Incorrect Inferences When Using Generated Regressors in Accounting Research

Abstract

We analyze the standard error bias associated with the use of generated regressors—independent variables generated from a first-step auxiliary regression—in accounting research settings. Under general conditions, the presence of generated regressors does not affect the consistency of coefficient estimates. However, commonly used generated regressors can cause standard errors to be understated, producing type I errors. Problematic generated regressors include predicted values, coefficient estimates, and measures derived from these estimates. Widely used generated regressors in the accounting literature include measures of earnings persistence, normal accruals, litigation risk, earnings predictability, conditional conservatism, and the likelihood of a tax shelter. Using simple regression models and simulation analyses, we demonstrate how generated regressors can impair inferences and lead to type I errors in accounting research settings. We also demonstrate how the magnitude of the standard error bias is inversely related to the precision of the generated regressor. Finally, we discuss bootstrapping as a correction for the standard error bias and demonstrate the paired cluster bootstrap as a tool to improve inferences in common accounting settings involving generated regressors.

Keywords: generated regressor; standard error bias; predicted values; type I errors; financial reporting quality; accrual quality; investment; litigation risk.