Risk Adjustment of the Credit-Card Augmented Divisia Monetary Aggregates

Abstract

While credit cards provide transactions services, as do currency and demand deposits, credit cards have never been included in measures of the money supply. The reason is accounting conventions, which do not permit adding liabilities, such as credit card balances, to assets, such as money. However, economic aggregation theory and index number theory measure service flows and are based on microeconomic theory, not accounting. Barnett et al. derived the aggregation and index number theory needed to measure the joint services of credit cards and money. They derived and applied the theory under the assumption of risk neutrality. But since credit card interest rates are high and volatile, risk aversion may not be negligible. We extend the theory by removing the assumption of risk neutrality to permit risk aversion in the decision of the representative consumer.

Financial Firm Production of Inside Monetary and Credit Card Services: An Aggregation Theoretic Approach

“…See, e.g, Cavalcanti and Wallace (1996), Spencer (1974), Brunner and Meltzer (1967,1990, Meltzer (1969), Tobin (1963), Gurley and Shaw (1960), Johnson (1969), Pesek and Saving (1967), Fisher (1961), Friedman and Schwartz (1963), and Cagan (1956). Even the early literature on real business cycle theory (RBC), which sought to remove money from macroeconomic models, also considered the separation of inside money from outside money to be central to RBC's 15 Barnett, Chauvet, Leiva-Leon, and Su (2016) use the Federal Reserve data sources for both js e and , as is customary in most applied macroeconomic research. But the supply side theory presented in this paper is potentially relevant to the national accounts, which are based upon very careful consideration of bank balance sheets and detailed data sources, as pointed out to us by Kimberley Zieschang.…”

“…Hence the Divisia index is equally as applicable to aggregating over the monetary services and credit card transaction services produced by the financial intermediary as over the monetary services and credit card transactions services by the consumers, as derived by Barnett, Chauvet, Leiva-Leon, and Su (2016). In addition, Simpson's rule produces the Törnqvist-Theil discrete time approximation Diewert (1976, p. 125)].…”

“…Our theory does not apply to debit cards, or to store cards, or to charge cards not providing a line of credit. 9 Barnett, Chauvet, Leiva-Leon, and Su (2016) In classical economics, the benchmark asset is a secured pure investment. In contrast, js e is not the interest rate on a secured asset and is subject to substantial default and fraud risk.…”

“…For example, an implicit part of that interest rate could be in the form of an increased price of the goods purchased or in the form of a periodic service fee or membership fee. But Barnett, Chauvet, Leiva-Leon, and Su (2016) use only the Federal Reserve's average explicit interest rate series, which is lower than the one that would include implicit interest. Nevertheless, that downward biased explicit rate of return to credit card companies, , aggregated over consumers, tends to be very high, far exceeding , even after substantial losses from fraud.…”

“…This imputation includes only explicit interest paid, averaged over all credit card accounts. 12 See, e.g.,Butaru, Chen, Clark, Das, Lo, and Siddique (2016).13 Barnett, Chauvet, Leiva-Leon, and Su (2016) follow the Center for Financial Stability (CFS) and the Bank of Israel in using the short-term bank loan rate as a proxy for the benchmark rate. That interest rate has always exceeded the interest rate paid by banks on deposit accounts and on all other monetary assets used in the CFS Divisia monetary aggregates, and has always been lower than the Federal Reserve's reported average interest rate charged on credit card balances.…”