1,721,072 research outputs found
"Dynamic Modelling in Economics and Finance" Special issue of Chaos, Solitons and Fractals in honour of Professor Carl Chiarella
No full textGrowing Through ChaoticIntervals
No full textWe consider a growth model proposed by Matsuyama [K. Matsuyama, Growing through cycles, Econometrica 67 (2) (1999) 335–347] which describes the interaction of two sources of economic growth: The mechanism of capital accumulation (Solow regime) and the process of technical change and innovation (Romer regime). In this model the dynamics often alternates between the two different regimes: There is a tradeoff between growth and innovation. Analytically the model is represented by a piecewise smooth one-dimensional unimodal map described by two different functions, each of which characterizes a different regime. The existence of regimes with attracting equilibria or 2-cycles was already known, but the transition to complex behavior never explained properly. This is the object of the present paper. We shown that no stable cycle can exist, except for a fixed point and a cycle of period two. The Necessary and Sufficient conditions for regular or chaotic regimes are formulated. The bifurcation structure of the two-dimensional parameter plane is completely explained. It is shown how the border-collision bifurcation may lead from the stable fixed point either to another equilibrium or to an attracting cycle of period two or directly to a pure chaotic regime (which consists either in 4-cyclical chaotic intervals, 2-cyclical chaotic intervals or in one chaotic interval). All the bifurcation parameters are analytically detected making use of the bifurcation curves of a piecewise linear map in canonical form, which can be determined analytically
Obtaining a hub position: A New Economic Geography analysis of industry location and trade network structures
No full textWe present a linear New Economic Geography model with three regions, one remote region and two regions that entertain a trade agreement with low bilateral trade costs. Only one of these two integrated regions has the outside option to conclude an additional trade agreement with the remote region and to obtain a hub position. We show that the new trade agreement has a substantial impact on industry location and trade patterns and that the effects strongly depend upon level of integration between the initial two regions. It is not always the region with the outside option that profits from using it. Finally, we also show that higher firm mobility may lead to complex dynamics
A propos Brexit: on the breaking up of integration areas – an NEG analysis
Full text linknspired by Brexit, the paper explores the effects of splitting an integration area or ‘Union’ on trade patterns and the spatial distribution of industry. A linear three-region New Economic Geography (NEG) model is developed and two possible situations before separation are considered: agglomeration and dispersion. By analogy with the Brexit options, soft and hard separation scenarios are considered. Firms in the leaving region may move to the larger Union market, even on the periphery, relocation substituting trade; or firms in the Union may move in the more isolated leaving region, escaping from competition. The paper also analyses deeper Union integration following separation. Instances of multistability and complex dynamics are found
Codimension-two border collision bifurcation in a two-class growth model with optimal saving and switch in behavior.
Full text linkWe consider a two-class growth model with optimal saving and switch in behavior. The dynamics of this model is described by a two-dimensional (2D) discontinuous map. We obtain stability conditions of the border and interior fixed points (known as Solow and Pasinetti equilibria, respectively) and investigate bifurcation structures observed in the parameter space of this map, associated with its attracting cycles and chaotic attractors. In particular, we show that on the x-axis, which is invariant, the map is reduced to a 1D piecewise increasing discontinuous map, and prove the existence of a corresponding period adding bifurcation structure issuing from a codimension-two border collision bifurcation point. Then, we describe how this structure evolves when the related attracting cycles on the x-axis lose their transverse stability via a transcritical bifurcation and the corresponding interior cycles appear. In particular, we show that the observed bifurcation structure, being associated with the 2D discontinuous map, is characterized by multistability, that is impossible in the case of a standard period adding bifurcation structure
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