Fermi Large Area Telescope data reveal an excess of GeV gamma rays from the direction of the Galactic Center and bulge. Several explanations have been proposed for this excess including an unresolved population of millisecond pulsars (MSPs) and self-annihilating dark matter. It has been claimed that a key discriminant for or against the MSP explanation can be extracted from the properties of the luminosity function describing this source population. Specifically, is the luminosity function of the putative MSPs in the Galactic Center consistent with that characterizing the resolved MSPs in the Galactic disk? To investigate this we have used a Bayesian Markov Chain Monte Carlo to evaluate the posterior distribution of the parameters of the MSP luminosity function describing both resolved MSPs and the Galactic Center excess. At variance with some other claims, our analysis reveals that, within current uncertainties, both data sets can be well fit with the same luminosity function.