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Incorrect Inferences When Using Residuals as Dependent Variables
Authors:WEI CHEN  PAUL HRIBAR  SAMUEL MELESSA
Institution:Tippie College of BusinessUniversity of Iowa
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.
Keywords:C18  G10  G30  M40  M41  two‐stage  residuals  coefficient bias  discretionary accruals  real earnings management
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