Joint aggregation over money and credit card services under risk

Modern aggregation theory and index number theory were introduced into monetary economics by Barnett (1980). The widely used Divisia monetary aggregates, provided to the public in monthly releases by the Center for Financial Stability in NY City, are based upon that paper. A key result upon which the rest of the theory depended was Barnett's derivation of the user-cost price of monetary assets. To make that critical part of Barnett's results available prior to publication in the Journal of Econometrics, Barnett (1978) repeated that important proof two years earlier in Economics Letters. The extension of that literature to risk with intertemporally non-separable preferences subsequently appeared in Barnett and Wu (2005). To make that result available prior to publication in the Annals of Finance, the paper's theory without proofs was provided a year earlier by Barnett and Wu (2004) in the Economic Bulletin. The theory was extended by Barnett and Su (2016a) to include the services of credit card transactions volumes under risk. The theory will appear in the proceedings volume of a conference to be held in Rome in June 2017. The proceedings will appear as a special issue of the journal, Macroeconomic Dynamics, in late 2019 at the earliest. We are making available the key results from that paper below, without the proofs. Prior to publication of Barnett and Su (2016a), the proofs will be available in the paper's online working paper version, Barnett and Su (2016b).