This paper examines the performances of the past five Federal Reserve chairmen using optimal control techniques and a macroeconometric model. Each chairman is evaluated in two ways. The first way is comparing the actual performance of the economy under his term relative to what the performance would have been had he behaved optimally. Comparing chairmen only on the basis of the actual performance of the economy is not appropriate because it does not control for different exogenous-variable values and shocks that the Fed has no control over. This comparison is done for a wide range of loss functions. It does not assume that the chairman necessarily behaved by minimizing a loss function; it just compares his actual behavior to what he could have done had he minimized a particular loss function. The second way, on the other hand, assumes that each chairman minimized a loss function, and it backs out an estimate of what this loss function was. A summary evaluation of each chairman is presented in Section 6.