CEO Bonuses as Studied by Robust Logistic Regression

Abstract

This investigation utilized a robust logistic regression method (BYLOGREG) to investigate CEO bonuses prior to the 2007-2009 financial crisis. The robust logistic regression analysis determined that the year and CEO tenure affected the probability that a CEO received a bonus in the 2004-2006 study period. The analysis refuted that ”management entrenchment” widely influenced CEO bonus compensation because the probability of receiving a bonus was negatively related to CEO tenure. The probability of receiving of bonus declined during the 2004-2006 study period because the percentage of CEOs that received a bonus was lowest in 2006. The robust logistic regression analysis found that the current year stock return was positively and statistically significantly related to the probability that a CEO received a bonus. The analysis also showed that managerial (financial) performance in the areas of growth of sales, ROE, and growth in earnings per share increased the probability that a CEO received a bonus. In this investigation, the size of the firm and the growth rate of equity were not statistically significant. Overall, robust logistic regression correctly classified 77% of the observations on the basis of the model variables, which indicated that most CEO bonuses could be explained by firm, CEO, and financial variables.The BY robust logistic regression proved to be robust to outliers in the CEO bonus sample studied. Interestingly, the relationship between stock return and the probability of a bonus was completely missed by a maximum likelihood (ML) logistic regression with the full CEO bonus sample, which contained outliers. After trimming the CEO bonus data set to remove outliers, the ML logistic regression coefficients changed dramatically. However, the BY robust logistic regression coefficients changed very little. Use of the residuals from the BY robust logistic equation should facilitate further inquiry into CEOs that received a bonus but were predicted to have a low probability of a bonus.