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International Financial Aggregation and Index Number Theory: A Chronological Half-century Empirical Overview

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Abstract

This paper comprises a survey of a half century of research on international monetary aggregate data. We argue that since monetary assets began yielding interest, the simple sum monetary aggregates have had no foundations in economic theory and have sequentially produced one source of misunderstanding after another. The bad data produced by simple sum aggregation have contaminated research in monetary economics, have resulted in needless “paradoxes,” and have produced decades of misunderstandings in international monetary economics research and policy. While better data, based correctly on index number theory and aggregation theory, now exist, the official central bank data most commonly used have not improved in most parts of the world. While aggregation theoretic monetary aggregates exist for internal use at the European Central Bank, the Bank of Japan, and many other central banks throughout the world, the only central banks that currently make aggregation theoretic monetary aggregates available to the public are the Bank of England and the St. Louis Federal Reserve Bank. No other area of economics has been so seriously damaged by data unrelated to valid index number and aggregation theory. In this paper we chronologically review the past research in this area and connect the data errors with the resulting policy and inference errors. Future research on monetary aggregation and policy can most advantageously focus on extensions to exchange rate risk and its implications for multilateral aggregation over monetary asset portfolios containing assets denominated in more than one currency. The relevant theory for multilateral aggregation with exchange rate risk has been derived by Barnett (J Econom 136(2):457–482, 2007) and Barnett and Wu (Ann Finance 1:35–50, 2005).

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Notes

  1. Other overviews of published theoretical and empirical results in this literature are available in Barnett et al. (1992) and Serletis (2006).

  2. In aggregation theory measurement error refers to the tracking error in a nonparametric index number’s approximation to the aggregator function of microeconomic theory, where the aggregator function is the subutility or subproduction function that is weakly separable within tastes or technology of an economic agent’s complete utility or production function. Consequently, aggregator functions are increasing and concave and need to be estimated econometrically. On the other hand, state space models use the term measurement error to mean un-modeled noise, which is not captured by the state variable or idiosyncratic terms. In this paper, measurement error refers to this latter definition, which can be expected to be correlated with the former, when the behavior of the data process is consistent with microeconomic theory. But it should be acknowledged that neither concept of measurement error can be directly derived from the other. In fact the state space model concept of measurement error is more directly connected with the statistical (“atomistic”) approach to index number theory than to the more recent “economic approach,” which is at its best when data is not aggregated over economic agents.

  3. Subsequently Barnett (1987) derived the formula for the user cost of supplied monetary services. A regulatory wedge can exist between the demand and supply-side user costs, if non-payment of interest on required reserves imposes an implicit tax on banks.

  4. Our research in this paper is not dependent upon this simple decision problem, as shown by Barnett (1987), who proved that the same aggregator function and index number theory applies, regardless of whether the initial model has money in the utility function, or money in a production function, or neither, so long as there is intertemporal separability of structure and certain assumptions are satisfied for aggregation over economic agents. The aggregator function is the derived function that has been shown in general equilibrium always to exist, if money has positive value in equilibrium, regardless of the motive for holding money.

  5. The multilateral open economy extension is available in Barnett (2007).

  6. To be an admissible quantity aggregator function, the function u must be weakly separable within the consumer’s complete utility function over all goods and services. Producing a reliable test for weak separability is the subject of much intensive research, most recently by Barnett and de Peretti (2008).

  7. In Eq. (4), it is understood that the result is in continuous time, so the time subscripts are a short hand for functions of time. We use t to be the time period in discrete time, but the instant of time in continuous time.

  8. Diewert (1976) defines a ‘superlative index number’ to be one that is exactly correct for a quadratic approximation to the aggregator function. The discretization (7) to the Divisia index is in the superlative class, since it is exact for the quadratic translog specification to an aggregator function.

  9. The Federal Reserve Bank of St. Louis Divisia database, which we use in this paper, is not risk corrected. In addition, it is not adjusted for differences in marginal taxation rates on different asset returns or for sweeps, and its clustering of components into groups was not based upon tests of weak separability, but rather on the Federal Reserve’s official clustering. The St. Louis Federal Reserve Bank is in the process of revising its MSI database, perhaps to incorporate some of those adjustments. Regarding sweep adjustment, see Jones et al. (2005). At the present stage of this research, we felt it was best to use data available from the Federal Reserve for purposes of replicability and comparability with the official simple sum data. As a result, we did not modify the St. Louis Federal Reserve’s MSI database or the Federal Reserve Board’s simple sum data in any ways. This decision should not be interpreted to imply advocacy by us of the official choices.

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Authors and Affiliations

  1. University of Kansas, Lawrence, KS, USA

    William A. Barnett

  2. University of California at Riverside, Riverside, CA, USA

    Marcelle Chauvet

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  1. William A. Barnett
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  2. Marcelle Chauvet
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Correspondence to William A. Barnett.

Appendix

Appendix

Figures 31 and 32.

Fig. 31
figure 31

Milton Friedman, Newsweek, Sept 26, 1983

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Fig. 32
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William Barnett, Forbes, Sept 26, 1983

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Barnett, W.A., Chauvet, M. International Financial Aggregation and Index Number Theory: A Chronological Half-century Empirical Overview. Open Econ Rev 20, 1–37 (2009). https://doi.org/10.1007/s11079-008-9099-z

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