Incorrect Inferences When Using Generated Regressors in Accounting Research

Abstract

We analyze the bias associated with the use of generated regressors, i.e., independent variables generated from a first-step auxiliary regression, in accounting research settings. Widely used generated regressors in accounting include discretionary accruals, the Dechow and Dichev [2002] measure of accrual quality, asymmetric timeliness coefficients, the Khan and Watts [2009] C-score, earnings persistence coefficients, real earnings management proxies, discretionary book-tax differences, and predicted values capturing litigation risk, bankruptcy risk, and the likelihood of a tax shelter. Under general conditions, the presence of generated regressors does not affect the consistency of coefficient estimates. However, commonly used generated regressors can bias standard errors towards zero, producing type I errors. We discuss various types of generated regressors (predicted values, residuals, coefficients, etc.) and demonstrate the associated standard error bias and factors affecting the bias using simple regression models and simulation analyses. We also show the bias can be substantial in common accounting settings by examining the magnitude of the bias when examining the effect of litigation risk on management forecast characteristics. Finally, we outline two corrections for the bias and show how the corrections, including bootstrapping standard errors, improve inferences.