导读：这是本专题的第一篇分享，是一篇实证研究方法类的文章，讨论用残差项做被解释变量是否会导致假设推断错误。由于残差项可以衡量异常情况，会计研究中有很多变量的衡量采用的是残差项，比如真实活动盈余管理、应计项目盈余管理与异常投资等。作者通过分析实证金融和会计领域中使用OLS回归残差项做被解释变量的文章发现，这种做法会导致估计系数和标准误有偏，造成错误的推断结果，错误类型可能是类型一也可能是类型二。作者们在四种会计研究的情况下检验了潜在偏误的情况，最后提出了三种解决方案。

Incorrect Inferences When Using Residuals as Dependent Variables

Journal of Accounting Research 2018 Volume56, Issue3
WEI CHEN PAUL HRIBAR SAMUEL MELESSA

ABSTRACT

We analyze a procedure common in empirical accounting and finance research where researchers use ordinary least squares to decompose a dependent variable into its predicted and residual components and use the residuals as the dependent variable in a second regression. This two‐step procedure is used to examine determinants of constructs such as discretionary accruals, real activities management, discretionary book‐tax differences, and abnormal investment. We show that the typical implementation of this procedure generates biased coefficients and standard errors that can lead to incorrect inferences, with both Type I and Type II errors. We further show that the magnitude of the bias in coefficients and standard errors is a function of the correlations between model regressors. We illustrate the potential magnitude of the bias in accounting research in four commonly used settings. Our results indicate significant bias in many of these settings. We offer three solutions to avoid the bias.

原文地址：https://onlinelibrary.wiley.com/doi/pdf/10.1111/1475-679X.12195