This paper estimates a model in which persistent fluctuations in expected consumption growth, expected inflation, and their time-varying volatility determine asset price variation. The model features Epstein-Zin recursive preferences, which determine the market price of macro risk factors. The analysis of the U.S. nominal term structure data from 1953 to 2006 shows that agents dislike high uncertainty and demand compensation for volatility risks. And the time variation of the term premium is driven by the compensation for inflation volatility risk that is distinct from consumption volatility risk. The central role of inflation volatility risk in explaining the time-varying term premium is consistent with other empirical evidence including survey data. In contrast, the existing long-run risks literature emphasizes consumption volatility risk and ignores inflation-specific time-varying volatility. The estimation results of this paper suggest that inflation-specific volatility risk is essential for fitting the time series of the U.S. nominal term structure data.