Changes in Probability Distributions and the Form of Compensation Contracts

We consider a standard principal-agent setting where the first-order approach to the effort choice problem applies. We decompose the effect of a change in the probability distribution of performances on the form of the optimal contract into three additive components. We also consider the specific cases of a linear likelihood ratio, a rightward or leftward translation of the likelihood ratio, and CRRA utility. The results shed light on the differences between the optimal contracts derived in the literature, notably depending on whether a linear likelihood ratio or a lognormally distributed performance measure is assumed