Earnings Distribution Discontinuity from a Continuous Model of Earnings Management

Abstract

A parsimonious model is developed to understand two perplexing, salient features of the distributions of earnings, earnings change, and earnings surprise. The model provides guidance for empirical work to uncover the unmanaged earnings important to firm valuation and public scrutiny, yet unobserved by outside parties. Simulation results based on the model show that the puzzling volcano shape of the distributions can arise from the mixture of a spiky distribution of managed earnings with a bell-shaped distribution of unmanaged earnings. The spiky distribution is due to cookie-jar earnings management that compresses unmanaged earnings from both sides toward an earnings benchmark, leading to a concentration of density around there. The mixture is due to the auditor's adjustment decision, which seems stochastic from the public's or client firm's perspective. Additional simulation results suggest that the widely documented discontinuity in the distributions can be partly due to a steep increase in density appearing like a discontinuity when a continuous distribution is plotted in terms of frequency counts in histogram bins. The main analytical results are a general characterization of the optimal earnings management strategy and the derivation of closed-form solutions for particular functional form assumptions. Potential applications include structurally estimating the model for policy analysis to assess the impact on earnings manipulation. (JEL M43/M49/K42)