What level of central bank reserves satiates banks’ demand for liquidity? We provide a model of the reserve demand curve in the United States and estimate it at daily frequency over 2010-21 using an instrumental-variable approach combined with a time-varying vector autoregressive model. This paper makes a methodological contribution in providing an approach that can address the three main issues affecting the estimation of the reserve demand curve: nonlinearity, time variation due to slow-moving structural changes, and endogeneity. We have three main empirical findings. First, as predicted by economic theory, the reserve demand curve is highly nonlinear with a clear satiation level: it is flat when reserves in the banking system are sufficiently abundant; and increasingly negatively sloped as reserves decline below the satiation point, moving from ample to scarce. Second, the reserve demand curve has shifted horizontally: in the earlier part of the sample, we observe a significantly negative slope when reserves are below 12 percent of banks’ assets; in the second half, when reserves drop below 13 percent. These findings suggest that banks’ demand for reserves has increased over time. Third, the curve has also shifted vertically, especially in the later period. This observation implies that the level of the federal funds-IORB spread may not be the appropriate summary statistic for the rate sensitivity to reserve shocks. Finally, we show that our methodology can be used in real-time to monitor the market for reserves and assess the ampleness of reserves.