As most states, France has been affected by the global financial crisis and has quickly taken appropriate steps to tackle its worst effects. Thus, France immediately took measures to respond to the liquidity crisis and recapitalised the most important banks in order for them to continue to finance the ‘real economy’. Some measures have been aimed directly at the ‘real economy’, such as the creation of a mediator for the distribution of credit and the establishment of a French sovereign wealth fund aimed at investing in strategic companies facing difficulties and in medium-sized companies. After the first wave of the crisis, France took a preventive measure concerning the remuneration of traders and a punitive measure by creating an exceptional taxation of traders' remuneration. But the crisis has also provoked a long-term reform of the French supervisory landscape, merging the supervisory authorities of the banking and the insurance landscape into a single body, the Authority for Prudential Control (Autorité de Contrôle Prudentiel).

The banking literature following Diamond and Dybvig [Journal of Political Economy 85, 191–206 (1983)] has assumed that all depositors are ex ante identical. This paper relaxes this assumption by introducing two types of agents. Whereas some agents are uncertain about their liquidity needs at the time they deposit in banks, other agents know exactly at what time they will want to withdraw their funds. Agents who know ex ante that they will want to withdraw in the short term will tend to disrupt the ability of a bank to serve customers who are uncertain about their timing of withdrawal. An adverse selection problem arises, where short-term deposits have the incentive to join the financial system and limit, or completely do away with, banks' liquidity provision service. On the other hand, potentially beneficial long-term funds will not be deposited in banks. Further, when unpredicted short-term withdrawal needs are sufficiently high, bank reserves are exhausted, and long-term investments need to be disrupted, causing a banking crisis.

We study how discount window policy affects the frequency of banking crises, the level of investment, and the scope for indeterminacy of equilibrium. Previous work has shown that providing costless liquidity through a discount window has mixed effects in terms of these criteria: It prevents episodes of high liquidity demand from causing crises but can lead to indeterminacy of stationary equilibrium and to inefficiently low levels of investment. We show how offering discount window loans at an above-market interest rate can be unambiguously beneficial. Such a policy generates a unique stationary equilibrium. Banking crises occur with positive probability in this equilibrium and the level of investment is suboptimal, but a proper combination of discount window and monetary policies can make the welfare effects of these inefficiencies arbitrarily small. The near-optimal policies can be viewed as approximately implementing the Friedman rule.