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Multilateral exchange rates: A multivariate regression framework

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  • Kunkler, Michael

Abstract

Currencies must be priced in terms of a numéraire when they are included in a regression model. The numéraire can be either a single-currency numéraire or a multicurrency numéraire: a weighted basket of numéraire currencies. Pricing currencies in terms of a multicurrency numéraire results in a system of multilateral exchange rates. A no-arbitrage condition enforces the movements in the system of multilateral exchange rates associated with the numéraire currencies to be a singular system, where the covariance matrix is singular and its ordinary inverse does not exist. Singular systems pose a methodological challenge in a multivariate regression model. This paper provides a solution to overcome this methodological challenge by imposing implicit restrictions on both the explanatory variables and the regression coefficients. In addition, the generalized least squares estimator is modified by replacing the ordinary inverse with the generalized inverse. The proposed solution provides a consistent multivariate regression model to explain the observed heterogeneity in the relative currency market.

Suggested Citation

  • Kunkler, Michael, 2023. "Multilateral exchange rates: A multivariate regression framework," Journal of Economics and Business, Elsevier, vol. 125.
    • Handle: RePEc:eee:jebusi:v:125-126:y:2023:i::s0148619523000255
    DOI: 10.1016/j.jeconbus.2023.106132
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    References listed on IDEAS

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    1. Jeremy J. Siegel, 1972. "Risk, Interest Rates and the Forward Exchange," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 86(2), pages 303-309.
    2. John Y. Campbell & Karine Serfaty‐De Medeiros & Luis M. Viceira, 2010. "Global Currency Hedging," Journal of Finance, American Finance Association, vol. 65(1), pages 87-121, February.
    3. Charles Engel & Kenneth D. West, 2005. "Exchange Rates and Fundamentals," Journal of Political Economy, University of Chicago Press, vol. 113(3), pages 485-517, June.
    4. repec:ebl:ecbull:v:3:y:2002:i:1:p:1-7 is not listed on IDEAS
    5. Haupt, Harry & Oberhofer, Walter, 2006. "Generalized adding-up in systems of regression equations," Economics Letters, Elsevier, vol. 92(2), pages 263-269, August.
    6. Kunkler, Michael & MacDonald, Ronald, 2015. "Half-lives of currencies and aggregation bias," Economics Letters, Elsevier, vol. 135(C), pages 58-60.
    7. Stephen A. Ross, 2013. "The Arbitrage Theory of Capital Asset Pricing," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 1, pages 11-30, World Scientific Publishing Co. Pte. Ltd..
    8. Kunkler, Michael, 2021. "The Chinese renminbi's co-movement with the US dollar: Addressing the numéraire issue," Finance Research Letters, Elsevier, vol. 40(C).
    9. Haynes, Stephen E. & Stone, Joe A., 1994. "The relationship between bilateral and multilateral models of exchange rates," Journal of International Money and Finance, Elsevier, vol. 13(1), pages 71-82, February.
    10. Jeffrey A. Frankel & Shang-Jin Wei, 1994. "Yen Bloc or Dollar Bloc? Exchange Rate Policies of the East Asian Economies," NBER Chapters, in: Macroeconomic Linkage: Savings, Exchange Rates, and Capital Flows, pages 295-333, National Bureau of Economic Research, Inc.
    11. BARTEN, Anton P., 1969. "Maximum likelihood estimation of a complete system of demand equations," LIDAM Reprints CORE 34, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. Meese, Richard A. & Rogoff, Kenneth, 1983. "Empirical exchange rate models of the seventies : Do they fit out of sample?," Journal of International Economics, Elsevier, vol. 14(1-2), pages 3-24, February.
    13. Harry Haupt & Walter Oberhofer, 2002. "Fully restricted linear regression: A pedagogical note," Economics Bulletin, AccessEcon, vol. 3(1), pages 1-7.
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    Keywords

    Multilateral exchange rates;

    JEL classification:

    • F31 - International Economics - - International Finance - - - Foreign Exchange

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