A Welfare Analysis of the Central Bank Balance Sheet
Abstract
During the period when interest rates were constrained at the effective lower bound, central banks relied on balance sheet expansions to set the stance of monetary policy. But in the long-run, when rates are away from their lower-bound, these balance sheet policies are not needed to provide stimulus.This paper asks: what is the socially optimal size for the central bank balance sheet in the long-run? I introduce a central bank into a simple endowment economy model in which banks are liquidity mismatched and prone to sudden "bank runs". In this framework, the long-run provision of central bank reserves can reduce the likelihood of bank runs, at the cost of crowding out more productive investments. I calibrate the model to conditions before the financial crisis, and demonstrate that the model can reproduce important non-linearities in the data on the demand curve for reserves, as reserve supply moves from scarce to abundant. I compute the socially optimal size of the central bank and find that it is optimal for the central bank to expand supply of reserves almost to the point where their marginal liquidity benefit is zero, and reserve demand is satiated, but no further.