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Limited-dependent rational expectations models with jumps

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  • M. Hashem Pesaran
  • Francisco J. Ruge-Murcia

Abstract

This paper develops a Limited-Dependent Rational Expectations (LD-RE) model where the bounds can be fixed for an extended period, but are subject to occasional jumps. In this case, the behavior of the endogenous variable is affected by the agent's expectations about both the occurrence and the size of the jump. The RE solution for the one-sided and two-sided band are derived and shown to encompass the cases of perfectly predictable and stochastically varying bounds examined by earlier literature. We demonstrate that the solution for the one-sided band exists and is unique when the coefficient of the expectational variable is less than one. In the case of a two-sided band, the RE solution exists for all the parameter values and is unique if the coefficient of the expectational variable is less than or equal to one. These results hold even when the jump probability is stochastically varying and the error terms are conditionally heteroskedastic. As an illustration, we estimate a model of exchange rate determination in a target zone using data for the Franc/Mark exchange rate. Empirical results provide support for the non-linear model with time-varying realignment probability and indicate that the agents correctly anticipated most of the observed changes in the central parity.

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Bibliographic Info

Paper provided by Federal Reserve Bank of Minneapolis in its series Discussion Paper / Institute for Empirical Macroeconomics with number 111.

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Date of creation: 1996
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Handle: RePEc:fip:fedmem:111

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Keywords: Rational expectations (Economic theory);

References

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  1. Bertola, Giuseppe & Svensson, Lars E O, 1991. "Stochastic Devaluation Risk and the Empirical Fit of Target Zone Models," CEPR Discussion Papers, C.E.P.R. Discussion Papers 513, C.E.P.R. Discussion Papers.
  2. Pesaran, M. Hashem & Samiei, Hossein, 1995. "Limited-dependent rational expectations models with future expectations," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 19(8), pages 1325-1353, November.
  3. Rose, Andrew K & Svensson, Lars E O, 1993. "European Exchange Rate Credibility Before the Fall," CEPR Discussion Papers, C.E.P.R. Discussion Papers 852, C.E.P.R. Discussion Papers.
  4. Lars E.O. Svensson, 1990. "The Term Structure of Interest Rate Differentials in a Target Zone: Theory and Swedish Data," NBER Working Papers 3374, National Bureau of Economic Research, Inc.
  5. Krugman, Paul R, 1991. "Target Zones and Exchange Rate Dynamics," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 106(3), pages 669-82, August.
  6. Miller, Marcus & Weller, Paul, 1991. "Exchange Rate Bands with Price Inertia," Economic Journal, Royal Economic Society, Royal Economic Society, vol. 101(409), pages 1380-99, November.
  7. Pierluigi Balduzzi & Giuseppe Bertola & Silverio Foresi, 1993. "A Model of Target Changes and the Term Structure of Interest Rates," NBER Working Papers 4347, National Bureau of Economic Research, Inc.
  8. Miller, Marcus & Weller, Paul, 1989. "Exchange Rate Bands and Realignments in a Stationary Stochastic Setting," CEPR Discussion Papers, C.E.P.R. Discussion Papers 299, C.E.P.R. Discussion Papers.
  9. Donald, Stephen G. & Maddala, G. S., 1992. "A note on the estimation of limited dependent variable models under rational expectations," Economics Letters, Elsevier, Elsevier, vol. 38(1), pages 17-23, January.
  10. Rose, Andrew K., 1993. "Sterling's ERM credibility : Did the dog bark in the night?," Economics Letters, Elsevier, Elsevier, vol. 41(4), pages 419-427.
  11. Pesaran, M. Hashem & Samiei, Hossein, 1992. "Estimating limited-dependent rational expectations models with an application to exchange rate determination in a target zone," Journal of Econometrics, Elsevier, Elsevier, vol. 53(1-3), pages 141-163.
  12. Dornbusch, Rudiger, 1976. "Expectations and Exchange Rate Dynamics," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 84(6), pages 1161-76, December.
  13. Kees G. Koedijk & Philip A. Stork & Casper G. De Vries, 1998. "An EMS target zone model in discrete time," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 13(1), pages 31-48.
  14. Pesaran, M.H. & Murcia, F.J., 1993. "Limited-Dependent Rational Expectations Models with Stochastic Thresholds," Cambridge Working Papers in Economics 9318, Faculty of Economics, University of Cambridge.
  15. Pesaran, M Hashem & Samiei, Hossein, 1992. "An Analysis of the Determination of Deutsche Mark/French Franc Exchange Rate in a Discrete-Time Target-Zone Model," Economic Journal, Royal Economic Society, Royal Economic Society, vol. 102(411), pages 388-401, March.
  16. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 11(01), pages 122-150, February.
  17. Lee, Lung-fei, 1994. "Rational expectations in limited dependent variable models," Economics Letters, Elsevier, Elsevier, vol. 46(2), pages 97-104, October.
  18. Robert B. Davies, 2002. "Hypothesis testing when a nuisance parameter is present only under the alternative: Linear model case," Biometrika, Biometrika Trust, Biometrika Trust, vol. 89(2), pages 484-489, June.
  19. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
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Cited by:
  1. Pesaran, M.H. & Murcia, F.J., 1993. "Limited-Dependent Rational Expectations Models with Stochastic Thresholds," Cambridge Working Papers in Economics 9318, Faculty of Economics, University of Cambridge.
  2. RUGE-MURCIA, Francisco J., 1998. "Uncovering Financial Markets Beliefs About Inflation Targets," Cahiers de recherche, Universite de Montreal, Departement de sciences economiques 9803, Universite de Montreal, Departement de sciences economiques.
  3. RUGE-MURCIA, Francisco J., 2002. "Some Implications of the Zero Lower Bound on Interest Rates for the Term Structure and Monetary Policy," Cahiers de recherche, Universite de Montreal, Departement de sciences economiques 2002-06, Universite de Montreal, Departement de sciences economiques.

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