Is the Tips Liquidity Premium Unspanned by the U.S. Term Structure of Interest Rates?

In this paper, I consider a joint Gaussian affine term structure model for zero-coupon U.S. Treasury and TIPS bonds, with an unspanned factor: liquidity risk. In the model, the liquidity factor is restricted to affect only the cross-section of yields but it is allowed to determine the bond risk premia. This is motivated by the fact that bond excess returns can be predicted by the TIPS liquidity premium, therefore liquidity can be considered as an unspanned factor that forecasts bond returns but does not span the yield curve. I present empirical evidence suggesting that the liquidity factor does not affect the dynamic of bonds under the pricing measure, but does affect them under the historical measure. Consequently, the information contained in the yield curve appears to be insufficient to completely characterize the variation in the price of curvature risk