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Interest Rate Rules And Nominal Determinacy

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  • BOYD III, J.H.
  • DOTSEY, M.

Abstract

Monetary economists have recently begun a serious study of money supply rules that allow the Fed to adjustably peg the nominal interest rate under rational expectations. These rules vary from procedures that produce stationary nominal magnitudes to those that generate nonstationarities in nominal variables. Our paper investigates the determinacy properties of three representative interest rate rules. ; We use Blanchard and Kahn's solution technique as a starting point. It doesn't directly apply, so we first modify their procedure. We then narrow the range of solutions by considering the ARMA solutions of Evans and Honkapohja and the global minimum state variable solution of McCallum. We then examine these solutions in light of the expectational stability notions employed by DeCanio, Bray and Evans. ; Two of the three classes of rules yield a unique admissible solution. The exclusion of bubbles usually rules out the general ARMA solutions present in Evans and Honkapohja and leads to unique solutions via a saddlepoint property. Nonetheless, the nonstationary money supply rules we examine do not generally yield a well determined system over all parameter values. We employ the global minimum state variable methodology of McCallum and Evans' expectational stability in an effort to insure uniqueness. Although these methods are usually in agreement, one of the nonstationary rules yields a global minimum state variable solution that is expectationally unstable when the central bank is sensitive to interest rate deviations. Moreover, under these conditions, an alternative (non-global) minimum state variable solution is expectationally stable, casting doubt on the applicability of McCallum's global procedure in this context.

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Bibliographic Info

Paper provided by University of Rochester - Center for Economic Research (RCER) in its series RCER Working Papers with number 222.

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Length: 24 pages
Date of creation: 1990
Date of revision:
Handle: RePEc:roc:rocher:222

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Postal: University of Rochester, Center for Economic Research, Department of Economics, Harkness 231 Rochester, New York 14627 U.S.A.

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Keywords: interest rate ; economic models ; banks;

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References

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  1. Gourieroux, C & Laffont, J J & Monfort, Alain, 1982. "Rational Expectations in Dynamic Linear Models: Analysis of the Solutions," Econometrica, Econometric Society, Econometric Society, vol. 50(2), pages 409-25, March.
  2. Michael Dotsey & Robert G. King, 1983. "Monetary Instruments and Policy Rules in a Rational Expectations Environment," NBER Working Papers 1114, National Bureau of Economic Research, Inc.
  3. Evans, George W., 1986. "Selection criteria for models with non-uniqueness," Journal of Monetary Economics, Elsevier, Elsevier, vol. 18(2), pages 147-157, September.
  4. McCallum, Bennett T., 1983. "On non-uniqueness in rational expectations models : An attempt at perspective," Journal of Monetary Economics, Elsevier, Elsevier, vol. 11(2), pages 139-168.
  5. Matthew B. Canzoneri & Dale W. Henderson & Kenneth S. Rogoff, 1981. "The information content of the interest rate and optimal monetary policy," International Finance Discussion Papers, Board of Governors of the Federal Reserve System (U.S.) 192, Board of Governors of the Federal Reserve System (U.S.).
  6. Marvin Goodfriend, 1986. "Interest rate smoothing and price level trend-stationarity," Working Paper, Federal Reserve Bank of Richmond 86-04, Federal Reserve Bank of Richmond.
  7. Blume, L. E. & Bray, M. M. & Easley, D., 1982. "Introduction to the stability of rational expectations equilibrium," Journal of Economic Theory, Elsevier, Elsevier, vol. 26(2), pages 313-317, April.
  8. Bennett T. McCallum, 1982. "Price Level Determinacy with an Interest Rate Policy Rule and Rational Expectations," NBER Working Papers 0559, National Bureau of Economic Research, Inc.
  9. Evans, George & Honkapohja, Seppo, 1986. "A Complete Characterization of ARMA Solutions to Linear Rational Expectations Models," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 53(2), pages 227-39, April.
  10. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, Econometric Society, vol. 48(5), pages 1305-11, July.
  11. DeCanio, Stephen J, 1979. "Rational Expectations and Learning from Experience," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 93(1), pages 47-57, February.
  12. Evans, George, 1985. "Expectational Stability and the Multiple Equilibria Problem in Linear Rational Expectations Models," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 100(4), pages 1217-33, November.
  13. Bennett T. McCallum, 1986. "Some Issues Concerning Interest Rate Pegging, Price Level Determinacy, and the Real Bills Doctrine," NBER Working Papers 1294, National Bureau of Economic Research, Inc.
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Citations

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Cited by:
  1. Michael Dotsey, 1996. "Some not-so-unpleasant monetarist arithmetic," Economic Quarterly, Federal Reserve Bank of Richmond, Federal Reserve Bank of Richmond, issue Fall, pages 73-91.
  2. Woodford, Michael, 1995. "Price-level determinacy without control of a monetary aggregate," Carnegie-Rochester Conference Series on Public Policy, Elsevier, Elsevier, vol. 43(1), pages 1-46, December.
  3. Onatski, Alexei, 2006. "Winding number criterion for existence and uniqueness of equilibrium in linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 30(2), pages 323-345, February.
  4. Michael Dotsey & Christopher Otrok, 1994. "M2 and monetary policy: a critical review of the recent debate," Economic Quarterly, Federal Reserve Bank of Richmond, Federal Reserve Bank of Richmond, issue Win, pages 41-49.
  5. Michael Dotsey & Andreas Hornstein, 2011. "On the implementation of Markov-perfect monetary policy," Working Papers 11-29, Federal Reserve Bank of Philadelphia.
  6. James B. Bullard, 1991. "Learning, rational expectations and policy: a summary of recent research," Review, Federal Reserve Bank of St. Louis, Federal Reserve Bank of St. Louis, issue Jan, pages 50-60.
  7. Michael Dotsey & Andreas Hornstein, 2011. "On the implementation of Markov-Perfect interest rate and money supply rules : global and local uniqueness," Working Paper, Federal Reserve Bank of Richmond 09-06, Federal Reserve Bank of Richmond.
  8. William Kerr & Robert G. King, 1996. "Limits on interest rate rules in the IS model," Economic Quarterly, Federal Reserve Bank of Richmond, Federal Reserve Bank of Richmond, issue Spr, pages 47-75.
  9. Frank Hespeler, 2008. "Solution Algorithm to a Class of Monetary Rational Equilibrium Macromodels with Optimal Monetary Policy Design," Computational Economics, Society for Computational Economics, Society for Computational Economics, vol. 31(3), pages 207-223, April.

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