Barnett, William A. and He, Susan (2009): Existence of Singularity Bifurcation in an Euler-Equations Model of the United States Economy: Grandmont was Right.
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Abstract: Grandmont (1985) found that the parameter space of the most classical dynamic general-equilibrium macroeconomic models are stratified into an infinite number of subsets supporting an infinite number of different kinds of dynamics, from monotonic stability at one extreme to chaos at the other extreme, and with all forms of multiperiodic dynamics between. But Grandmont provided his result with a model in which all policies are Ricardian equivalent, no frictions exist, employment is always full, competition is perfect, and all solutions are Pareto optimal. Hence he was not able to reach conclusions about the policy relevance of his dramatic discovery. As a result, Barnett and He (1999, 2001, 2002) investigated a Keynesian structural model, and found results supporting Grandmont’s conclusions within the parameter space of the Bergstrom-Wymer continuous-time dynamic macroeconometric model of the UK economy. That prototypical Keynesian model was produced from a system of second order differential equations. The model contains frictions through adjustment lags, displays reasonable dynamics fitting the UK economy’s data, and is clearly policy relevant. In addition, results by Barnett and Duzhak (2008,2009) demonstrate the existence of Hopf and flip (period doubling) bifurcation within the parameter space of recent New Keynesian models. Lucas-critique criticism of Keynesian structural models has motivated development of Euler equations models having policy-invariant deep parameters, which are invariant to policy rule changes. Hence, we continue the investigation of policy-relevant bifurcation by searching the parameter space of the best known of the Euler equations general-equilibrium macroeconometric models: the path-breaking Leeper and Sims (1994) model. We find the existence of singularity bifurcation boundaries within the parameter space. Although never before found in an economic model, singularity bifurcation may be a common property of Euler equations models, which often do not have closed form solutions. Our results further confirm Grandmont’s views. Beginning with Grandmont’s findings with a classical model, we continue to follow the path from the Bergstrom-Wymer policy-relevant Keynesian model, to New Keynesian models, and now to Euler equations macroeconomic models having deep parameters.
|Item Type:||MPRA Paper|
|Original Title:||Existence of Singularity Bifurcation in an Euler-Equations Model of the United States Economy: Grandmont was Right|
|Keywords:||Bifurcation; inference; dynamic general equilibrium; Pareto optimality; Hopf bifurcation; Euler equations; Leeper and Sims model; singularity bifurcation; stability|
|Subjects:||E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles > E32 - Business Fluctuations; Cycles
C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C14 - Semiparametric and Nonparametric Methods: General
C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C52 - Model Evaluation, Validation, and Selection
E - Macroeconomics and Monetary Economics > E5 - Monetary Policy, Central Banking, and the Supply of Money and Credit > E52 - Monetary Policy
C - Mathematical and Quantitative Methods > C2 - Single Equation Models; Single Variables > C22 - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles > E37 - Forecasting and Simulation: Models and Applications
E - Macroeconomics and Monetary Economics > E6 - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, Macroeconomic Policy, and General Outlook > E61 - Policy Objectives; Policy Designs and Consistency; Policy Coordination
|Depositing User:||William A. Barnett|
|Date Deposited:||17. Jan 2009 09:44|
|Last Modified:||15. Feb 2013 22:57|
Bala V. A pitchfork bifurcation in the tatonement process. Economic Theory 1997; 10; 521-530.
Barnett WA., Chen P. The aggregation theoretic monetary aggregates are chaotic and have strange attractors: an econometric application of mathematical chaos. In: Barnett WA, Berndt ER, White H (Eds.), Dynamic econometric modeling. Cambridge University Press: Cambridge, UK; 1988. p.199-246.
Barnett WA and Duzhak EA. Non-robust dynamic inferences from macroeconometric models: bifurcation of confidence regions. Physica A, vol 387, no 15, June, 2008, pp. 3817-3825.
Barnett WA and Duzhak EA. Empirical assessment of bifurcation regions within new Keynesian models. Economic Theory 2009, forthcoming.
Barnett WA., He Y. Analysis and control of bifurcations in continuous time macroeconometric systems. Proceedings of the 37th IEEE Conference on Decision and Control. December 16-18, 1998; Tampa, Florida; p. 2455-2460.
Barnett WA., He Y. Stability analysis of continuous time macroeconometric systems. Studies in Nonlinear Dynamics and Econometrics 1999; 3; 169-188.
Barnett WA, He Y. Nonlinearity, chaos, and bifurcation: a competition and an experiment. In: Negishi T, Ramachandran R, Mino K (Eds.), Economic theory, dynamics and markets: essays in honor of Ryuzo Sato. Kluwer Academic Publishers: Amsterdam; 2001. p. 167-187.
Barnett WA., He Y. Stabilization policy as bifurcation selection: would stabilization policy work if the economy really were unstable? Macroeconomic Dynamics 2002; 6; 713-747.
Barnett WA., He Y. Bifurcations in macroeconomic models. In: Dowrick S, Rohan P, Turnovsky S (Eds), Economic growth and macroeconomic dynamics: recent developments in economic theory. Cambridge University Press: Cambridge, UK; 2004. p. 95-112.
Barnett W., He Y. Singularity bifurcations. Journal of Macroeconomics 2006; 28; 5-22.
Barnett WA., Deissenberg C, Feichtinger G. Economic complexity: non-linear dynamics, multi-agents economies, and learning. North Holland: Amsterdam; 2004.
Barnett, WA., Geweke J, Shell K. Economic complexity: chaos, sunspots, bubbles, and nonlinearity. Cambridge University Press: Cambridge, UK; 2005.
Benhabib, J. The Hopf bifurcation and the existence and stability of closed orbits in multisector models of optimal economic growth. Journal of Economic Theory 1979; 21; 421-444.
Bergstrom AR Survey of continuous time econometrics. In: Barnett WA, Gandolfo G, Hillinger C. (Eds.), Dynamic disequilibrium modeling. Cambridge University Press: Cambridge, UK; 1996. p. 3-26.
Bergstrom AR, Nowman KB. A continuous time econometric model of the United Kingdom with stochastic trends. Cambridge University Press: Cambridge, UK; 2006.
Bergstrom AR, Wymer CR. A model of disequilibrium neoclassic growth and its application to the United Kingdom. In: Bergstrom AR (Ed.), Statistical inference in continuous time economic models. North Holland: Amsterdam; 1976, p. 267-327.
Bergstrom AR, Nowman KB, Wandasiewicz S. Monetary and fiscal policy in a second-order continuous time macroeconometric model of the United Kingdom. Journal of Economic Dynamics and Control 1994; 18; 731-761.
Bergstrom AR., Nowman KB., Wymer CR. Gaussian estimation of a second order continuous time macroeconometric model of the United Kingdom. Economic Modelling 1992; 9; 313-352.
Binder M, Pesaran MH. Stochastic growth models and their econometric implications. Journal of Economic Growth 1999; 4; 139-183.
Boldrin M and Woodford M. Equilibrium models displaying endogenous fluctuations and chaos: a survey. Journal of Monetary Economics 1990; 25; 189-222.
Cobb JD. On the solutions of linear differential equations with singular coefficients. Journal of Differential Equations 1982; 46; 310-323.
Cobb JD. A further interpretation of inconsistent initial conditions in descriptor variable systems. IEEE Transactions on Automatic Control 1983; 28; 920-922.
Gandolfo G. Economic Dynamics. Springer: New York; 1996
Gantmacher FR. The Theory of Matrices. Chelsea: New York; 1974.
Grandmont JM. Expectations formation and stability of large socioeconomic systems. Econometrica 1998; 66; 741-782.
Kim J. Constructing and estimating a realistic optimizing model of monetary policy. Journal of Monetary Economics 2000; 45; 329-359.
Leeper E, Sims C. Toward a modern macro model usable for policy analysis. NBER Macroeconomics Annual 1994; 81-117.
Lucas RE. Econometric policy evaluation: A critique. In Brunner K, Meltzer AH (Eds.), The Phillips curve and labor markets. Journal of Monetary Economics, supplement; 1976. p. 19-46.
Medio A. Chaotic dynamics: theory and applications to economics. Cambridge University Press: Cambridge, UK; 1992.
Nieuwenhuis HJ, Schoonbeek L. Stability and the structure of continuous-time economic models. Economic Modelling 1997; 14; 311-340.
Nishimura K, Takahashi H. Factor intensity and Hopf bifurcations. In Feichtinger G (Eds.), Dynamic Economic Models and Optimal Control; 1992. p. 135-149.
Powell A, Murphy C. Inside a modern macroeconometric model: a guide to the Murphy model. Springer: Heidelberg; 1997
Scarf H. Some examples of global instability of competitive equilibrium. Internationial Economic Review 1960; 1; 157-172.
Swamy PAVB, Tavlas GS, Chang IL. How stable are monetary policy rules: estimating the time-varying coefficients in monetary policy reaction function for the US. Computational Statistics & Data Analysis 2005; 49(2); 575-590
Wymer CR. Structural nonlinear continuous time models in econometrics. Macroeconomic Dynamics 1997; 1; 518-548.