Consistency of Linear Forecasts in a Nonlinear Stochastic Economy

  • Cars HommesEmail author
  • Gerhard Sorger
  • Florian Wagener


The notion of consistent expectations equilibrium is extended to economies that are described by a nonlinear stochastic system. Agents in the model do not know the nonlinear law of motion and use a simple linear forecasting rule to form their expectations. Along a stochastic consistent expectations equilibrium (SCEE), these expectations are correct in a linear statistical sense, i.e., the unconditional mean and autocovariances of the actual (but unknown) nonlinear stochastic process coincide with those of the linear stochastic process on which the agents base their beliefs. In general, the linear forecasts do not coincide with the true conditional expectation, but an SCEE is an ‘approximate rational expectations equilibrium’ in the sense that forecasting errors are unbiased and uncorrelated. Adaptive learning of SCEE is studied in an overlapping generations framework.


Bounded rationality Expectation formation Consistent expectations Sample autocorrelation learning Path dependence 



Earlier versions of this paper have been presented at the IFAC symposium Computational Economics, Finance and Engineering, Barcelona, July 6–8, 2000, the CeNDEF workshops on Economic Dynamics, Amsterdam, January 4–6, 2001 and Leiden, June 17–28, 2002, the 8th Viennese workshop on Optimal Control, Dynamic Games and Nonlinear Dynamics, Vienna, May 14–16, 2003 as well as various department seminars. Stimulating discussions with participants are gratefully acknowledged. In particular, we would like to thank Buz Brock, Jim Bullard, George Evans, Jean-Michel Grandmont and Seppo Honkapohja for stimulating discussions. This research has been supported by the Netherlands Organization for Scientific Research (NWO).


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.CeNDEFUniversity of AmsterdamAmsterdamThe Netherlands
  2. 2.University of ViennaViennaAustria

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