User cost of credit card services under risk with intertemporal nonseparability

Abstract

This paper derives the user cost of monetary assets and credit card services with interest rate risk under the assumption of intertemporal non-separability. Barnett and Su (2016) derived theory permitting inclusion of credit card transaction services into Divisia monetary aggregates. The risk adjustment in their theory is based on CCAPM 1 under intertemporal separability. The equity premium puzzle focusses on downward bias in the CCAPM risk adjustment to common stock returns. Despite the high risk of credit card interest rates, the risk adjustment under the CCAPM assumption of intertemporal separability might nevertheless be similarly small. While the known downward bias of CCAPM risk adjustments are of little concern with Divisia monetary aggregates containing only low risk monetary assets, that downward bias cannot be ignored, once high risk credit card services are included. We believe that extending to intertemporal non-separability could provide a non-negligible risk adjustment, as has been emphasized by Barnett and Wu (2015). In this paper, we extend the credit-card-augmented Divisia monetary quantity aggregates to the case of risk aversion and intertemporal non-separability in consumption. 1 CCAPM is the "consumptions capital asset pricing model," as opposed to the conventional "capital asset pricing model," CAPM. Our results are for the "representative consumer" aggregated over all consumers. While credit-card interest-rate risk may be low for some consumers, the volatility of credit card interest rates for the representative consumer is high, as reflected by the high volatility of the Federal Reserve's data on credit card interest rates aggregated over consumers. 2 One method of introducing intertemporal non-separability is to assume habit formation. We explore that possibility. To implement our theory, we introduce a pricing kernel, in accordance with the approach advocated by Barnett and Wu (2015). We assume that the pricing kernel is a linear function of the rate of return on a well-diversified wealth portfolio. We find that the risk adjustment of the credit-card-services user cost to its certainty equivalence level can be measured by its beta. That beta depends upon the covariance between the interest rates on credit card services and on the wealth portfolio of the consumer, in a manner analogous to the standard CAPM adjustment. As a result, credit card services' risk premia depend on their market portfolio risk exposure, which is measured by the beta of the credit card interest rates. We are currently conducting research on empirical implementation of the theory proposed in this paper. We believe that under intertemporal non-separability, we will be able to generate an accurate credit-card-augmented Divisia monetary index to explain the available empirical data.

Credit Cards, the Demand for Money, and Monetary Aggregation

“…The positive Morishima elasticities of substitution between credit card transaction services and traditional monetary assets suggest that credit card transaction services and traditional monetary assets are substitutes and that the credit card transaction services should be included in the monetary aggregates. Our results support Barnett et al (2016), Liu (2019), and who argue that much of the policy relevance of the Divisia monetary aggregates could be strengthened by the use of credit card-augmented Divisia monetary aggregates.…”

“…The interest rate and risk on credit cards transactions are high and volatile. Barnett and Su (2019) and Barnett and Liu (2019) extend the theoretical credit card-augmented Divisia monetary aggregates under uncertainty, and more recently Barnett et al (2021) further extend the existing theory of monetary services aggregation under risk to decisions under Knightian uncertainty. The credit card user cost under risk with intertemporal nonseparability is still ongoing research.…”

“…In this regard, Duca and Whitesell (1995) provide crosssectional evidence that credit card ownership is associated with lower holdings of monetary transactions balances and Barnett et al (2016, p. 2) conjecture that "credit card services are a substitute for the services of monetary transactions balances, perhaps to a much higher degree than the services of many of the assets included in traditional monetary aggregates." Barnett and Su (2019) and Barnett and Liu (2019) use the CAPM and CCAPM, respectively, to study how to include credit card transaction services into liquidity measures under risk. This is the first paper to use the microeconomics approach to empirically estimate the demand system of the credit card-augmented monetary aggregates and thus substantiate the microeconomic foundations of the credit card-augmented monetary aggregates.…”

The credit card-augmented Divisia monetary aggregates: an analysis based on recurrence plots and visual boundary recurrence plots

“…That might be because of changes in the fluctuations of these monetary aggregates around the year 2020. Hence, the application of the visual boundary recurrence plots provides an additional support to the arguments of Barnett and Liu (2019), , and Barnett et al (2023) that much of the policy relevance of the Divisia monetary aggregates could be strengthened by the use of the credit-augmented Divisia aggregates.…”

“…There are three kinds of the Divisia monetary aggregates, currently available by the Center for Financial Stability in New York City, the conventional Divisia monetary aggregates constructed by Barnett (1978Barnett ( , 1980 and the credit card-augmented Divisia monetary aggregates and credit card-augmented Divisia inside monetary aggregates, the latter two constructed more recently by Barnett and Su (2016, 2018 and Barnett et al (2023). A further extension to the case of risk with intertemporal nonseparability can be found in Barnett and Liu (2019). As already noted, and are the first papers to empirically examine the inference ability of the credit card-augmented Divisia monetary aggregates.…”