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.
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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.
 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.
 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.
 F. Hespeler, “On Boundary Conditions within the Solution of Macroeconomic Dynamic Models with Rational Expectations,” Ben-Gurion University of the Negev, 2008.
 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.
 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
 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
 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.
 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.
 P. Kowal, “An Algorithm for Solving Srbitrary Linear Rational Expectations Model,” EconWPA, 2005.
 C. A. Sims, “Solving Linear Rational Expectations Models,” Computational Economics, Vol. 20, No. 1-2, 2002, pp. 1-20. doi:10.1023/A:1020517101123
 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.