Various inflation forecasting models are compared using a simulated out-of-sample forecasting framework. We focus on the question of whether monetary aggregates are useful for forecasting inflation, but unlike previous work we examine a wide range of forecast horizons and allow for estimated as well as theoretically specified cointegrating relationships in some of our models. Our findings indicate that there are forecasting gains from allowing monetary aggregates to enter into prediction models via cointegrating restrictions among money, prices, and output derived from a simple version of the quantity theory, but only when the cointegrating relations are specified a priori based on economic theory. When estimated cointegrating relations are used in a vector error correction (VEC) model, a vector autoregression (VAR) model in differences predicts better. These results hold, even during the 1990s, and evidence is presented suggesting that previous findings of a breakdown in the cointegrating relationship among prices, money, and output is the result of a failure of M2 as a measure of the money stock, and is not due to money demand instabilities. Two Monte Carlo experiments that lend credence to our findings are also reported on. The first shows that cointegration vector parameter estimation error is crucial when using VEC models for forecasting, and helps to explain previous findings of the failure of VEC models to forecast better than VAR models. The second shows that random walk and other atheoretical models routinely forecast better than correctly specified alternative models, due to parameter estimation error, indicating that caution needs to be exercised when interpreting the results of such comparisons, particularly when making statements concerning the usefulness of empirical models for use in policy-setting.