Discussion of Aggarwal and Samwick (1999)

This paper links up CEO compensation (relative performance evaluation) with product market competition. However, instead of addressing the effect of RPE on product market competition, the paper studies the effect of product market competition (Bertrand or Cournot) on the use of RPE. But the paper has implications for the effect of RPE on product market competition: it toughens it. Therefore, the paper concludes that in order to soften competition on the product market, sometimes RPE is not used.
The paper has an analytical part and an empirical part. The two figures of the analytical part, which tell everything, are impressive.
In the empirical part, the authors specify the regression as compensation on firm performance (own and rival), Herfindahl index, their interaction and a dummy indicating whether it's a CEO. To minimize omitted correlated variable problems, the authors use change in the dependent variable and change in both dependent and independent variables specifications. The empirical methods are fairly rigorous. One interesting result is that the coefficient on the interaction between RPE and Herfindahl index is consistently negative, indicating that competition limits the effect of RPE on compensation. But in some specifications (change in short-term compensation), the coefficient on the effect of rival firm performance is negative, indicating the existence of RPE.
But one thing with the paper is that in the analytical part the authors show that in the optimal contract compensation depends positively on both own firm and rival firm performance for the Bertrand competition case and didn't really examine RPE. In the empirical part, the authors use regressions to analyze whether RPE is used or whether it's the Bertrand or Cournot case. But if I know firms use RPE, can I test RPE's effect on competition or collusion?