تعهدات پرداخت، نرخ ذخیره قانونی، و تقاضا برای موازنه بانک مرکزی

We develop a model in which a bank's demand for reserves depends on the joint distribution of transactions, reserve requirements, and the interest rate. By devoting resources to its liquidity management, a bank can save on costly reserves required to settle its payments on time. We test the model with data from the largest banks in the Swiss Interbank Clearing system. We find that the turnover ratio (the speed with which a bank turns over its reserves in the payment system) depends largely on the aggregate value of its payments. We also find that reserve requirements impose a highly uneven burden on the banks.

In most countries, commercial banks have two reasons to hold central bank balances. First, banks can use these balances to meet their obligations in the interbank payment system. The second reason is that banks are obliged by law to maintain a certain minimum amount of reserves. The literature that explains the demand for cash balances with payments or transactions motives was initiated by Baumol and by Tobin and has been expanding prolificly ever since. By adding uncertainty over the cash flows to a Baumol–Tobin framework, Miller and Orr (1966) show that the demand for money depends not only on the interest rate and transaction costs, but also on the variance of the cash flows. In Baltensperger (1974), banks have the ability to influence uncertainty over net withdrawals. By investing in what he calls planning, the banks can reduce the variance of the withdrawals, which enables them to hold fewer central bank balances. Planning is a substitute for reserves. In these early models, only Poole (1968) explicitly incorporates both reserve requirements and stochastic payment flows into a demand function for reserves. Empirically, it is commonly observed that the turnover ratio, defined as the average value of a bank's payments divided by its average overnight reserves, varies greatly across banks. Data from the Swiss Interbank Clearing System (SIC), for instance, reveal that some banks’ turnover ratios are consistently above 100, while other banks have turnovers that never exceed 20. Based on the predictions of our model we argue that the reason for these large differences is twofold. First, following Baltensperger (1974) and more recently Furfine and Stehm (1998), we assume that liquidity management is a substitute for reserves. In other words, a bank can reduce holding the (costly) central bank balances that it needs to fulfill its payment obligations by investing in its cash or liquidity management. We model this function in such a way that there are increasing returns to scale. The more payments a bank has to make, the more investment in liquidity management pays off. In a modern payment system in which payment instructions are settled continuously and individually, factors such as clever bundling, sequencing, and timing of payments are important determinants of the balances needed to settle all obligations when due. In addition, active participation in the money market—be it by borrowing or lending—also influences the amount of reserves kept overnight in the central bank accounts. Of course, all of these activities are costly and a bank has to weigh these costs against the benefits of being able to reduce its end-of-day balances with the central bank. Second, we assume that the presence of legal reserve requirements can considerably influence a bank's demand for central bank balances. Reserve requirements impose an upper bound on the turnover ratios, and since the relationship between transaction value and reserve requirements can vary across banks, so can the turnover ratio. The reserve requirement being a function of the short-term liabilities of a bank is itself a random variable. Solving this more complex optimization problem, we find that the optimal turnover ratio of a bank is a function of the whole joint distribution of transactions, reserve requirements, and interest rates. Such joint distributions naturally depend on the business sectors in which a bank is active, thus contributing to the heterogenous turnover ratios we observe empirically. In this paper, we derive an exact solution to an individual bank's optimization problem, subject to uncertainty and stochastic reserve requirements. We test this model with data from the 40 largest participants in the Swiss Interbank Clearing system (SIC) for the period from 1992 to 1998. We find that the value of payments is the most important factor in determining the turnover ratio. We also find that the cost of reserve requirements imposed on different banks is fairly skewed, being basically nil for the majority, and moderate for the others.

We present a model in which the demand for central bank reserves arises from the liquidity needs of the interbank payment system as well as from reserve requirements. A bank's problem is to optimize the amount of non-remunerated central bank balances it holds so as to minimize the sum of the opportunity cost of liquidity and the cost of resources it uses for managing liquidity and payment operations. The model shows that—in the absence of reserve requirements—demand for liquidity depends on the (expected) levels of the interest rate and the payment flows as well as on the covariance between the two. The volatilities of the interest rate and of the payments flows do not influence the optimal behavior of a bank. Reserve requirements complicate the analysis. If they are high enough, they can for some banks lower the optimal turnover ratio, since they limit the potential benefits from an improved liquidity management. In addition, the volatility of payments is no longer neutral with respect to a bank's demand for settlement balances. With three stochastic variables—the interest rate, the volume of transactions, and the reserve requirements—the whole covariance matrix becomes relevant in the bank's optimization problem. The econometric investigation using data from the Swiss Interbank Clearing system (SIC) confirms that banks that are heavily involved in payment activities have invested more in their liquidity management than those who are less involved. Also, we find evidence that reserve requirements are detrimental to investments in liquidity management. Moreover, we are able to estimate the costs imposed on banks by the reserve requirements. It appears that these costs are not evenly distributed: The majority of banks are not affected by the reserve requirements, but for some they impose a significant cost.