This paper utilizes a profit maximizing banking model to analyze sweeping behavior. Comparative statics results indicate that sweeping responds positively to increases in bank loan rates and reserve ratios and negatively to increases in the interest rate on reserves or to exogenous increases in bank deposits or equity. Sweeping generates greater responsiveness in lending to changes in loan rates or the interest rate on reserves and lower responsiveness to exogenous changes in reserve ratios or equity. Empirical analysis of an explicit condition that we derive relating sweeping to the interest rate on reserves suggests with an unchanged reserve requirement, the Fed could eliminate sweeping by setting the interest rate on reserves to no less than 3.67 percentage points below the market loan rate. The range of interest rates on reserves that lead to zero sweeping increases sharply, however, as the required reserve ratio is reduced.
VanHoose, David D. and Dutkowsky, Donald H., "Interest on Bank Reserves and Optimal Sweeping" (2008). Economics Faculty Scholarship. 147.
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