We model the interbank market for overnight credit with heterogeneous banks and asymmetric information. An unsophisticated bank just trades to compensate its liquidity imbalance, while a sophisticated bank will exploit its private information about the liquidity situation in the market. It is shown that with positive probability, the liquidity effect (Hamilton, 1997) is reversed, i.e., a liquidity drainage from the banking system may generate an overall decrease in the market rate. The phenomenon does not disappear when the number of banks increases. We also show that private information mitigates the effect of an unexpected liquidity shock on the market rate, suggesting a conservative information policy from a central bank perspective.