Singularity bifurcations

Euler equation models represent an important class of macroeconomic systems. Our ongoing research [He, Y., Barnett, W.A., 2003. New phenomena identified in a stochastic dynamic macroeconometric model: A bifurcation perspective. Working Paper, University of Kansas] on the Leeper and Sims [Leeper, E., Sims, C., 1994. Toward a modern macro model usable for policy analysis. NBER Macroeconomics Annual, National Bureau of Economic Research, New York, pp. 81–117] Euler equations macroeconometric model is revealing the existence of singularity-induced bifurcations, when the model’s parameters are within a confidence region about the parameter estimates. Although known to engineers, singularity bifurcation has not previously been seen in the economics literature. Knowledge of the nature of singularity-induced bifurcations is likely to become important in understanding the dynamics of modern macroeconometric models. This paper explains singularity-induced bifurcation, its nature, and its identification and contrasts this class of bifurcations with the more common forms of bifurcation we have previously encountered within the parameter space of the Bergstrom and Wymer [Bergstrom, A.R., Wymer, C.R., 1976. A model of disequilibrium neoclassic growth and its application to the United Kingdom. In: Bergstrom, A.R. (Ed.), Statistical Inference in Continuous Time Economic Models, North-Holland, Amsterdam, pp. 267–327] continuous time macroeconometric model of the UK economy (see, e.g., [Barnett, W.A., He, Y., 1999. Stability analysis of continuous-time, macroeconometric systems. Studies in Nonlinear Dynamics and Econometrics 3, 169–188; Barnett, W.A., He, Y., 2002. Stabilization policy as bifurcation selection: Would stabilization policy work if the economy really were unstable? Macroeconomic Dynamics 6, 713–747]).