This study investigates the interrelation between the household leverage cycle, collateral constraints, and monetary policy. Using data on the U.S. economy, we find that a contractionary monetary policy shock leads to a large and significant fall in economic activity during periods of household deleveraging. In contrast, monetary policy shocks only have insignificant effects during a household leveraging state. These results are robust to alternative definitions of leveraging and deleveraging periods, different ways of identifying monetary policy shocks, controlling for the state of the business cycle, the level of households debt, and financial stress. To provide a structural interpretation for these empirical findings, we estimate a monetary DSGE model with financial frictions and occasionally binding collateral constraints. The model estimates reveal that household deleveraging periods in the data on average coincide with periods of binding collateral constraints whereas constraints tend to turn slack during leveraging episodes. Moreover, the model produces an amplification of monetary policy shocks that is quantitatively comparable to our empirical estimates. These findings indicate that the state-dependent tightness of collateral constraints accounts for the asymmetric effects of monetary policy across the household leverage cycle as found in the data.