A Theory on the Discontinuity in Earnings Distributions

Abstract

This paper presents a model of financial reporting in which investors infer both pre-managed earnings and the precision of earnings from reported earnings. Over-reporting earnings has two opposing pricing effects: investors infer higher pre-managed earnings from an inflated positive earnings surprise (i.e., positive effect); however, investors also infer a lower earnings precision at the same time, leading to a lower pricing weight placed on the higher surprise (i.e., negative effect). For firms with (relatively) strongly positively autocorrelated earnings, in equilibrium, the trade-off between the two opposing effects creates a pooled report right above the prior mean of the earnings distribution and a no-reporting "hole" right below the prior mean (i.e., an earnings discontinuity consistent with empirical findings). Further, the model predicts cross-sectional variation in the earnings discontinuity phenomenon yet to be explored. In particular, the model shows and predicts: (1) no earnings discontinuity exists for firms with negatively or (relatively) weakly positively autocorrelated earnings, and (2) the earnings discontinuity is more pronounced for firms with more positively autocorrelated earnings.

Keywords: earnings discontinuity, earnings precision, earnings distribution, financial reporting

JEL Classification: M41