This seems unlikely. JCP's CEO apparently gets ~.5%-1% of JCP's profits (i.e. ~.01-.02% of revenues, dependent on performance). 0.01% of revenues is not enough

This seems unlikely. JCP's CEO apparently gets ~.5%-1% of JCP's profits (i.e. ~.01-.02% of revenues, dependent on performance). 0.01% of revenues is not enough that a company will actually feel the CEO's salary, but it seems very likely that a marginally better CEO can raise profits by 0.01% of revenues (which would allow a doubled base salary!) More likely explanations: various inefficiencies interfere with getting the best, (good) CEOs are not easily attracted by even larger salaries, companies in dire straits need to pay for the damage they're likely to do to a CEO's resume, the study is simply too small. (Teasing out a 0.01% effect is hard!)