We infer determinants of Latin American hyperinflations and stabilizations by using the method of maximum likelihood to estimate a hidden Markov model that potentially assigns roles both to fundamentals in the form of government deficits that are financed by money creation and to destabilizing expectations dynamics that can occasionally divorce inflation from fundamentals. Our maximum likelihood estimates allow us to interpret observed inflation rates in terms of variations in the deficits, sequences of shocks that trigger temporary episodes of expectations driven hyperinflations, and occasional superficial reforms that cut inflation without reforming deficits. Our estimates also allow us to infer the deficit adjustments that seem to have permanently stabilized inflation processes. Our results show how the available inflation, deficit, and other macroeconomic data had left informed economists like Rudiger Dornbusch and Stanley Fischer undecided about the ultimate sources of inflation dynamics.