Is the Probability Distribution of Earnings Bimodal
This paper analyses how earnings’ tendency to covary non-linearly with firm size shapes its probability distribution. This tendency creates a positive correlation between profits and size but a negative correlation between losses and size. Therefore, large companies do not generate profits close to zero. Instead, large companies generate either large profits or large losses. Hence, this covariation with size tends to create two modes in the probability distribution of earnings conditional on size: one is in the profit region and one is in the loss region. A related argument shows that covariation with firm size tends to create two modes in the distribution of deflated earnings. The results of this paper mainly support the existence of two modes. The modes are close to each other, and the profit mode is larger than the loss mode. As a result, histograms of earnings exhibit a “discontinuity” at zero. The existence of two modes implies that tests that infer earnings management from earnings distributions are misspecified because these tests assume unimodal distributions absent earnings management. This paper suggests a unified, alternative explanation for such “discontinuities” in the distributions of performance metrics, which have heretofore been explained by managerial opportunism.
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