Decomposition Error in Accruals and Cash Flows: Implications for Inferences about Accrual Quality

Abstract

Prior research documents that measuring accruals using year-over-year changes in balance sheet (BS) accounts introduces non-articulation measurement error (Hribar & Collins, 2002). When these mismeasured accruals are used to derive cash flows (i.e., earnings minus accruals), the non-articulation error transfers into cash flow measurement, resulting in negatively correlated decomposition errors in accruals and cash flows. We demonstrate analytically and empirically that, when BS measures of accruals and cash flows are used as regressors, the negatively correlated errors bias the coefficient estimates on accruals and cash flows toward each other. We further demonstrate that this bias can contribute to errors of inference (particularly Type II errors) in studies using differential persistence as a measure of accrual quality. Our paper is broadly relevant to research using decomposed variables as regressors.

Keywords: negatively correlated measurement error, decomposition, backed-into variable, differential persistence, balance sheet accruals, type I error, type II error