Two-Stage Regression Analysis and Biased Estimates in Accounting Research: An Application of the Frisch-Waugh-Lovell Theorem

Abstract

We analyze a two-step estimation methodology common in empirical accounting 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-step regression. This research design is frequently used to examine determinants of constructs such as discretionary accruals, excess compensation, and discretionary permanent book-tax differences. We demonstrate that this two-step procedure produces biased coefficients and standard errors and can lead to both type I and type II errors. We further show that magnitude of the bias in coefficients and standard errors is a function of the correlations between model regressors. Our analyses indicate that these biases hamper the ability of researchers to make accurate inferences in common accounting settings.