The overnight interest rate is the price paid for one day loans and defines the short end of the yield curve. It is the equilibrium outcome of supply and demand for bank reserves. This paper models the intertemporal decision problems in the reserve market for both central and commercial banks. All important institutional features of the euro area reserve market are included. The model is then estimated with euro area data. A permanent change in reserve supply of one billion euro moves the overnight rate by eight basis points into the opposite direction, hence, there is a substantial liquidity effect. Most of the predictable patterns for the mean and the volatility of the overnight rate are related to monetary policy implementation, but also some calendar day effects are present. Banks react sluggishly to new information. Implications for market efficiency, endogeneity of reserve supply and underbidding are studied.