We propose a no-arbitrage model of the nominal and real term structures that accommodates the different persistence and volatility of distinct inflation components. Core, food, and energy inflation combine into a single total inflation measure that ties nominal and real risk-free bond prices together. The model successfully extracts market participants’ expectations of future inflation from nominal yields and inflation data. Estimation uncovers a factor structure common to core inflation and interest rates and downplays the pass-through effect of short-lived food and energy shocks on inflation and interest rates. Model forecasts systematically outperform survey forecasts and other benchmarks.