This study is extremely weak. The "unobtrusive measures" they use as proxies for narcissism are poorly correlated. It's also a bad sign they need to devote such substantial portions of the paper trying to defend Study 1's questionable proxy measures.

There are obvious confounding variable and alternate explanations for these factors starting with the fact relative compensation metrics vary by industry norms, sector dynamics, and company maturity. This feels like a paper where they went looking for a correlation they hoped to find and then did a lot of work to rationalize weak correlations and coax their preferred narrative past peer review.

While the conclusion is sure to find a sympathetic audience among employees psycho-analyzing the personality flaws of "the boss" around the water-cooler, the paper fails to adequately support its conclusions.