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

Abstract

Outlying observations can bias regression estimates, requiring the use of outlier-robust estimators. Comparing robust estimates to those obtained using ordinary least squares (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