8. Extensions and Variations
8.4. The Benchmark Yield Proxy and Extension to Risk Aversion
Since risk in exchange rates can be considerable, the extension of our results to the case of risk aversion could be explored in later research, using the approach in Barnett and Serletis (2000, chapter 12). Improvements to this approach are possible using the newest methodology on capital asset pricing in the finance literature. Regarding the
recommended procedure for producing a benchmark rate proxy, see the Appendix.
9. Conclusions
We advocate use of Barnett’s (1980) representative agent approach to Divisia
aggregation within euro area countries and then our heterogeneous countries approach to aggregation over countries. Our stochastic approach to aggregation over countries lends itself naturally to computation of Divisia second moments. We advocate computation of Divisia variance growth rates about the Divisia means across countries. Those Divisia second moments could provide useful information about the distribution effects of policy and about progess towards convergence over the euro area.
We introduce a new method of computation of the benchmark yield. Our approach is based upon summing premia extracted from the rate structure. Prior to introduction of the euro, our proposed procedure for computing the benchmark yield would produce a different benchmark rate for each country. At some time after the introduction of the euro, our procedure would equate the benchmark yields across euro area countries. The special case of a common benchmark yield across countries equates our heterogeneous-countries stochastic approach to another approach that we introduce: the multilateral representative agent approach. Hence either interpretation of our formulas can be applied, when the benchmark yield becomes the same for all countries in the euro area.
But prior to the establishment of a common benchmark yield across euro area countries, our more general stochastic heterogeneous countries approach should be preferred to the multilateral representative agent approach.
We define and produce the theory relevant to a third very restrictive case, which we call the unilateral representative agent approach. This approach, which we show to be implied by some earlier studies of euro-area monetary aggregation, is not recommended for use either before or after the introduction of the euro.
With the heterogeneous countries or multilateral representative agent approach, we find the need for two different consumer price indexes: one for use in deflating nominal to real monetary balances after aggregation over countries, and one for deflating nominal to real consumer goods expenditure. Only under the unreasonably restrictive homogeneous multilateral representative agent assumptions or the even more unreasonable unilateral representative agent assumptions, do the growth rates of the two consumer price indexes become equal.
While this result may seem surprising, we believe that it is represents the usual case, rather than an exceptional case. We find that the source of the wedge between the two needed price indexes is the existence of different true-cost-of living indexes for different countries. But in fact it is well known that true-cost-of-living indexes are not only different for different countries and different regions of countries, but also for different consumers. The true cost of living index depends upon tastes, and hence is different for different consumers, even if the law of one price holds so that goods prices are the same for all consumers.49
49 Consider two consumers faced with a rising price of rice, when one consumer likes rice and the other does not. The consumer who likes rice will experience an increase in cost of living and the other will not.
In addition, for nontraded goods, there is no reason to believe that even the price of the same good will be the same for consumers in different locations. The fact that consumers are price takers provides no reason to believe that they face the same true cost of living index, and hence the usual view that consumer goods and monetary assets should be deflated by the same price index cannot be supported by theory.
Appendix: The Benchmark Rate
The benchmark rate of return is the expected rate of return received on a pure investment providing no services other than its yield. Hence the market subtracts no liquidity premia, denomination premia, or other service premia from the benchmark yield. It is unlikely that any country has ever had a securities market for the benchmark asset. In fact in principal the benchmark asset cannot have a well organized secondary market, since the existence of such a market would itself be a liquidity service excluded by the definition of the benchmark asset. Rates of return are not easily available on assets having low liquidity, such as human capital stock or small firms having no publicly traded securities. The benchmark rate must be at least as high as the upper envelope over all of the monetary aggregates’ component yield-curve-adjusted rates of return. But that envelope must be raised further to include premia already removed by the market from those assets’ returns by the existence of markets for the assets.50
To get from the upper envelope over the component yield-curve-adjusted rates of return to the benchmark rate, it is necessary to add to the upper envelope a rate structure premium representing the premium for giving up the liquidity of the assets within the envelope. Such a rate structure premium must be a rate differential extracted from the rate structure. We recommend using the difference between a corporate bond rate of moderate quality and the Treasury security rate of the same maturity. Within the euro area, that corporate bond would need to be selected from a country having a good market for that bond within the relevant sample period and a corresponding Treasury security of the same maturity.51
In theory the benchmark rate is an expected rate of return, not an ex-post rate of return.
Since the rate differential between a bond rate and the corresponding Treasury security yield is likely to be much more volatile than the expected value of that rate differential, we advocate smoothing or forecasting that rate differential (e.g., by time series or moving average methods) before adding it to the upper envelope.
Earlier approaches to approximating the premium over the envelope usually involved either adding the full level of a bond rate to the envelope, or including a bond rate within the assets used in generating the envelope. Those approaches are not relevant to
extracting premia from the rate structure, and therefore are not recommended.
50 At some date following the introduction of the euro, a single benchmark yield could be imputed to all countries in the euro area. Prior to introduction of the euro, investment in a totally illiquid asset in a foreign country was probably uncommon, except by investors planning to move to the foreign country.
Since introduction of the euro greatly facilitates cross border investment, and removes the exchange rate risk associated with investing in a totally illiquid asset in another country, the upper envelope should be over the yield-curve-adjusted rates of return on all component assets in all euro area countries at some point following the introduction of the euro. This convergence of the benchmark rate to a common benchmark rate for the euro area would imply full integration in retail banking and financial markets in the euro, such that all rates available within the euro area become available to all residents of the euro area.
51 Although the upper envelope can differ across countries prior to the convergence of those envelopes, the same rate structure premium over that envelope could be used for all countries within the EMU, even before the appearance of the euro, since the rate structure premium is inherently an imputed proxy, rather
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For a complete list of Working Papers published by the ECB, please visit the ECB’s website (http://www.ecb.int).
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