In this paper we construct model-free and model-based indicators for the inflation risk premium in the US and the euro area. We study the impact of market liquidity, surprises from inflation data releases, inflation volatility and deflation fears on the inflation risk premium. For our analysis, we construct a special dataset with a broad range of indicators. The dataset is carefully constructed to ensure that at every point in time the series are aligned with the information set available to traders. Furthermore, we adopt a Bayesian variable selection procedure to deal with the strong multicollinearity in the variables that potentially can explain the movements in the inflation risk premium. We find that the inflation risk premium turned negative, on both sides of the Atlantic, during the post-Lehman period. This confirms the recent finding by Camp- bell et al. (2016) that nominal bonds are no longer "inflation bet" but have turned into "deflation hedges". We also find, and contrary to common beliefs, that indicators of inflation uncertainty alone cannot explain the movements in the inflation risk premium in the post-Lehman period. The decline in the inflation risk premium seems mostly related to increased deflation fears and the belief that inflation will stay far away from the monetary policy target rather than declining inflation uncertainty. This in turn would suggest that central banks should not be complacent with low or even negative inflation risk premia.