User cost of credit card services under risk with intertemporal nonseparability

Please cite the paper as:
William A. Barnett, Jinan Liu, (2018), User cost of credit card services under risk with intertemporal nonseparability, World Economics Association (WEA) Conferences, No. 1 2018, Monetary Policy after the Global Crisis, 19th February to 2nd April, 2018


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 CCAPM1 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.

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. 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.

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2 comment

  • monetarypolicyconferenceadmin says:

    Look forward to the empirical verification. It seems very relevant to me.

  • Periklis Gogas says:

    A brilliant idea and a novel application of something that is actually terra incognita in money supply in the field of monetary economics and macroeconomics. The use of credit-cards as an additional component of money quantity in the economy is surely something that has been overlooked all previous years, especially from the supply-side of the financial system as it is examined in this paper. I truly look forward to the extension of this work as there are many theoretical and empirical aspects that need exploring further. For this reason, an empirical application with actual data from the US and other countries would provide further support and will help to clarify and illustrate the theoretical part more. Nevertheless, an interesting topic would be to include debit cards in the sample as in many countries (especially european and developing) debit cards are also a substantial part of the overall transactions.

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