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The Exact Theoretical Rational Expectations Monetary Aggregate

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Author Info

  • William A. Barnett

    (Washington University in St. Louis)

  • Melvin J. Hinich

    (University of Texas - Austin)

  • Piyu Yue

    (IC2 Institute at the U. of Texas at Austin)

Abstract

In aggregation theory, index numbers are judged relative to their ability to track the exact aggregator functions nested within the economy's structure. Within the monetary sector, Barnett, Liu, and Jensen (1997) compared two statistical index numbers: the Divisia monetary aggregate and the simple sum monetary aggregate. They produced those comparisons using simulated data. In this paper, we again compare those two statistical index numbers with the exact rational expectations monetary aggregate, but we use actual data. Since we are not using simulated data, we estimate the parameters of the Euler equations and thereby of the nested monetary aggregator function using generalized method of moments. We explore the tracking errors of the two index numbers relative to the estimated exact aggregate. We investigate the circumstances under which risk aversion increases tracking error. We also use polyspectral methods to test for the existence of remaining nonlinear structure in the residual tracking errors

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Bibliographic Info

Paper provided by EconWPA in its series Macroeconomics with number 0003004.

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Length: 46 pages
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Handle: RePEc:wpa:wuwpma:0003004

Note: Type of Document - word doc, pdf and ps; prepared on Win 95; pages: 46 ; figures included.
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Keywords: Monetary aggregation; index number theory; spectral analysis; nonlinearity;

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References

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  1. Hinich, Melvin J. & Patterson, Douglas M., 1985. "Identification of the coefficients in a non-linear : time series of the quadratic type," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 269-288.
  2. James M. Poterba & Julio J. Rotemberg, 1988. "Money in the Utility Function: An Empirical Implementation," NBER Working Papers 1796, National Bureau of Economic Research, Inc.
  3. Barnett, William A. & Ronald Gallant, A. & Hinich, Melvin J. & Jungeilges, Jochen A. & Kaplan, Daniel T. & Jensen, Mark J., 1995. "Robustness of nonlinearity and chaos tests to measurement error, inference method, and sample size," Journal of Economic Behavior & Organization, Elsevier, vol. 27(2), pages 301-320, July.
  4. Barnett, William A. & Geweke, John & Wolfe, Michael, 1991. "Seminonparametric Bayesian estimation of the asymptotically ideal production model," Journal of Econometrics, Elsevier, vol. 49(1-2), pages 5-50.
  5. repec:fip:fedlpr:y:1994:i:mar:p:73-109 is not listed on IDEAS
  6. Belongia, Michael T, 1996. "Measurement Matters: Recent Results from Monetary Economics Reexamined," Journal of Political Economy, University of Chicago Press, vol. 104(5), pages 1065-83, October.
  7. repec:att:wimass:9520 is not listed on IDEAS
  8. William A. Barnett & A. Ronald Gallant & Melvin J. Hinich & Jochen A. Jungeilges & Daniel T. Kaplan & Mark J. Jensen, 1996. "A Single-Blind Controlled Competition among Tests for Nonlinearity and Chaos," Econometrics 9602005, EconWPA, revised 20 Sep 1996.
  9. Belongia, Michael T & Chalfant, James A, 1989. "The Changing Empirical Definition of Money: Some Estimates from a Model of the Demand for Money Substitutes," Journal of Political Economy, University of Chicago Press, vol. 97(2), pages 387-97, April.
  10. William A. Barnett & Melvin Hinich & Piyu Yue, 1989. "Monitoring monetary aggregates under risk aversion," Proceedings, Federal Reserve Bank of St. Louis, pages 189-245.
  11. K. Alec Chrystal & Ronald MacDonald, 1994. "Empirical evidence on the recent behavior and usefulness of simple-sum and weighted measures of the money stock," Review, Federal Reserve Bank of St. Louis, issue Mar, pages 73-109.
  12. William Barnett, 2005. "Monetary Aggregation," Macroeconomics 0503017, EconWPA.
  13. Feenstra, Robert C., 1986. "Functional equivalence between liquidity costs and the utility of money," Journal of Monetary Economics, Elsevier, vol. 17(2), pages 271-291, March.
  14. Hong, Yongmiao, 1996. "Consistent Testing for Serial Correlation of Unknown Form," Econometrica, Econometric Society, vol. 64(4), pages 837-64, July.
  15. 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.
  16. Barnett, William A & Offenbacher, Edward K & Spindt, Paul A, 1984. "The New Divisia Monetary Aggregates," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 1049-85, December.
  17. Daniel L. Thornton & Piyu Yue, 1992. "An extended series of divisia monetary aggregates," Review, Federal Reserve Bank of St. Louis, issue Nov, pages 35-52.
  18. 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.
  19. Barnett, William A & Fisher, Douglas & Serletis, Apostolos, 1992. "Consumer Theory and the Demand for Money," Journal of Economic Literature, American Economic Association, vol. 30(4), pages 2086-2119, December.
  20. Barnett, William A & Kirova, Milka & Pasupathy, Meenakshi, 1995. "Estimating Policy-Invariant Deep Parameters in the Financial Sector When Risk and Growth Matter," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 27(4), pages 1402-29, November.
  21. Swofford, James L & Whitney, Gerald A, 1987. "Nonparametric Tests of Utility Maximization and Weak Separability for Consumption, Leisure and Money," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 458-64, August.
  22. Hansen, Lars Peter & Singleton, Kenneth J, 1982. "Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 50(5), pages 1269-86, September.
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Citations

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Cited by:
  1. William A. Barnett & Shu Wu, 2005. "On user costs of risky monetary assets," Annals of Finance, Springer, vol. 1(1), pages 35-50, 01.
  2. Barnett, William A. & Chauvet, Marcelle & Tierney, Heather L. R., 2008. "Measurement Error in Monetary Aggregates: A Markov Switching Factor Approach," MPRA Paper 10179, University Library of Munich, Germany.
  3. William Barnett & Shu Wu, 2004. "Intertemporally non-separable monetary-asset risk adjustment and aggregation," Economics Bulletin, AccessEcon, vol. 5(13), pages 1-9.
  4. William Barnett & Unja Chae & John Keating, 2005. "Forecast Design in Monetary Capital Stock Measurement," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200516, University of Kansas, Department of Economics, revised Aug 2005.
  5. Binner, Jane & Elger, Thomas, 2002. "The UK Personal Sector Demand for Risky Money," Working Papers 2002:9, Lund University, Department of Economics.
  6. repec:ebl:ecbull:v:5:y:2004:i:13:p:1-9 is not listed on IDEAS
  7. Michael T. Belongia, 1992. "Selecting an intermediate target variable for monetary policy when the goal is price stability," Working Papers 1992-008, Federal Reserve Bank of St. Louis.
  8. Binner, Jane & Elger, Thomas & de Peretti, Philipe, 2002. "Is UK Risky Money Weakly Separable? A Stochastic Approach," Working Papers 2002:13, Lund University, Department of Economics.

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