Incorrect Inferences When Using Residuals as Dependent Variables

Posted: 15 Aug 2018

See all articles by Wei Chen

Wei Chen

University of Iowa - Henry B. Tippie College of Business

Paul Hribar

University of Iowa - Henry B. Tippie College of Business

Sam Melessa

University of Iowa - Department of Accounting

Multiple version iconThere are 2 versions of this paper

Date Written: June 1, 2018

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: two-stage; residuals; coefficient bias; discretionary accruals; real earnings management

JEL Classification: C18; G10; G30; M40; M41

Suggested Citation

Chen, Wei and Hribar, Paul and Melessa, Sam, Incorrect Inferences When Using Residuals as Dependent Variables (June 1, 2018). Journal of Accounting Research, Vol. 56, No. 3, 2018. Available at SSRN: https://ssrn.com/abstract=3224630

Wei Chen

University of Iowa - Henry B. Tippie College of Business ( email )

Department of Accounting
Iowa City, IA 52242-1000
United States

Paul Hribar

University of Iowa - Henry B. Tippie College of Business ( email )

Dept. of Accounting
Iowa City, IA 52242-1000
United States
319-335-1008 (Phone)

Sam Melessa (Contact Author)

University of Iowa - Department of Accounting ( email )

108 Pappajohn Business Building
Iowa City, IA 52242-1000
United States

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