Dynamic agglomeration patterns in a two-country new economic geography model with four regions

Two aspects of New Economic Geography models are often singled out for criticism, especially by geographers: the treatment of geography, typically as a pre-given, fixed and highly idealized abstract geometric space; and the treatment of history, typically as ‘logical’ time (the movement to equilibrium in a model's solution space) rather than real history. In this paper we examine the basis for these criticisms, and explore how far and in what ways NEG models might be made more credible with respect to their representation of geography and history, and particularly whether and to what extent the work of geographers themselves provides some insights in this regard. We argue that the conceptualization of space and time is in fact a challenge for both NEG theorists and economic geographers, and that, notwithstanding their ontological and epistemological differences, both groups would benefit from an interchange of ideas on this front. Réinventer les (nouveaux) modèles de géographie économique: comment prendre la géographie et l'histoire plus au sérieux Rèsumè Deux aspects particuliers des modèles de la nouvelle géographie économique sont souvent l'objet de critiques, notamment de la part des géographes, à savoir: le traitement de la géographie, généralement comme un espace géométrique abstrait prédéterminé, fixe et extrêmement idéalisé, et le traitement de l'histoire, généralement comme un créneau ‘logique’ (un mouvement vers l’équilibre dans un espace à solution du modèle) et non pas comme l'histoire réelle. Dans la présente communication, nous nous penchons sur le fondement de ces critiques, et nous examinons dans quelle mesure les modèles de la NEG pourraient devenir plus plausibles sur le plan de la façon dont ils représentent la géographie et l'histoire, notamment si le travail des géographes apporte de nouveaux éléments sur cette question, et dans quelle mesure. Nous soutenons que la conceptualisation de l'espace et du temps constitue, en fait, un défi tant pour les théoriciens de la NEG que pour les géographes économiques, et qu'au-delà de leurs différences ontologiques et épistémologiques, un échange d'idées sur ce sujet serait bénéfique pour ces deux groupes. Reconsideración de modelos de (Nueva) Geografía Económica: Tomando más en serio la geografía y la historia Extracto A menudo, existen dos aspectos particulares de los modelos de Nueva Geografía Económica que reciben críticas, especialmente por parte de los geógrafos: el tratamiento de la geografía, típicamente como un espacio geométrico abstracto altamente idealizado, fijo y predeterminado; y, el tratamiento de la historia, típicamente como un tiempo ‘lógico’ (el movimiento hacia el equilibrio en el espacio de solución de un modelo), en lugar de como historia real. En este estudio examinamos la base de estas críticas y exploramos hasta qué punto y de qué formas, los modelos NEG podrían hacerse más creíbles con respecto a su representación de la geografía e historia, y particularmente, si, y hasta qué punto el trabajo de los geógrafos mismos proporciona algún tipo de visión interna en esta cuestión. Discutimos que la conceptualización del espacio y el tiempo es, de hecho, un reto para los teóricos NEG y los geógrafos económicos, y que, independientemente de sus diferencias ontológicas y epistemológicas, ambos grupos se beneficiarían de un intercambio de ideas en este campo.

In the article Llibre and Vulpe (Rocky Mt J Math 38:1301–1373, 2006) the family of cubic polynomial differential systems possessing invariant straight lines of total multiplicity 9 was considered and 23 such classes of systems were detected. We recall that 9 invariant straight lines taking into account their multiplicities is the maximum number of straight lines that a cubic polynomial differential systems can have if this number is finite. Here we complete the classification given in Llibre and Vulpe (Rocky Mt J Math 38:1301–1373, 2006) by adding a new class of such cubic systems and for each one of these 24 such classes we perform the corresponding first integral as well as its phase portrait. Moreover we present necessary and sufficient affine invariant conditions for the realization of each one of the detected classes of cubic systems with maximum number of invariant straight lines when this number is finite.

Typical bifurcation scenario in a three region identical New Economic Geography model

New Economic Geography models describe a cumulative process of spatial agglomeration: Firms tend to cluster in locations with good access to demand, and similarly, workers are drawn to regions where market potential is high because the price index is lower there. This paper provides an empirical assessment of this forward linkage that relates labour migrations to the geography of production through real wage differentials. In the spirit of Hanson (1998), we use bilateral migration data for five European countries over the 1980s and 1990s to perform quasi-structural estimations of a new economic geography model derived from Krugman (1991). The results show strong evidence in favor of this model. As expected, migrants do follow market potential. Moreover, we provide estimates for all key parameters of the model. These estimates suggest that a sudden emergence of a core-periphery pattern is unlikely within European countries: centripetal forces are too limited in geographical scope, and mobility costs are too high.

In this work we consider the problem of classifying all configurations of invariant lines of total multiplicity eight (including the line at infinity) of real planar cubic differential systems. The classification was initiated in Bujac and Vulpe (J Math Anal Appl 423:1025–1080, 2015) where the cubic systems which possess 4 distinct infinite singularities are considered and 17 such distinct configurations were detected. That work was continued in Bujac and Vulpe (Qual Theory Dyn Syst 14(1):109–137, 2015) where the classification was done for the family of cubic systems with three distinct infinite singularities and where the existence of 5 distinct configurations was proved. The cubic systems with 2 infinite singularities are considered in Bujac (Bul Acad Stiinte Repub Mold Mat 1:48–86, 2015) and Bujac and Vulpe (Classification of a subfamily of cubic differential systems with invariant straight lines of total multiplicity eight. Universitat Autonoma de Barselona, 35, 2015) where 25 configurations were constructed. This article deals with the last remaining subfamily of cubic systems. We prove here a classification theorem (Main Theorem) of real planar cubic vector fields which possess exactly one infinite singular point and eight invariant straight lines, including the line at infinity and including their multiplicities. We show that these systems could possess only 4 such configurations. We underline that the classifications of all the above mentioned families of cubic systems are taken modulo the action of the group of real affine transformations and time rescaling and are given in terms of invariant polynomials. The algebraic invariants and comitants allow one to verify for any given real cubic system whether or not it has invariant lines of total multiplicity eight, and to specify its configuration of lines endowed with their corresponding real singularities of this system. The calculations can be implemented on computer and the results can therefore be applied for any family of cubic systems, given in any normal form.

In this article we prove a classification theorem (Main Theorem) of real planar cubic vector fields which possess eight invariant straight lines, including the line at infinity and including their multiplicities and in addition they possess three distinct infinite singularities. This classification, which is taken modulo the action of the group of real affine transformations and time rescaling, is given in terms of affine invariant polynomials. The invariant polynomials allow one to verify for any given real cubic system whether or not it has invariant straight lines of total multiplicity eight, and to specify its configuration of straight lines endowed with their corresponding real singularities of this system. The calculations can be implemented on computer and the results can therefore be applied for any family of cubic systems in this class, given in any normal form.

Coping with inefficiencies in a New Economic Geography model: The unintended consequences of policy interventions

We present a pricing kernel that summarizes well the main features of the dynamics of interest rates and risk in postwar U.S. data and use it to uncover how the pricing kernel has moved with the short rate in this data. Our findings imply that standard monetary models miss an essential link between the central bank instrument and the economic activity that monetary policy is intended to affect, and thus we call for a new approach to monetary policy analysis. We sketch a new approach using an economic model based on our pricing kernel. The model incorporates the key relationships between policy and risk movements in an unconventional way: the central bank's policy changes are viewed as primarily intended to compensate for exogenous business cycle fluctuations in risk that threaten to push inflation off target. This model, while an improvement on standard models, is considered just a starting point for their revision. It leads to critical questions that researchers need to answer as they continue to revise their approach to monetary policy analysis. Copyright © 2009 by the National Bureau of Economic Research.

We study the integrability of homogeneous rational linear and homo-geneous rational quadratic differential equations. We prove that these equations can be integrated by using their algebraic solutions which are invariant straight lines.

By using techniques of differential geometry we answer the following open problem proposed by Chavarriga, Giacomini, Giné, and Llibre in 1999. For a given two dimensional flow, what is the maximal order of differentiability of a first integral on a canonical region in function of the order of differentiability of the flow? Moreover, we prove that for every planar polynomial differential system there exist finitely many invariant curves and singular points <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="gamma Subscript i Baseline comma i equals 1 comma 2 comma midline-horizontal-ellipsis comma l"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi> γ </mml:mi> <mml:mi>i</mml:mi> </mml:msub> <mml:mo>,</mml:mo> <mml:mspace width="thinmathspace"/> <mml:mi>i</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mo> ⋯ </mml:mo> <mml:mo>,</mml:mo> <mml:mi>l</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\gamma _i,\,i=1,2,\cdots ,l</mml:annotation> </mml:semantics> </mml:math> </inline-formula> , such that <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper R squared minus left-parenthesis union Underscript i equals 1 Overscript l Endscripts gamma Subscript i Baseline right-parenthesis"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">R</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:mi class="MJX-variant" mathvariant="normal"> ∖ </mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:munderover> <mml:mo> ⋃ </mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>i</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>l</mml:mi> </mml:mrow> </mml:munderover> <mml:msub> <mml:mi> γ </mml:mi> <mml:mi>i</mml:mi> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathbb R^2\backslash \left (\bigcup ^{l}_{i=1}\gamma _i\right )</mml:annotation> </mml:semantics> </mml:math> </inline-formula> has finitely many connected open components, and that on each of these connected sets the system has an analytic first integral. For a homogeneous polynomial differential system in <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper R cubed"> <mml:semantics> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">R</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msup> <mml:annotation encoding="application/x-tex">\mathbb R^3</mml:annotation> </mml:semantics> </mml:math> </inline-formula> , there exist finitely many invariant straight lines and invariant conical surfaces such that their complement in <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper R cubed"> <mml:semantics> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">R</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msup> <mml:annotation encoding="application/x-tex">\mathbb R^3</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is the union of finitely many open connected components, and that on each of these connected open components the system has an analytic first integral.

We investigate how containerization impacts local economic activity. Containerization is premised on a simple insight: packaging goods for waterborne trade into a standardized container makes them dramatically cheaper to move. We use a novel cost-shifter instrument -- port depth pre-containerization -- to contend with the non-random adoption of containerization by ports. Container ships sit much deeper in the water than their predecessors, making initially deep ports cheaper to containerize. Consistent with New Economic Geography models, we find that counties near container ports grow an additional 70 percent from 1950 to 2010. Gains predominate in counties with initially low population density and manufacturing.

EU enlargement and the internal geography of countries

In this paper a New Economic Geography model is used to analyse the distribution of educational attainment levels in the European Union. The results show that educational attainment levels decrease with distance to large consumer markets, proving that the theoretical predictions of the model are verified empirically.

International Integration and Regional Inequalities: How Important is National Infrastructure?

Trade and Industrial Location with Heterogeneous Labor