We document that the Spanning Hypothesis, which is implied by most macro-finance term structure models, is violated asymmetrically along the U.S. yield curve. After controlling for information in bond prices, we find that macroeconomic variables help predict short-maturity bond returns with statistical and economic significance, while the evidence for long-maturity bonds is much weaker. To understand this pattern, we provide a new decomposition of bond excess returns in terms of innovations of short-, medium- and long-run factors of the yield curve. We show that, in fact, macro data only contains unspanned predictive information about the short-run factor. This extra predictability varies over time and is stronger when inflation is high.