Mixture and Continuous 'Discontinuity' Hypotheses: An Earnings Management Model with Auditor-Required Adjustment

A model emphasizing cookie-jar earnings management and the effect of auditor-required adjustment is formulated, with the optimal misreporting strategy generally characterized and the closed-form solutions for particular functional form assumptions derived. Using simulation results based on the model, I show that the widely documented discontinuity in the earnings triplet distributions (i.e., earnings, earnings change, and earnings surprise) 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. Additionally, I point out the puzzling volcano shape of the earnings triplet distributions that can be found in prior studies. Simulation results show that the model is capable of accommodating this phenomenon, which can arise from the mixture of a spiky distribution of managed earnings with a bell-shaped distribution of unmanaged earnings. This mixture is due to the auditor’s adjustment decision, which seems stochastic from the public’s or client firm’s perspective. Taken together, the results of this paper provide a unified explanation to two perplexing, salient features of the earnings triplet distributions. Potential applications of the model are suggested, including the construction of an earnings manipulation measure distinct from but complementary to abnormal accruals.