Hostname: page-component-8448b6f56d-wq2xx Total loading time: 0 Render date: 2024-04-18T12:27:16.113Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimal Management of Bank Reserves

Published online by Cambridge University Press:  19 October 2009

George F. Brown Jr.
Get access Rights & Permissions [Opens in a new window]

Extract

This paper has considered the sequence of optimal credit expansion decisions of a bank operating under the legal structure imposed by the Federal Reserve System. Two alternative structures are considered, one relating to the pre-September 1968 period and the other to the currently enforced one. Using dynamic programming techniques, a closed-form equation for the optimal credit expansion decision has been derived in each case. The optimal level of credit expansion has been shown to be a nonlinear function of the prevailing interest rate, the parameters of the distribution of reserve losses, and several parameters set by Federal Reserve policy. The presence of uncertainty in the model has been shown to have an indefinite effect; however, several policy parameters may be chosen so as either to restrict or to encourage expansion to levels below or above the simple certainty prediction. These results are intuitively in accord with those of general inventory studies.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 7 , Issue 5 , December 1972 , pp. 2031 - 2054
Copyright
Copyright © School of Business Administration, University of Washington 1972

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Barro, Robert J. “Theory of Partial Adjustment and Expectations Mechanisms.” Unpublished research proposal, Brown University, 1970.Google Scholar
[2]Baumol, William. “The Transactions Demand for Cash: An Inventory Theoretical Approach.” Quarterly Journal of Economics, 1952.CrossRefGoogle Scholar
[3]Bellman, Richard E.Dynamic Programming. Princeton, N.J.: Princeton University Press, 1957.Google ScholarPubMed
[4]Belsley, D. A.Industry Production Behavior; The Order Stock Distinction. Amsterdam: North Holland Publishing Company, 1969.Google Scholar
[5]Brown, G. F. Jr., and Lloyd, R. M.. “Static Models of Bank Credit Expansion.” Journal of Financial and Quantitative Analysis, June 1971.CrossRefGoogle Scholar
[6]Brown, G. F. Jr. “Dynamic Models of Bank Credit Expansion Under Certainty.” Center for Naval Analyses, Professional Paper Number 12, 1969.Google Scholar
[7]Brown, G. F. Jr. “Fixed Penalty Costs and the Classical Inventory Model.” Forthcoming in Naval Research Logistics Quarterly.Google Scholar
[8]Brunner, K., and Meltzer, A. H.. “Some Further Investigations of Demand and Supply Functions for Money.” Journal of Finance, 1964.CrossRefGoogle Scholar
[9]Chitre, V. S. “Some Dynamic Programming Models of Transactions and Precautionary Demand for Money.” Ph.D. dissertation. University of Rochester, 1967.Google Scholar
[10]Crick, W. F. “The Genesis of Bank Deposits.” Economica, 1927.CrossRefGoogle Scholar
[11]Dreyfus, Stuart E.Dynamic Programming and the Calculus of Variations. Santa Monica, Calif.: The RAND Corporation, 1965.Google Scholar
[12]Eppen, G. D., and Fama, E. F.. “Cash Balance and Simple Dynamic Portfolio Problems with Proportional Costs.” International Economic Review, 1969.CrossRefGoogle Scholar
[13]Holt, C.; Modigliani, F.; Muth, J.; and Simon, H.. Planning Production, Inventories, and Work Force. Englewood Cliffs, N.J.: Prentice-Hall.Google Scholar
[14]Lloyd, Richmond M. “Dynamic Programming Models of Short Term Bank Reserve Management.” Ph.D. dissertation, University of Rochester, 1970.Google Scholar
[15]Lucas, R. E. “Optimal Investment Policy and the Flexible Accelerator.” International Economic Review, 1967.CrossRefGoogle Scholar
[16]Lucas, R. E. “Adjustment Costs and the Theory of Supply.” Journal of Political Economy, 1967.CrossRefGoogle Scholar
[17]Mellon, W. G., and Orr, D.. “Stochastic Reserve Losses and Expansion of Bank Credit.” American Economic Review, 1961.Google Scholar
[18]Morrison, George R.Liquidity Preferences of Commercial Banks. Chicago, Illinois: University of Chicago Press, 1966.Google Scholar
[19]Nerlove, Marc. “Two Very Simple Models of Optimal Investment Policy for the Competitive Firm under Dynamic Conditions.” Mathematical Social Science Board Workshop Paper No. 2, University of Chicago, 1970.Google Scholar
[20]Phillips, C. A.Bank Credit. New York, N.Y.: Macmillan and Co., 1920.Google Scholar
[21]Poole, William. “Commercial Bank Reserve Management in a Stochastic Model: Implications for Monetary Policy.” Journal of Finance, 1968.CrossRefGoogle Scholar
[22]Scarf, H. E. “A Survey of Analytic Techniques in Inventory Theory.” In Multistage Inventory Models and Techniques, edited by Scarf, H., Gilford, D., and Shelly, M., chap. 7. Stanford, Calif.: Stanford University Press, 1960.Google Scholar
[23]Taylor, Lance. “The Existence of Optimal Distributed Lags.” Review of Economic Studies, 1970.CrossRefGoogle Scholar
[24]Treadway, A. B. “Optimal Entrepreneurial Behavior and Distributed Lag Investment Equations.” Review of Economic Studies, 1969.CrossRefGoogle Scholar
[25]Tobin, James. “The Interest Elasticity of the Transactions Demand for Money.” Review of Economics and Statistics, 1954.Google Scholar
[26]Veinott, A. F. Jr. “The Status of Mathematical Inventory Theory.”Management Science, 1966.CrossRefGoogle Scholar
[27]Zabel, Edward. “The Competitive Firm, Uncertainty, and Capital Accumulation.” University of Rochester, 1970.Google Scholar