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Incorrect Inferences When Using Residuals as Dependent Variables

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... Full description

Journal Title: Journal of Accounting Research June 2018, Vol.56(3), pp.751-796
Main Author: Chen, Wei
Other Authors: Hribar, Paul , Melessa, Samuel
Format: Electronic Article Electronic Article
Language:
Subjects:
C18
G10
G30
M40
M41
ID: ISSN: 0021-8456 ; E-ISSN: 1475-679X ; DOI: 10.1111/1475-679X.12195
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recordid: wj10.1111/1475-679X.12195
title: Incorrect Inferences When Using Residuals as Dependent Variables
format: Article
creator:
  • Chen, Wei
  • Hribar, Paul
  • Melessa, Samuel
subjects:
  • C18
  • G10
  • G30
  • M40
  • M41
  • Two‐Stage
  • Residuals
  • Coefficient Bias
  • Discretionary Accruals
  • Real Earnings Management
ispartof: Journal of Accounting Research, June 2018, Vol.56(3), pp.751-796
description: 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.
language:
source:
identifier: ISSN: 0021-8456 ; E-ISSN: 1475-679X ; DOI: 10.1111/1475-679X.12195
fulltext: fulltext
issn:
  • 0021-8456
  • 00218456
  • 1475-679X
  • 1475679X
url: Link


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descriptionWe 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.
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titleIncorrect Inferences When Using Residuals as Dependent Variables
descriptionWe 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.
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abstractWe 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.
doi10.1111/1475-679X.12195
pages751-796
date2018-06