Empiricism in ecological economics: a perspective from complex systems theory

Economies are open complex adaptive systems far from thermodynamic equilibrium, and neo-classical environmental economics seems not to be the best way to describe the behaviour of such systems. Standard econometric analysis (i.e. time series) takes a deterministic and predictive approach, which encourages the search for predictive policy to ‘correct’ environmental problems. Rather, it seems that, because of the characteristics of economic systems, an ex-post analysis is more appropriate, which describes the emergence of such systems’ properties, and which sees policy as a social steering mechanism. With this background, some of the recent empirical work published in the field of ecological economics that follows the approach defended here is presented. Finally, the conclusion is reached that a predictive use of econometrics (i.e. time series analysis) in ecological economics should be limited to cases in which uncertainty decreases, which is not the normal situation when analysing the evolution of economic systems. However, that does not mean we should not use empirical analysis. On the contrary, this is to be encouraged, but from a structural and ex-post point of view.Ecological economics, neo-classical environmental economics, empiricism, predictive analysis, complexity, post-normal science, policy.

Non-exact present value relations

One of the most cornmonly used and, at the same time. rejected models in finance and macroeconomics is the exact present value model (PVM), where a variable Yt is expressed as the expected value at time t of the sum of discounted future values of another variable Xt. This paper generalizes the PVM by making it non-exact (NEPVM) in a simple way, allowing us to study situations with time varying discount factors, transitory deviations from the exact PVM, as well as situations with correlated market returns. The proposed NEPVM satisfies all the equilibrium conditions the exact PVM does, but at the same time it is more robust in the sense that rejections produced by the standard volatility and cross-equation restriction tests are not enough to reject the NEPVM. The paper presents the new variance bounds and cross-equation restrictions implied by the NEPVM and it shows how to test them. This paper also shows how to discriminate between the exact PVM and the NEPVM by testing for a deeper level of cointegration: multicointegration. The paper finished by analyzing empirically the cases of stock prices and dividens. short-and long-term interest rates and farmland prices. Although the exact PVM is rejected in the first two examples, as the literature has largely reported, we are unable to reject the NEPVM. This fact, together with the theoretical results contained in the paper, suggests that the pro po sed NEPVM could be compatible with sorne of the empírical findings in the literature

Gravitomagnetic currents in the inflationary universe from WIMT

Using the Weitzenb\"ock representation of a Riemann-flat 5D spacetime, we study the possible existence of primordial gravito-magnetic currents from Gravito-electromagnetic Inflation (GEMI). We found that these currents decrease exponentially in the Weitzenb\"ock representation, but they are null in a Levi-Civita representation because we are dealing with a 5D Riemann-flat spacetime without structure or torsion.Comment: Version to be published in European Phys. J.

Quantized gravitomagnetic charges from WIMT: cosmological consequences

Using the formalism of Weitzenb\"ock induced matter theory (WIMT) we calculate the gravito-magnetic charge on a topological string which is induced through a foliation on a five-dimensional (5D) gravito-electromagnetic vacuum defined on a 5D Ricci-flat metric, which produces a symmetry breaking on an axis. We obtain the resonant result that the quantized charges are induced on the effective four-dimensional hypersurface. This quantization describes the behavior of a test gravito-electric charge in the vicinity of a point gravito-magnetic monopole, both geometrically induced from a 5D vacuum. We demonstrate how gravito-magnetic monopoles would decrease exponentially during the inflationary expansion of the universe.Comment: Final version to be published in Can. J. Phy

Convergence Time Towards Periodic Orbits in Discrete Dynamical Systems

We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we use linearized equations to examine the evolution near that neighborhood. The underlying idea is that points of stable periodic orbit are associated with intervals. We state and prove a theorem that details what regions of phase space are mapped into these intervals (once they are known) and how many iterations are required to get there. We also construct algorithms that allow our theoretical results to be implemented successfully in practice.Comment: 17 pages; 7 figure

Societal Metabolism of Societies: The bifurcation between Spain and Ecuador

This paper presents an application of the Multiple-Scale Integrated Assessment of Societal Metabolism to the recent economic history of Ecuador and Spain. Understanding the relationship between the Gross Domestic Product (GDP) and the throughput of matter and energy over time in modern societies is crucial for understanding the sustainability predicament as it is linked to economic growth. When considering the dynamics of economic development, Spain was able to take a different path than Ecuador thanks to the different characteristics of its energy budget and other key variables. This and other changes are described using economic and biophysical variables (both extensive and intensive referring to different hierarchical levels). The representation of these parallel changes (on different levels and describable only using different variables) can be kept in coherence by adopting the frame provided by MSIASM.MSIASM, Societal Metabolism, Development, Energy, Ecuador, Spain.

On the numerical stability of Fourier extensions

An effective means to approximate an analytic, nonperiodic function on a bounded interval is by using a Fourier series on a larger domain. When constructed appropriately, this so-called Fourier extension is known to converge geometrically fast in the truncation parameter. Unfortunately, computing a Fourier extension requires solving an ill-conditioned linear system, and hence one might expect such rapid convergence to be destroyed when carrying out computations in finite precision. The purpose of this paper is to show that this is not the case. Specifically, we show that Fourier extensions are actually numerically stable when implemented in finite arithmetic, and achieve a convergence rate that is at least superalgebraic. Thus, in this instance, ill-conditioning of the linear system does not prohibit a good approximation. In the second part of this paper we consider the issue of computing Fourier extensions from equispaced data. A result of Platte, Trefethen & Kuijlaars states that no method for this problem can be both numerically stable and exponentially convergent. We explain how Fourier extensions relate to this theoretical barrier, and demonstrate that they are particularly well suited for this problem: namely, they obtain at least superalgebraic convergence in a numerically stable manner