Existence of Bifurcation in Macroeconomic Dynamics: Grandmont was Right

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, initial results by Barnett and Duzhak (2006) indicate the possible existence of Hopf 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 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, our explanation of the relevant theory reveals that singularity bifurcation may be a common property of Euler equations models. These 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. Grandmont was right.Bifurcation, inference, dynamic general equilibrium, Pareto optimality, Hopf bifurcation, Euler equations, Leeper and Sims model, singularity bifurcation, stability.

Using remote sensing method analysis characteristic of Bohai Sea and Yellow Sea mixed zone

In this paper, we use ASCAT and MODIS data to analyze wind field, the temperature and the chlorophyll concentration distribution in Bohai Sea and Yellow Sea mixed zone and compare characteristics with the first 10 years (Except the wind field, it is only 6 years with ASCAT data). We found that high wind weather is too few in winter of 2013, the northerly winds are dominant, and the sea surface temperatures are also high and low chlorophyll concentration into the mixing zone of Yellow Sea and the Bohai Sea trend. There is 6 degrees C to 8 degrees C sea water into the Bohai Sea.</p

Robustness of Inferences to Singularity Bifurcations

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.bifurcation macroeconometrics dynamics nonlinearity singularity

The infuence ofoilspilland enteromorphaon syntheticaperture radar backscatter coefficient

In this Paper presentation, compare the normal Radar backscatter coefficient between oil spill area, clean sea area, Ship, platform area and Enteromorpha area. The result display the backscatter coefficient of oil spill area is lower than clean sea and the Enteromorpha area, ship, platform area is higher than clean sea.</p