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.

中文翻译：

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检验回归模型中是否存在异常值*

我们针对回归模型中异常值的总体存在提出了两组测试。首先，“简单”测试检测到的异常值的比例和数量是否偏离其预期值。其次，“缩放”测试异常值的比例是否随着用于检测异常值的截止值而降低。_{我们将我们的测试应用于运输 CO 2}排放的面板差异模型，以响应北美首个主要碳税的引入。我们的测试表明，未征税的对照组存在显着异常值，这导致高估了税收的估计影响。