Does raising an inflation target require increasing the nominal interest rate in the short run? We answer this question using a standard New Keynesian model with rich backward-looking elements. We first analytically show that the short-run comovement between inflation and the nominal interest rate is less likely to be positive, all else equal, as the monetary authority reacts more aggressively to the deviation of inflation from its target or as more backward-looking elements are incorporated into the model. Meanwhile, features of the model that enhance forward-looking behavior, such as partial price indexation to the inflation target or a lower degree of price rigidity, are shown to help increase the likelihood of positive comovement. However, we find that this so called Neo-Fisherism is most likely to hold even with a significant degree of backward-lookingness in the model, unless the monetary authority reacts to inflation in an extremely aggressive manner, close to strict inflation targeting. In addition, we estimate New Keynesian models of the U.S. economy and confirm our results that the U.S. economy exhibits Neo-Fisherism: raising the inflation target necessitates a short-run increase in the nominal interest rate. This finding is robust to empirically-plausible parameterizations of the model and to the specification of price indexation to the inflation target in firms’ price-setting process.