The estimation of three-dimensional fixed effects panel data models

The paper introduces for the most frequently used three-dimensional fixed effects panel data models the appropriate Within estimators. It analyzes the behaviour of these estimators in the case of no-self-flow data, unbalanced data and dynamic autoregressive models.panel data, unbalanced panel, dynamic panel data model, multidimensional panel data, fixed effects, trade models, gravity models, FDI

Entropy production in diffusion-reaction systems: The reactive random Lorentz gas

We report the study of a random Lorentz gas with a reaction of isomerization $A\rightleftharpoons B$ between the two colors of moving particles elastically bouncing on hard disks. The reaction occurs when the moving particles collide on catalytic disks which constitute a fraction of all the disks. Under the dilute-gas conditions, the reaction-diffusion process is ruled by two coupled Boltzmann-Lorentz equations for the distribution functions of the colors. The macroscopic reaction-diffusion equations with cross-diffusion terms induced by the chemical reaction are derived from the kinetic equations. We use a $H$-theorem of the kinetic theory in order to derive a macroscopic entropy depending on the gradients of color densities and which has a non-negative entropy production in agreement with the second law of thermodynamics.Comment: 14 pages, 3 eps-figure

GATT/WTO membership does promote international trade after all – Some new empirical evidence

The declared objective of the General Agreement on Tariffs and Trade (GATT) and the World Trade Organization (WTO) is to promote free trade between member states. Nonetheless, an exhaustive study of bilateral merchandise trade based on a large panel data set led Rose (2004) to conclude that there is no compelling empirical evidence to show that GATT/WTO membership does actually encourage international trade. This unanticipated finding generated a great deal of attention in the literature and several scholars put forward various explanations for it. In this paper we set up a new international trade data set which, unlike Rose’s, allows us to model exports and imports separately and to study the extensive margin of trade, i.e., the number of bilateral trade relationships. Using this data set and a gravity framework, first we demonstrate how to obtain puzzling negative results and so explain the previous unintuitive findings. Then we show that GATT/WTO membership does indeed encourage international trade, so the most obvious reason for Rose’s negative outcome is the lack of zero bilateral trade observations in his data set.GATT/WTO; international trade; gravity model; multidimensional panel data

Analytic solutions for the one-dimensional compressible Euler equation with heat conduction closed with different kind of equation of states

We present analytic self-similar or traveling wave solutions for a one-dimensional coupled system of continuity, compressible Euler and heat conduction equations. Different kind of equation of states are investigated. In certain forms of the equation of state one can arrive to a picture regarding the long time behavior of density and pressure. The impact of these quantities on the evolution of temperature is also discussed.Comment: 3 figures, will be submitted to Physics of Fluid

Thermodynamic Cross-Effects from Dynamical Systems

We give a thermodynamically consistent description of simultaneous heat and particle transport, as well as of the associated cross-effects, in the framework of a chaotic dynamical system, a generalized multibaker map. Besides the density, a second field with appropriate source terms is included in order to mimic, after coarse graining, a spatial temperature distribution and its time evolution. A new expression is derived for the irreversible entropy production in a steady state, as the average of the growth rate of the relative density, a unique combination of the two fields.Comment: 4 pages, 2 postscript figure

A MultiBaker Map for Thermodynamic Cross-Effects in Dynamical Systems

A consistent description of simultaneous heat and particle transport, including cross effects, and the associated entropy balance is given in the framework of a deterministic dynamical system. This is achieved by a multibaker map where, besides the phase-space density of the multibaker, a second field with appropriate source terms is included in order to mimic a spatial temperature distribution and its time evolution. Conditions are given to ensure consistency in an appropriately defined continuum limit with the thermodynamic entropy balance. They leave as the only free parameter of the model the entropy flux let directly into a surroundings. If it vanishes in the bulk, the transport properties of the model are described by the thermodynamic transport equations. Another choice leads to a uniform temperature distribution. It represents transport problems treated by means of a thermostatting algorithm, similar to the one considered in non-equilibrium molecular dynamics.Comment: 18 pages, 3 postscript figure

Escape-rate formalism, decay to steady states, and divergences in the entropy-production rate

In summer 1997 we were sitting with Bob Dorfman and a few other friends interested in chaotic systems and transport theory on a terrace close to Oktogon in Budapest. While taking our (decaf) coffee after a very nice Italian meal, we discussed about logarithmic divergences in the entropy production of systems with absorbing boundary conditions and their consequences for the escape-rate formalism. It was guessed at that time that the problem could be resolved by a careful discussion of the physical content of the absorbing boundary conditions. To our knowledge a thorough analysis of this long-standing question is still missing. We dedicate it hereby to Bob on occasion of his 65th birthday.Comment: 16 pages; RevTex 4 with graphicx package; eps-figure

Fixed effects models

In recent years the massive emergence of multi-dimensional panels has led to an increasing demand for more sophisticated model formulations with respect to the well known two-dimensional ones to address properly the additional heterogeneity in the data. This chapter deals with the most relevant three-dimensional fixed effects model specifications and derives appropriate Least Squares Dummy Variables and Within estimators for them. The main results of the chapter are also generalized for unbalanced panels, cross-sectional dependence in the error terms, and higher dimensional data. Some thoughts on models with varying slope coefficients are also presented