Effect of minimum wage on higher levels of pay Suppose the minimum wage increases to \$$x$. Is there any evidence on the effect (if any) this is likely to have upon the wage profile of workers higher in the hierarchy, who are already paid more than \$$x$?

My question is inspired by the following comment from the Financial Times (paywalled link):


  As an employer with an annual payroll of around £650k pa the impact of the introduction of the minimum wage in 1997 led us to pay our lowest paid staff ( casual bar staff back then on about £3ph ) the increased minimum wage so they at least benefited. Everyone else higher in the hierachy ( full timers, supervisors, asst managers, managers) all suffered because at every opportunity ( as people left and needed to be replaced) we tried to replace these higher paid staff with the same caliber person but on lower wages. And we were successful at dong this; and we had to be because we could not afford our overall wage bill to increase. So in 2000 I was paying a General Manager 35k a year. Now I can find and pay a general manager 25k pa and thats a massive nominal decline over 15 years. So the real impact of the minimum wage introduction in the real world of small husiness was to pay the lowest casual staff a little more but most of the higher paid staff ended up being paid less .


Is there any evidence to support the claim that the described response is a widespread phenomenon?
This phenomenon is sometimes called "wage compression" because the range of wages is compressed by the minimum wage laws. 
One paper on this subject is The Impact of the Minimum Wage on Other Wages