On a statistical method to detect discontinuity in the distribution function of reported earnings

In the study of earnings management, researchers attempt to know the reason managers manipulate earnings of a company. Some preceding studies have focused on the distribution of reported earnings, and they treat the evidence of manipulation on earnings as discontinuity (at most cases around zero earnings) in the distribution function of reported earnings. They used statistical tests to detect the discontinuity, though, none of the tests they proposed were shown their derivation and examined their properties. This study tries to find a proper procedure for such kinds of study. In this study, we focus on the test proposed by Burgstahler and Dichev among tests. From the results by Monte Carlo simulation, for over moderate sample size, the size of the test is almost correct and the test has good power. In addition, we find that the test is able to detect discontinuity for a small jump in continuous distribution. Thus, we conclude that the test is available for various situations.