We propose two sets of tests for the overall presence of outliers in regression models. First, ‘simple’ tests on whether the proportion and the number of detected outliers deviate from their expected values. Second, ‘scaling’ tests on whether the proportion of outliers decreases with the cut-off used to detect outliers. We apply our tests to a panel difference-in-differences model of transport CO2 emissions in response to the introduction of North America's first major carbon tax. Our tests show the presence of significant outliers in the un-taxed control group, which results in an overestimation of the estimated impacts of the tax.
Jiao, X. & Pretis, F. (2022) 'Testing the presence of outliers in regression models', Oxford Bulletin of Economics and Statistics.