We study the pay of chief executives of higher education institutions in the UK, known as Vice Chancellors (VCs), over a ten-year period. As different institutions might have different missions and follow different performance objectives, we use the LASSO method in a novel way to choose which performance parameters are most strongly associated with VC pay for each institution. Moreover, we use the same method in order to decide if and how institutions benchmark against other institutions in terms of VC pay by constructing a set of benchmarks for each one of them. We find that while institutions at the lower and medium end of the pay distribution benchmark primarily against institutions with larger VC pay than themselves, the institutions at the higher end of the pay distribution benchmark are primarily towards performance parameters. This type of behaviour can explain the recent inflation in pay observed in the sector. Empirical evidence as well as results from simulations motivate a policy recommendation that symmetric benchmarking by all institutions would prevent upward ratcheting of average VC pay. While we are looking at data stemming from the academic sector in the UK, the method and the recommendations can equally apply to other salaries that are benchmarked such as the ones of professional athletes or CEOs worldwide and therefore, bear generality.