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User Cost of Credit Card Services under Risk with Intertemporal Nonseparability


  • Barnett, William
  • Liu, Jinan


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 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.

Suggested Citation

  • Barnett, William & Liu, Jinan, 2017. "User Cost of Credit Card Services under Risk with Intertemporal Nonseparability," MPRA Paper 81461, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:81461

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    References listed on IDEAS

    1. William A. Barnett & Shu Wu, 2011. "On User Costs of Risky Monetary Assets," World Scientific Book Chapters,in: Financial Aggregation And Index Number Theory, chapter 3, pages 85-105 World Scientific Publishing Co. Pte. Ltd..
    2. William Barnett & Apostolos Serletis & W. Erwin Diewert, 2005. "The Theory of Monetary Aggregation (book front matter)," Macroeconomics 0511008, University Library of Munich, Germany.
    3. William A. Barnett & Unja Chae & John W. Keating, 2011. "The Discounted Economic Stock of Money with VAR Forecasting," World Scientific Book Chapters,in: Financial Aggregation And Index Number Theory, chapter 4, pages 107-150 World Scientific Publishing Co. Pte. Ltd..
    4. Barnett, William & Chauvet, Marcelle & Leiva-Leon, Danilo & Su, Liting, 2016. "Nowcasting nominal gdp with the credit-card augmented Divisia monetary aggregates," MPRA Paper 73246, University Library of Munich, Germany.
    5. William Barnett & Marcelle Chauvet & Danilo Leiva-Leon & Liting Su, 2016. "The Credit-Card-Services Augmented Divisia Monetary Aggregates," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201604, University of Kansas, Department of Economics, revised Aug 2016.
    6. Barnett, William A., 1980. "Economic monetary aggregates an application of index number and aggregation theory," Journal of Econometrics, Elsevier, vol. 14(1), pages 11-48, September.
    7. Barnett, William A. & Liu, Yi & Jensen, Mark, 1997. "Capm Risk Adjustment For Exact Aggregation Over Financial Assets," Macroeconomic Dynamics, Cambridge University Press, vol. 1(02), pages 485-512, June.
    8. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
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    More about this item


    Divisia Index; monetary aggregation; intertemporal non-separability; credit card services; risk adjustment.;

    JEL classification:

    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • E03 - Macroeconomics and Monetary Economics - - General - - - Behavioral Macroeconomics
    • E40 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - General
    • E41 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Demand for Money
    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy
    • E51 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Money Supply; Credit; Money Multipliers
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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