Episodes of low natural interest rates, even transitory, pose a challenge to monetary policy, by possibly causing the effective lower bound (ELB) on the policy rate to bind. Those episodes are more likely to occur not only when the natural rate is low on average but also when fluctuations around its average level are large. We study the responsiveness of the natural interest rate to structural aggregate shocks affecting the aggregate supply of and demand for savings. Using a quantitative overlapping-generations model, we trace back this responsiveness to the slopes of aggregate savings supply and demand curves and argue that both curves have likely flattened over the past four decades in the US This implies a greater sensitivity of the natural interest rate to structural shocks affecting the supply of and demand for aggregate savings — making it more likely, all else equal, that it fall into negative territory.