This paper decomposes the excess return predictability in inflation-indexed and nominal government bonds into effects from liquidity, market segmentation, real interest rate risk and inflation risk. We estimate a large and variable liquidity premium in US Treasury Inflation Protected Securities (TIPS) from the co-movement of breakeven inflation with liquidity proxies. The liquidity premium is around 70 basis points in normal times, but much larger during the early years of TIPS issuance and during the height of the financial crisis in 2008-2009. The liquidity premium explains the high excess returns on TIPS as compared to nominal Treasuries over the period 1999-2009. Liquidity-adjusted breakeven inflation appears stable, suggesting stable inflation expectations over our sample period. We find predictability in both inflation-indexed bond excess returns and in the spread between nominal and inflation-indexed bond excess returns even after adjusting for liquidity, providing evidence for both time-varying real interest rate risk premia and time-varying inflation risk premia. Liquidity appears uncorrelated with real interest rate and inflation risk premia. We test whether bond return predictability is due to segmentation between nominal and inflation-indexed bond markets but find no evidence in either the US or in the UK.