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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
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Handle: RePEc:fip:fedmem:111
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  1. Svensson, Lars E. O., 1991. "The term structure of interest rate differentials in a target zone : Theory and Swedish data," Journal of Monetary Economics, Elsevier, vol. 28(1), pages 87-116, August.
  2. Rose, Andrew K., 1993. "Sterling's ERM credibility : Did the dog bark in the night?," Economics Letters, Elsevier, vol. 41(4), pages 419-427.
  3. 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.
  4. Andrew K. Rose & Lars E.O. Svensson, 1993. "European Exchange Rate Credibility Before the Fall," NBER Working Papers 4495, National Bureau of Economic Research, Inc.
  5. 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.
  6. 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.
  7. 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.
  8. Miller, Marcus & Weller, Paul, 1990. "Exchange Rate Bands with Price Inertia," CEPR Discussion Papers 421, C.E.P.R. Discussion Papers.
  9. 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.
  10. Dornbusch, Rudiger, 1976. "Expectations and Exchange Rate Dynamics," Journal of Political Economy, University of Chicago Press, vol. 84(6), pages 1161-76, December.
  11. 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.
  12. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
  13. Lee, Lung-fei, 1994. "Rational expectations in limited dependent variable models," Economics Letters, Elsevier, vol. 46(2), pages 97-104, October.
  14. Giuseppe Bertola & Lars E.O. Svensson, 1991. "Stochastic Devaluation Risk and the Empirical Fit of Target Zone Models," NBER Working Papers 3576, National Bureau of Economic Research, Inc.
  15. Krugman, Paul R, 1991. "Target Zones and Exchange Rate Dynamics," The Quarterly Journal of Economics, MIT Press, vol. 106(3), pages 669-82, August.
  16. 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.
  17. 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.
  18. Miller, Marcus & Weller, Paul, 1989. "Exchange Rate Bands and Realignments in a Stationary Stochastic Setting," CEPR Discussion Papers 299, C.E.P.R. Discussion Papers.
  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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