Summary: On several occasions during the period 2001-2003, the European Central Bank (ECB) decided to deviate from its "neutral" benchmark allotment rule, with the effect of not alleviating a temporary liquidity shortage in the banking system. This is remarkable because it implied the possibility of short-term interest rates raising significantly above the main policy rate. In the present paper, we show that when the monetary authority cares for both liquidity and interest rate conditions, the optimal allotment policy may entail a discontinuous reaction to initial conditions. More precisely, we prove that there is a threshold level for the accumulated aggregate liquidity position in the banking system prior to the last operation in a given maintenance period, so that the benchmark allotment is optimal whenever liquidity conditions are above the threshold, and a tight allotment is optimal whenever liquidity conditions are below the threshold.
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