DEPOSIT‐RUN MODEL OF MEMBER BANK BORROWINGS*

Abstract

THE PURPOSE of this study is to develop and test a model of the demand for memberbank borrowings from the Federal Reserve System. The theoretical structure used to derive the demand for borrowed reserves is based on a single-stage optimal-inventory model under uncertainty. In this model a bank begins the period with a given inventory of reserves along with a set of subjective probability-density functions for a vector of interest rates and the net deposit drain. Following the technique set out in the seminal article on optimal inventory policy by Arrow, Harris, and Marschak, this information is incorporated in the form of an expected-loss function. Given this information, the quantity of reserves that minimizes the expected total loss is determined. Under this interpretation the demand for member-bank borrowings is viewed as a derived demand from holding an optimal stock of reserves. The quantity of borrowings demanded is then given by the difference between the optimal and beginning stock of reserves. The microeconomic responses of individual banks are then aggregated to form an aggregate demand function for member-bank borrowings from the Federal Reserve. The model is tested with the monthly time-series data for all member banks, running from January 1954 to January 1967. The estimation procedure uses a distributed-lag scheme similar to that developed by Cagan and Friedman to determine expected values of the independent variables and a multiple-regression analysis with ordinary least squares to determine the coefficients and stability of the demand function. The empirical results reveal a number of interesting aspects of the borrowing behavior of commercial banks, provides some information on the length of lag for all member banks, and shows that a stable demand function can be isolated from available data. The results confirm the importance of unborrowed reserves and the spread between market interest rates and the discount rate as independent variables. With the exception of the 1959-60 period when approximately $2.5 billion in vault cash was added to member-bank reserves, the signs on all coeffcients are those expected from economic theory. The distributed-lag procedure yields average lags for the expected values of the independent variables behind their measured values of between four and five months. These lags declined slightly over the 13-year period giving support to the hypothesis that the development of the money markets has quickened the reaction of banks to variables that affect their behavior. In addition, this study relates developments in the federal-funds market to changes taking place in the demand function for discounts and presents a critical review of the literature.