Second-Order Dynamics in the Collective Evolution of Coupled Maps and Automata

We review recent numerical studies and the phenomenology of spatially synchronized collective states in many-body dynamical systems. These states exhibit thermodynamic noise superimposed on the collective, quasiperiodic order parameter evolution with typically one basic irrational frequency. We concentrate on the description of the global temporal properties in terms of second-order difference equations.Comment: 11 pages (plain TeX), 4 figures (PostScript), preprint OUTP-92-51

On computational complexity of Siegel Julia sets

It has been previously shown by two of the authors that some polynomial Julia sets are algorithmically impossible to draw with arbitrary magnification. On the other hand, for a large class of examples the problem of drawing a picture has polynomial complexity. In this paper we demonstrate the existence of computable quadratic Julia sets whose computational complexity is arbitrarily high.Comment: Updated version, to appear in Commun. Math. Phy

Life-Cycle Models and Cross-Country Analysis of Saving

This paper develops a rational expectations life-cycle model designed as a framework for the cross-country analysis of (private) saving decisions. It is shown that a broad range of life-cycle models that have been used in the literature to study aggregate time series on consumption and saving fail to deliver plausible predictions for the purpose of analyzing saving decisions across countries as they imply that the level of saving has a constant mean and that the long-run saving rate may tend to zero. Introducing a utility specification that ties the long-run evolution of consumers' aspired consumption paths to that of aggregate labor income, an analytically tractable life-cycle model is proposed that has plausible long-run properties, including the implication that the net asset-labor income ratio, the saving rate, and the consumption-labor income ratio have meaningful long-run distributions. The moments of the long-run saving rate are shown to depend in a precise way on various characteristics of consumers' preferences, the real rate of interest, the growth rate and volatility of labor income, the government consumption-labor income ratio, and the government debt-labor income ratio. Employing a data set on saving rates and asset holdings across OECD economies and using techniques for the estimation of dynamic heterogeneous panels, the paper will also adduce empirical evidence assessing the model's ability to explain differences in the saving patterns across these economies.

Estimation and Inference in Short Panel Vector Autoregressions with Unit Roots and Cointegration

This paper considers estimation and inference in panel vector autoregressions (PVARs) with fixed effects when the time dimension of the panel is finite, and the cross-sectional dimension is large. A Maximum Likelihood (ML) estimator based on a transformed likelihood function is proposed and shown to be consistent and asymptotically normally distributed irrespective of the unit root and cointegrating properties of the underlying PVAR model. The transformed likelihood framework is also used to derive unit root and cointegration tests in panels with short time dimension; these tests have the attractive feature that they are based on standard chi-squared and normal distributed statistics. Examining Generalised Method of Moments (GMM) estimation as an alternative to our proposed ML estimator, it is shown that conventional GMM estimators based on standard orthogonality conditions break down if the underlying time series contain unit roots.Panel vector autoregressions, Fixed effects, Unit roots, Cointegration

On the Symmetry of Universal Finite-Size Scaling Functions in Anisotropic Systems

In this work a symmetry of universal finite-size scaling functions under a certain anisotropic scale transformation is postulated. This transformation connects the properties of a finite two-dimensional system at criticality with generalized aspect ratio $\rho > 1$ to a system with $\rho < 1$. The symmetry is formulated within a finite-size scaling theory, and expressions for several universal amplitude ratios are derived. The predictions are confirmed within the exactly solvable weakly anisotropic two-dimensional Ising model and are checked within the two-dimensional dipolar in-plane Ising model using Monte Carlo simulations. This model shows a strongly anisotropic phase transition with different correlation length exponents $\nu_{||} \neq \nu_\perp$ parallel and perpendicular to the spin axis.Comment: RevTeX4, 4 pages, 3 figure

Non-monotonous crossover between capillary condensation and interface localisation/delocalisation transition in binary polymer blends

Within self-consistent field theory we study the phase behaviour of a symmetric binary AB polymer blend confined into a thin film. The film surfaces interact with the monomers via short range potentials. One surface attracts the A component and the corresponding semi-infinite system exhibits a first order wetting transition. The surface interaction of the opposite surface is varied as to study the crossover from capillary condensation for symmetric surface fields to the interface localisation/delocalisation transition for antisymmetric surface fields. In the former case the phase diagram has a single critical point close to the bulk critical point. In the latter case the phase diagram exhibits two critical points which correspond to the prewetting critical points of the semi-infinite system. The crossover between these qualitatively different limiting behaviours occurs gradually, however, the critical temperature and the critical composition exhibit a non-monotonic dependence on the surface field.Comment: to appear in Europhys.Let

Macroeconometric Modelling with a Global Perspective

This paper provides a synthesis and further development of a global modelling approach introduced in Pesaran, Schuermann and Weiner (2004), where country specific models in the form of VARX* structures are estimated relating a vector of domestic variables to their foreign counterparts and then consistently combined to form a Global VAR (GVAR). It is shown that VARX* models can be derived as the solution to a dynamic stochastic general equilibrium (DSGE) model where over-identifying long-run theoretical relations can be tested and imposed if acceptable. Similarly, short-run over-identifying theoretical restrictions can be tested and imposed if accepted. The assumption of the weak exogeneity of the foreign variables for the long-run parameters can be tested, where foreign variables can be interpreted as proxies for global factors. Rather than using deviations from ad hoc statistical trends, the equilibrium values of the variables reflecting the long-run theory embodied in the model can be calculated