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Limited-dependent rational expectations models with jumps

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

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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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
Date of revision:
Handle: RePEc:fip:fedmem:111
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  1. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  2. Bertola, Giuseppe & Svensson, Lars E O, 1991. "Stochastic Devaluation Risk and the Empirical Fit of Target Zone Models," CEPR Discussion Papers 513, C.E.P.R. Discussion Papers.
  3. Miller, M. & Weller, P., 1988. "Exchange Rate Bands And Realignments In A Stationary Stochastic Setting," The Warwick Economics Research Paper Series (TWERPS) 317, University of Warwick, Department of Economics.
  4. Balduzzi, Pierluigi & Bertola, Giuseppe & Foresi, Silverio, 1997. "A model of target changes and the term structure of interest rates," Journal of Monetary Economics, Elsevier, vol. 39(2), pages 223-249, July.
  5. Pesaran, M.H. & Samiei, H., 1993. "Limited-Dependaent Rational Expectations Models with Future Expectations," Cambridge Working Papers in Economics 9321, Faculty of Economics, University of Cambridge.
  6. Rose, A.K. & Svensson, L.E.O., 1993. "European Exchange Rate Credibility Before the Fall," Papers 542, Stockholm - International Economic Studies.
  7. Lee, Lung-fei, 1994. "Rational expectations in limited dependent variable models," Economics Letters, Elsevier, vol. 46(2), pages 97-104, October.
  8. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
  9. Pesaran, M.H. & Samiei, H., 1991. "An Analysis of the determination of Dutsche Mark/French Franc Exchange rate in a Discrete-Time Target-Zone Model," Papers 38, California Los Angeles - Applied Econometrics.
  10. Svensson, Lars E O, 1991. "The Term Structure of Interest Rate Differentials in a Target Zone: Theory and Swedish Data," CEPR Discussion Papers 495, C.E.P.R. Discussion Papers.
  11. Donald, Stephen G. & Maddala, G. S., 1992. "A note on the estimation of limited dependent variable models under rational expectations," Economics Letters, Elsevier, vol. 38(1), pages 17-23, January.
  12. Miller, Marcus & Weller, Paul, 1991. "Exchange Rate Bands with Price Inertia," Economic Journal, Royal Economic Society, vol. 101(409), pages 1380-99, November.
  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., vol. 13(1), pages 31-48.
  14. Paul R. Krugman, 1988. "Target Zones and Exchange Rate Dynamics," NBER Working Papers 2481, National Bureau of Economic Research, Inc.
  15. 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, vol. 53(1-3), pages 141-163.
  16. Rose, Andrew K., 1993. "Sterling's ERM credibility : Did the dog bark in the night?," Economics Letters, Elsevier, vol. 41(4), pages 419-427.
  17. Robert B. Davies, 2002. "Hypothesis testing when a nuisance parameter is present only under the alternative: Linear model case," Biometrika, Biometrika Trust, vol. 89(2), pages 484-489, June.
  18. Hashem Pesaran, M. & Ruge-Murcia, Francisco J., 1996. "Limited-dependent rational expectations models with stochastic thresholds," Economics Letters, Elsevier, vol. 51(3), pages 267-276, June.
  19. Dornbusch, Rudiger, 1976. "Expectations and Exchange Rate Dynamics," Journal of Political Economy, University of Chicago Press, vol. 84(6), pages 1161-76, December.
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