Solution for Rational Expectation Models Free of Complex Numbers

Author(s)
Frank Hespeler

ABSTRACT

This paper approaches the problem of the potential for complex-valued solutions within linear macroeconomic models with rational expectations. It finds that these problems are associated with a specific solution method for the underlying model. The paper establishes that the danger of complex-valued solutions always can be eliminated by forcing those solutions to fulfill additional constraints. These constraints are essentially restrictions on the degrees of freedoms in indeterminate solutions.

This paper approaches the problem of the potential for complex-valued solutions within linear macroeconomic models with rational expectations. It finds that these problems are associated with a specific solution method for the underlying model. The paper establishes that the danger of complex-valued solutions always can be eliminated by forcing those solutions to fulfill additional constraints. These constraints are essentially restrictions on the degrees of freedoms in indeterminate solutions.

Cite this paper

nullF. Hespeler, "Solution for Rational Expectation Models Free of Complex Numbers,"*Theoretical Economics Letters*, Vol. 1 No. 3, 2011, pp. 47-52. doi: 10.4236/tel.2011.13011.

nullF. Hespeler, "Solution for Rational Expectation Models Free of Complex Numbers,"

References

[1] P. J. Stemp, “A Review of Jumps in Macroeconomic Mo- dels: With Special Reference to the Case When Eigenvalues Are Complex,” The University of Melbourne, De- partment of Economics, Research Paper Number: 920, 2004.

[2] T. A. Lubik and F. Schorfheide, “Computing Sunsport Equilibria in Linear Rational Expectations Models,” Jour- nal of Economic Dynamics and Control, Vol. 28, No. 3, 2003, pp. 273-285. doi:10.1016/S0165-1889(02)00153-7

[3] F. Hespeler, “On Boundary Conditions within the Solution of Macroeconomic Dynamic Models with Rational Expectations,” Ben-Gurion University of the Negev, 2008.

[4] O. J. Blanchard and C. M. Kahn, “The Solution of Linear Difference Models under Rational Expectations,” Econometrica, Vol. 48, No. 5, 1980, pp. 1305-1311. doi:10.2307/1912186

[5] F. Hespeler, “Solution Algprithm to a Class of Monetary Rational Equilibrium Macromodels with Optimal Monetary Policy,” Computational Economics, Vol. 31, No. 3, 2008, pp. 207-223. doi:10.1007/s10614-007-9114-2

[6] R. G. King and M. W. Watson, “The Solution of Singular Linear Difference Systems under Rational Expectations,” International Economic Review, Vol. 39, No. 4, 1998, pp. 1015-1028. doi:10.2307/2527350

[7] R. G. King and M. W. Watson, “System Reduction and Solution Algorithms for Singular Linear Difference Systems under Rational Expectations,” Computational Economics, Vol. 20, No. 1-2, 2002, pp. 57-68. doi:10.1023/A:1020576911923

[8] P. Klein, “Using the Generalized Schur form to Solve a Multivariate Linear Rational Expectations Model,” Journal of Economic Dynamics and Control, Vol. 24, No. 10, 2000, pp. 1405-1423. doi:10.1016/S0165-1889(99)00045-7

[9] P. Kowal, “An Algorithm for Solving Srbitrary Linear Rational Expectations Model,” EconWPA, 2005.

[10] C. A. Sims, “Solving Linear Rational Expectations Models,” Computational Economics, Vol. 20, No. 1-2, 2002, pp. 1-20. doi:10.1023/A:1020517101123

[11] C. Moler and G. Stewart, “An Algorithm for Generalized Matrix Eigenvalue Problems,” SIAM Journal on Nume- rical Analysis, Vol. 10, No. 2, 1973, pp. 241-256. doi:10.1137/0710024

[1] P. J. Stemp, “A Review of Jumps in Macroeconomic Mo- dels: With Special Reference to the Case When Eigenvalues Are Complex,” The University of Melbourne, De- partment of Economics, Research Paper Number: 920, 2004.

[2] T. A. Lubik and F. Schorfheide, “Computing Sunsport Equilibria in Linear Rational Expectations Models,” Jour- nal of Economic Dynamics and Control, Vol. 28, No. 3, 2003, pp. 273-285. doi:10.1016/S0165-1889(02)00153-7

[3] F. Hespeler, “On Boundary Conditions within the Solution of Macroeconomic Dynamic Models with Rational Expectations,” Ben-Gurion University of the Negev, 2008.

[4] O. J. Blanchard and C. M. Kahn, “The Solution of Linear Difference Models under Rational Expectations,” Econometrica, Vol. 48, No. 5, 1980, pp. 1305-1311. doi:10.2307/1912186

[5] F. Hespeler, “Solution Algprithm to a Class of Monetary Rational Equilibrium Macromodels with Optimal Monetary Policy,” Computational Economics, Vol. 31, No. 3, 2008, pp. 207-223. doi:10.1007/s10614-007-9114-2

[6] R. G. King and M. W. Watson, “The Solution of Singular Linear Difference Systems under Rational Expectations,” International Economic Review, Vol. 39, No. 4, 1998, pp. 1015-1028. doi:10.2307/2527350

[7] R. G. King and M. W. Watson, “System Reduction and Solution Algorithms for Singular Linear Difference Systems under Rational Expectations,” Computational Economics, Vol. 20, No. 1-2, 2002, pp. 57-68. doi:10.1023/A:1020576911923

[8] P. Klein, “Using the Generalized Schur form to Solve a Multivariate Linear Rational Expectations Model,” Journal of Economic Dynamics and Control, Vol. 24, No. 10, 2000, pp. 1405-1423. doi:10.1016/S0165-1889(99)00045-7

[9] P. Kowal, “An Algorithm for Solving Srbitrary Linear Rational Expectations Model,” EconWPA, 2005.

[10] C. A. Sims, “Solving Linear Rational Expectations Models,” Computational Economics, Vol. 20, No. 1-2, 2002, pp. 1-20. doi:10.1023/A:1020517101123

[11] C. Moler and G. Stewart, “An Algorithm for Generalized Matrix Eigenvalue Problems,” SIAM Journal on Nume- rical Analysis, Vol. 10, No. 2, 1973, pp. 241-256. doi:10.1137/0710024