Vector autoregressions (VARs) are popular for forecasting, but ill‐suited to handle occasionally binding constraints, like the effective lower bound on nominal interest rates. We examine reduced‐form “shadow rate VARs” that model interest rates as censored observations of a latent shadow rate process and develop an efficient Bayesian estimation algorithm that accommodates large models. When compared to a standard VAR, our better‐performing shadow rate VARs generate superior predictions for interest rates and broadly similar predictions for macroeconomic variables. We obtain this result for shadow rate VARs in which the federal funds rate is the only interest rate and in models including additional interest rates. Our shadow rate VARs also deliver notable gains in forecast accuracy relative to a VAR that omits shorter‐term interest rate data in order to avoid modeling the lower bound.