A two-step quantile regression method for discretionary accounting

This paper proposes an analytical approach that complements the traditional two-step linear regression and one-single step linear regression suggested by Chen et al. (J Account Res 56:751–796, 2018). Using the regression residual as the dependent variable in a second regression is a procedure commonly used in studying discretionary accounting. Chen et al. (J Account Res 56:751–796, 2018) propose to adopt one-step regression to avoid estimation bias and inference error. However, the mean level effect estimated by one-step OLS regression is not sufficient to capture the overall spectrum of discretionary accounting behaviors and thus may mislead its user in drawing implications. We use two-stage quantile regression to examine determinants of discretionary accounting such as discretionary accruals, discretionary expense, discretionary book-tax differences, and abnormal investment in different quantiles. We illustrate the differences between the one-step regression and our two-step quantile regression using four common discretionary accounting studies. Our results and implications reconcile, to some extent, the contradictory findings between results of the one-step OLS regression and the previous established works based on two-step regression.