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The Effect of Omitted Variables on the Sign of Regression Coefficients
arXiv - STAT - Methodology Pub Date : 2022-08-01 , DOI: arxiv-2208.00552
Matthew A. Masten, Alexandre Poirier

Omitted variables are a common concern in empirical research. We show that "Oster's delta" (Oster 2019), a commonly reported measure of regression coefficient robustness to the presence of omitted variables, does not capture sign changes in the parameter of interest. Specifically, we show that any time this measure is large--suggesting that omitted variables may be unimportant--a much smaller value can actually reverse the sign of the parameter of interest. Relatedly, we show that selection bias adjusted estimands can be extremely sensitive to the choice of the sensitivity parameter. Specifically, researchers commonly compute a bias adjustment under the assumption that Oster's delta equals one. Under the alternative assumption that delta is very close to one, but not exactly equal to one, we show that the bias can instead be arbitrarily large. To address these concerns, we propose a modified measure of robustness that accounts for such sign changes, and discuss best practices for assessing sensitivity to omitted variables. We demonstrate this sign flipping behavior in an empirical application to social capital and the rise of the Nazi party, where we show how it can overturn conclusions about robustness, and how our proposed modifications can be used to regain robustness. We implement our proposed methods in the companion Stata module regsensitivity for easy use in practice.

中文翻译:

省略变量对回归系数符号的影响

遗漏变量是实证研究中普遍关注的问题。我们表明,“Oster 的 delta”(Oster 2019)是一种常用的回归系数对存在遗漏变量的稳健性的度量,它没有捕捉到感兴趣参数的符号变化。具体来说,我们表明,只要这个度量很大——表明遗漏的变量可能不重要——一个小得多的值实际上可以反转感兴趣参数的符号。相关地,我们表明选择偏差调整的估计值对灵敏度参数的选择非常敏感。具体来说,研究人员通常在 Oster 的 delta 等于 1 的假设下计算偏差调整。在delta非常接近一但不完全等于一的替代假设下,我们表明偏差可以任意大。为了解决这些问题,我们提出了一种修正的稳健性度量来解释这种符号变化,并讨论评估对遗漏变量的敏感性的最佳实践。我们在对社会资本和纳粹党崛起的实证应用中展示了这种符号翻转行为,我们展示了它如何推翻关于稳健性的结论,以及我们提出的修改如何用于恢复稳健性。我们在配套的 Stata 模块 regsensitive 中实现了我们提出的方法,以便在实践中轻松使用。我们在对社会资本和纳粹党崛起的实证应用中展示了这种符号翻转行为,我们展示了它如何推翻关于稳健性的结论,以及我们提出的修改如何用于恢复稳健性。我们在配套的 Stata 模块 regsensitive 中实现了我们提出的方法,以便在实践中轻松使用。我们在对社会资本和纳粹党崛起的实证应用中展示了这种符号翻转行为,我们展示了它如何推翻关于稳健性的结论,以及我们提出的修改如何用于恢复稳健性。我们在配套的 Stata 模块 regsensitive 中实现了我们提出的方法,以便在实践中轻松使用。
更新日期:2022-08-02
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