Within a New Keynesian business cycle model, we study variables that are normally unobservable but are very important for the conduct of monetary policy, namely expected inflation and inflation risk premia. We solve the model using a third-order approximation that allows us to study time-varying risk premia. Our model is consistent with rejection of the expectations hypothesis and the businesscycle behaviour of nominal interest rates in US data. We find that inflation risk premia are very small and display little volatility. Hence, monetary policy authorities can use the difference between nominal and real interest rates from index-linked bonds as a proxy for inflation expectations. Moreover, for short maturities current inflation is a good predictor of inflation risk premia. We also find that short-term real interest rates and expected inflation are significantly negatively correlated and that short-term real interest rates display greater volatility than expected inflation. These results are consistent with empirical studies that use survey data and index-linked bonds to obtain measures of expected inflation and real interest rates. Finally, we show that our economy is consistent with the Mundell-Tobin effect: increases in inflation are associated with higher nominal interest rates, but lower real interest rates.