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Project Rational Expectations

General† Results

 

This part of my work contributes to the solution of rational expectations model. In "Solution algorithm to a class of monetary rational equilibrium macromodels with optimal monetary policy design" I presented a method to solve rational expectations models even for the case that the influence of expectational errors on stable endogenous variables can not be eliminated. In this case, the expectational errors can be directly explained by the underlying fundamental shocks to the economy. Hence, solutions to the model still exist. However, those solutions are frequently characterized by indeterminacy issues. Fortunately, as it is demonstrated in "On boundary conditions within the solution of macroeconomic dynamic models with rational expectations", the modelís transversality constraint, when interpreted as a restriction on current growth rates, contains information, which can be used in order to reduce the degree of indeterminacy in the modelís solution. Therefore, this information helps to exclude a substantial subset of all those solutions obtained by either traditional solution methods or the methodology outlaid above.
Finally, the use of the Generalized Schur Decomposition within the solution of difference equations or differential equations involves the risk of receiving solutions which include complex numbers. However, as shown in
"Solution for rational expectation models free of complex numbers", this risk can potentially be eliminated by choosing only those solutions, whose degrees of indeterminacies within the imaginary parts of all the solutionís coefficients for endogenous variables or shock terms allow the elimination of those imaginary parts by an appropriate choice for the undetermined factors.

In "Solving Near-Rational Expectations Models: A (Linear?) Perturbation Approach." my co-author Marco Maria Sorge and I discuss the role of first-order approximate solutions to near-rational dynamic stochastic models. Under near-rationality, subjective beliefs are distorted away from rational expectations via a change of measure process which fulfills some regularity conditions. Our results show that equilibrium indeterminacy may arise even when the martingale representation of beliefs distortion depends on the economy's fundamentals solely. This provides theoretical support to the modeling assumptions of Woodfordís 2010 paper in American Economic Review 100, 274-333.

 

Any comments on this line of work or the contributions presented above are highly appreciated. Please feel free to contact me with all your remarks or questions.

 

Monetary Economics, Macroeconomics, Computational Economics and Financial Stability