Liquidity Hoarding

We present a model of banks' liquidity management where banks choose a portfolio of liquid and illiquid assets, and later on decide to lend or hoard liquidity. Ex ante, banks choose whether to be "liquid", by holding both liquid and illiquid assets, or "illiquid", by holding only illiquid assets. At later dates, banks receive random liquidity shocks, where an illiquid bank hit by the shock has to sell its asset to liquid banks. When deciding whether to supply liquidity, a liquid bank takes into account that it may itself receive a liquidity shock in the next period. If a bank gives up its liquidity today and receives a shock tomorrow, it needs to sell its illiquid assets but the price of liquidity may be very high if the demand for liquidity is high. This may lead the bank to hoard liquidity, rather than lend, due to the "precautionary" motive. Furthermore, in the event that the liquid bank does not receive a liquidity shock next period, it may profit from a firesale of illiquid assets if demand for liquidity is high, namely, the "speculative" motive. We show that laisser-faire economy is constrained inefficient and is characterized by excessive liquidity hoarding and an inefficiently low level of liquidity accumulation compared to the constrained efficient allocation from the planner's problem. We show that several policies such as liquidity and lending requirements can improve on the laisser-faire allocation