Standard Error Biases When Using Generated Regressors in Accounting Research

We analyze the standard error bias associated with the use of generated regressors—independent variables generated from first-step regressions—in accounting research settings. Under general conditions, generated regressors do not affect the consistency of coefficient estimates. However, commonly used generated regressors can cause standard errors to be understated. Problematic generated regressors include predicted values, coefficient estimates, and measures derived from these estimates. Widely used generated regressors in accounting include measures of earnings persistence, normal accruals, litigation risk, and conditional conservatism. Using simple regression models and simulation, we demonstrate how generated regressors can produce understated standard 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 bias and demonstrate the pairs cluster bootstrap as a tool to improve inferences in common accounting settings involving generated regressors.