic Thinking at the Oxford Martin School

Date Written: August 31, 2021

Abstract

Outlying observations can bias regression estimates, requiring the use of robust estimators. Comparing robust estimates to those obtained using OLS is a common robustness check, however, such comparisons have been mostly informal due to the lack of available tests. Here we introduce a formal test for coefficient distortion due to outliers in regression models. Our proposed test is based on the difference between OLS and robust estimates obtained using a class of Huber-skip M-type estimators (such as Impulse Indicator Saturation or Robustified Least Squares). Establishing asymptotics of the corresponding Huber-skip M-estimators using an empirical process CLT recently developed in the literature, we show that our distortion test has an asymptotic chi-squared distribution. The test is valid for cross-sectional, as well as panel, and stationary or deterministically-trending time series models. To improve finite sample performance and to alleviate concerns on distributional assumptions, we explore several bootstrap testing schemes. We apply our outlier distortion test to estimates of the macro-economic impacts of climate change allowing for adaptation.

Keywords: outlier robustness, robust estimation, iterated 1-step Huber-skip M-estimator, indicator saturation, climate econometrics, climate change, adaptation

JEL Classification: C12, C52, Q54

Suggested Citation

Jiao, Xiyu and Pretis, Felix and Schwarz, Moritz, Testing for Coefficient Distortion due to Outliers with an Application to the Economic Impacts of Climate Change (August 31, 2021). Available at SSRN: https://ssrn.com/abstract=3915040 or http://dx.doi.org/10.2139/ssrn.3915040

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

Moritz Schwarz

Smith School of Enterprise and the Environment, University of Oxford ( email )

South Parks Road
Oxford, OX1 3QY
United Kingdom

HOME PAGE: http://www.moritzschwarz.org

Climate Econometrics, Institute for New Economic Thinking at the Oxford Martin School ( email )

Oxford
United Kingdom

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