Nonlinear and Complex Dynamics in Economics

This paper is an up-to-date survey of the state-of-the-art in dynamical systems theory relevant to high levels of dynamical complexity, characterizing chaos and near chaos, as commonly found in the physical sciences. The paper also surveys applications in economics and �finance. This survey does not include bifurcation analyses at lower levels of dynamical complexity, such as Hopf and transcritical bifurcations, which arise closer to the stable region of the parameter space. We discuss the geometric approach (based on the theory of differential/difference equations) to dynamical systems and make the basic notions of complexity, chaos, and other related concepts precise, having in mind their (actual or potential) applications to economically motivated questions. We also introduce specifi�c applications in microeconomics, macroeconomics, and �finance, and discuss the policy relevancy of chaos

Measuring Consumer Preferences and Estimating Demand Systems.

This chapter is an up-to-date survey of the state-of-the art in consumer demand analysis. We review (and evaluate) advances in a number of related areas, in the spirit of the recent survey paper by Barnett and Serletis (2008). In doing so, we only deal with consumer choice in a static framework, ignoring a number of important issues, such as, for example, the effects of demographic or other variables that affect demand, welfare comparisons across households (equivalence scales), and the many issues concerning aggregation across consumers.Demand systems, Consumer preferences, Theoretical regularity.

The Differential Approach to Demand Analysis and the Rotterdam Model.

This paper presents the differential approach to applied demand analysis. The demand systems of this approach are general, having coefficients which are not neces- sarily constant. We consider the Rotterdam parameterization of differential demand systems and derive the absolute and relative price versions of the Rotterdam model, due to Theil (1965) and Barten (1966). We address estimation issues and point out that, unlike most parametric and semi-nonparametric demand systems, the Rotterdam model is econometrically regular.Diffrential demand systems, Theoretical regularity, Econometric regularity.

A Primal Divisia Technical Change Index Based on the Output Distance Function

We derive a primal Divisia technical change index based on the output distance function and further show the validity of this index from both economic and axiomatic points of view. In particular, we derive the primal Divisia technical change index by total differentiation of the output distance function with respect to a time trend. We then show that this index is dual to the Jorgenson and Griliches (1967) dual Divisia total factor productivity growth (TFPG) index when both the output and input markets are competitive; dual to the Diewert and Fox (2008) markup-adjusted revenue-share based dual Divisia technical change index when market power is limited to output markets; dual to the Denny et al. (1981) and Fuss (1994) cost-elasticity-share based dual Divisia TFPG index when market power is limited to output markets and constant returns to scale is present; and also dual to a markup-and-markdown adjusted Divisia technical change index when market power is present in both output and input markets. Finally, we show that the primal Divisia technical change index satisfies the properties of identity, commensurability, monotonicity, and time reversal. It also satisfies the property of proportionality in the presence of path independence, which in turn requires separability between inputs and outputs and homogeneity of subaggregator functions.Output distance function; Divisia technical change index; Imperfect competition; Axiomatic properties; Path independence.

Output growth and the variability of exports and imports growth: international evidence from Granger causality tests

Economic development was from the very beginning the focus of classical political economy and presently retains its original human welfare mission and intellectual attraction through insightful anthropological, sociological, and historical investigations.1 Within the context of complex and constantly evolving sociospheres, the objective of a sustained better life for the masses is enhanced, according to Nobel Prize winner Amartya K. Sen (1983, 1988), by functionings and entitlements which cannot be implemented without a public commitment and a deep government involvement. Notwithstanding the inevitability of semantical differences, the real challenge of development does not lie in eliminating definitional disputes pertaining to the objective of development but in illuminating those pertinent instrumental relations which are relevant in each social milieu, and which, when properly activated, generate an internal development dynamic. Such a dynamic would exhibit characteristics of uniformity in countries with high degrees of similarity in human and natural resources, in institutions and in individual preferences. If advanced industrial countries converge toward similar patterns, the same cannot be observed in developing countries whose differences are more pronounced than their similarities. The task of establishing meaningful patterns of uniformity in the highly differentiated developing world is not easy, but if accomplished, it would guarantee substantial benefits in the formulation of effective strategies and policies. An area in which the search for such patterns goes on unabated is that of international trade and openness. Forces of dependence, autarky, balance of payments, international competition, vulnerability to external shocks affect the objective of developing countries to achieve some degree of balanced growth,2 and most certainly influence their patterns of trade. Although these forces are important, they are beyond the scope of this paper, which focuses on the investigation of possible trade patterns and their impact on growth. In the course of this investigation the paper is organized as follows. In the next section the role of openness is examined along with citations of empirical studies that analyze the impact of export growth and export growth volatility on the growth of GNP. In the third section the rationale of Granger causality, which constitutes the core of the paper, is presented, followed by short sections on unit root tests, cointegration tests, and volatility tests that are accompanied by a brief analysis of the respective statistical results. In the final section the conclusions of the paper are summarized.

Do real exchange rates have autoregressive unit roots? a test under the alternative of long memory and breaks

In this paper, we estimate (by maximum likelihood) the parameters of univariate fractionally integrated real exchange rate time series models, and test for autoregressive unit roots on the alternative of a covariance stationary long-memory process. We use quarterly dollar-based real exchange rates (since 1957) for seventeen OECD countries, and that the finding of unit autoregressive roots does not go away even with this more sophisticated alternative.Foreign exchange rates ; Time-series analysis

Nominal stylized facts of U. S. business cycles

The authors investigate the basic nominal stylized facts of business cycles in the United States, using monthly data from 1960:1 to 1993:4 and the methodology suggested by Kydland and Prescott (1990). They make comparisons among simple sum and Divisia aggregates, using the Thornton and Yue (1992) series of Divisia monetary aggregates, and they investigate the robustness of the results to relevant nonstochastic stationarity-inducing transformations.Business cycles

A Note on Imposing Local Curvature in Generalized Leontief Models

In this paper, we build on Ryan and Wales (1998) and Moschini (1999) and impose curvature conditions locally on the generalized Leontief model, introduced by Diewert (1974). In doing so, we exploit the Hessian matrix of second order derivatives of the reciprocal indirect utility function, unlike Ryan and Wales (1998) and Moschini (1999) who exploit the Slutsky matrix.

Consumer preferences and demand systems

This paper is an up-to-date survey of the state-of-the-art in consumer demand modelling. We review and evaluate advances in a number of related areas, including different approaches to empirical demand analysis, such as the differential approach, the locally �flexible functional forms approach, the semi-nonparametric approach, and a nonparametric approach. We also address estimation issues, including sampling theoretic and Bayesian estimation methods, and discuss the limitations of the currently common approaches. We also highlight the challenge inherent in achieving economic regularity, for consistency with the assumptions of the underlying neoclassical economic theory, as well as econometric regularity, when variables are nonstationary.Representative consumer; Engel curves; rank; flexible functional forms; parametric tests; nonparametric tests; theoretical regularity

The Differential Approach to Demand Analysis and the Rotterdam Model

This paper presents the differential approach to applied demand analysis. The demand systems of this approach are general, having coefficients which are not necessarily constant. We consider the Rotterdam parameterization of differential demand systems and derive the absolute and relative price versions of the Rotterdam model, due to Theil (1965) and Barten (1966). We address estimation issues and point out that, unlike most parametric and semi-nonparametric demand systems, the Rotterdam model is econometrically regular.differential demand systems; theoretical regularity; econometric regularity