A first-order linear difference system under rational expectations is, AEyt+1|It=Byt+C(F)Ext|It , where yt is a vector of endogenous variables;xt is a vector ofexogenous variables; Eyt+1|It is the expectation ofyt+1 givendate t information; and C(F)Ext|It =C0xt+C1Ext+1|It+∣dot;s +CnExt+n|It. If the model issolvable, then yt can be decomposed into two sets of variables:dynamicvariables dt that evolve according toEdt+1|It = Wdt + ¶sid(F)Ext|It and other variables thatobey the dynamicidentities ft =−Kdt−¶sif(F)Ext|It. We developan algorithm for carrying out this decomposition and for constructing theimplied dynamic system. We also provide algorithms for (i) computing perfectforesight solutions and Markov decision rules; and (ii) solutions to relatedmodels that involve informational subperiods.
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Baxter, Marianne and Crucini, Mario J. (1993). Explaining saving-investment correlations. American Economic Review, 83(3), 416-436.
Blanchard, Olivier J. and Kahn, Charles (1980). The solution of linear difference models under rational expectations. Econometrica, 48(5), 1305–1311.
Boyd, John H. III and Dotsey, Michael (1993). Interest rate rules and nominal determinacy. Federal Reserve Bank of Richmond, Working Paper, revised February 1994.
Christiano, Lawrence J. and Eichenbaum, Martin (1992). Liquidity effects and the monetary transmission mechanism. American-Economic-Review 82(2), 346–353.
Crucini, Mario (1991). Transmission of business cycles in the open economy. Ph.D. dissertation, University of Rochester.
Farmer, Roger E.A. (1993). The Macroeconomics of Self-Fulfilling Prophecies, MIT Press.
Golub, G.H. and Van Loan, C.F. (1989). Matrix Computations, 2nd edn., Johns Hopkins University Press, Baltimore.
King, R.G., Plosser, C.I., and Rebelo, S.T. (1988a). Production, growth and business cycles, I: The basic neoclassical model. Journal of Monetary Economics, 21(2/3), 195–232.
King, R.G., Plosser, C.I., and Rebelo, S.T. (1988b). Production, growth and business cycles, technical appendix. University of Rochester Working Paper.
King, R.G. and Watson, M.W. (1996). Money, interest rates, prices and the business cycle. Review of Economics and Statistics.
King, R.G. and Watson, M.W. (1998). The solution of singular linear difference systems under rational expectations. IER.
King, R.G. and Watson, M.W. (1995a). The solution of singular linear difference systems under rational expectations. Working Paper.
King, R.G. and Watson, M.W. (1995b). Research notes on timing models.
Luenberger, David (1977). Dynamic equations in descriptor form. IEEE Transactions on Automatic Control, AC-22(3), 312–321.
Luenberger, David, (1978). Time invariant descriptor systems. Automatica, 14(5), 473–480.
Luenberger, David (1979). Introduction to Dynamic Systems: Theory, Models and Applications, John Wiley and Sons, New York.
McCallum, Bennett T. (1983). Non-uniqueness in rational expectations models: An attempt at perspective. Journal of Monetary Economics, 11(2), 139–168.
Moler, Cleve B. and Stewart, G.W. (1973). An algorithm for generalized matrix eigenvalue problems. SIAM Journal of Numerical Analysis, 10(2), 241–256.
Sargent, Thomas J. (1979). Macroeconomic Theory. Academic Press, New York.
Sims, Christopher A. (1989). Solving non-linear stochastic optimization problems backwards. Discussion Paper 15, Institute for Empirical Macroeconomics, FRB Minneapolis.
Svensson, Lars E.O. (1985). Money and asset prices in a cash in advance economy. Journal of Political Economy, 93, 919–944.
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King, R.G., Watson, M.W. System Reduction and Solution Algorithms for Singular Linear Difference Systems under Rational Expectations. Computational Economics 20, 57–86 (2002). https://doi.org/10.1023/A:1020576911923