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Robustness of Inferences to Singularity Bifurcations


  • Yijun He

    (Washington State University)

  • William Barnett

    (University of Kansas)


Euler equation models represent an important class of macroeconomic systems. Our research on the Leeper and Sims Euler equations macroeconomic model reveals 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. We earlier encountered more common forms of bifurcation within the parameter space of the Bergstrom and Wymer continuous time macroeconometric model of the UK economomy. We have found that in each of those models, the point estimates of the parameters are near a bifurcation boundary that intersects the confidence region. Because dynamics are different on each side of a bifurcation boundary, this problem creates a substantial loss in robustness of inferences regarding dynamics. Since singularity bifurcation is more troubling than the types more widely known to economists, we find that the transition in econometrics from earlier structural models to Euler equation models with 'deep' parameters may cause these robustness problems to become more difficult to analyze.

Suggested Citation

  • Yijun He & William Barnett, 2005. "Robustness of Inferences to Singularity Bifurcations," Macroeconomics 0510019, University Library of Munich, Germany, revised 24 Oct 2005.
  • Handle: RePEc:wpa:wuwpma:0510019
    Note: Type of Document - pdf; pages: 12. This paper is forthcoming in the Proceedings of the Joint Statistical Meetings of the American Statistical Association, 2005.

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    bifurcation macroeconometrics dynamics nonlinearity singularity;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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