Non-linear externalities in firm localization

ABSTRACT

Non-linear externalities in firm localization. Regional Studies. This paper presents a model of firm localization in which the intrinsic advantages of regions are disentangled from localized externalities, while this latter force is allowed to have a quadratic shape. Through inferential analysis, it is verified whether the quadratic component of localized externalities is statistically different from zero. Such a term can reflect more-than-linear positive feedbacks as well as congestion effects, so that the sign of the interdependencies stemming from localization is not assumed a priori to be positive. The main result is that the quadratic term is virtually never statistically different from zero across Italian sectors observed at the scale of commuting zones, so that localized externalities seem to be well approximated by a linear specification.

摘要

厂商在地化的非线性外部性。区域研究。本文呈现厂商在地化的模式，其中区域固有的优势将与在地化的外部性区分开来，而在地化的外部性驱力则被允许拥有二次方的形态。透过推理分析，证实在地化的外部性之二次项是否在统计上不同于零。此项能够反映超越线性的正向反馈以及认知效应，如此从地方化衍生而来的相互依赖之信号，便不被先验地预设为正向。主要的研究结果是，在通勤区域尺度中所观察到的意大利部门间的二次项，实际上在统计上永远不会不同于零，因此在地化的外部性似乎可透过限性设定充分逼近。

RÉSUMÉ

Externalités non linéaires dans la localisation des entreprises. Regional Studies. La présente communication présente un modèle de localisation des entreprises, dans laquelle on dissocie les avantages intrinsèques des régions des externalités localisées, bien que l’on accorde à cette dernière force une configuration quadratique. Par le biais d’une analyse par inférence, on établit si la composante quadratique des externalités localisées est statistiquement différente de zéro. Ce terme peut refléter des commentaires positifs plus-que-linéaires, ainsi que des effets de la congestion, afin de ne pas supposer que le signe des interdépendances découlant de la location n’est pas à priori positif. Le principal résultat st que l’expression quadratique n’est, d’un point de vue statistique, pratiquement jamais différente de zéro dans les secteurs italiens observés à l’échelle des zones de migrations pendulaires, et que, par conséquent, une spécification linéaire semble être une bonne approximation des externalités localisées.

ZUSAMMENFASSUNG

Nichtlineare Externalitäten bei der Firmenlokalisierung. Regional Studies. In diesem Beitrag wird ein Modell der Firmenlokalisierung vorgestellt, bei dem die inhärenten Vorteile von Regionen von lokalisierten Externalitäten entflochten werden, während dieser zweiten Kraft eine quadratische Form zugestanden wird. Mithilfe einer Inferenzanalyse wird überprüft, ob sich die quadratische Komponente der lokalisierten Externalitäten in statistischer Hinsicht von Null unterscheidet. In einem solchen Term können sich stärker als linear ausfallende positive Rückkoppelungen sowie Engpasseffekte widerspiegeln, weshalb das Vorzeichen der von der Lokalisierung stammenden Wechselwirkungen nicht a priori als positiv angenommen wird. Das wichtigste Ergebnis lautet, dass der quadratische Term in sämtlichen auf der Ebene der Berufsverkehrszonen beobachteten italienischen Sektoren praktisch niemals statistisch unterschiedlich von Null ausfällt, weshalb sich eine lineare Spezifikation offenbar gut für eine Annäherung an lokalisierte Externalitäten eignet.

RESUMEN

Efectos externos no lineales en la localización de empresas. Regional Studies. En este artículo presentamos un modelo de localización de empresas en el que las ventajas intrínsecas de las regiones están separadas de los efectos externos localizados, y se permite que la segunda fuerza tenga una forma cuadrática. Mediante un análisis inferencial, verificamos si el componente cuadrático de los efectos externos localizados es estadísticamente diferente a cero. Este término puede reflejar respuestas positivas más que lineales así como efectos de congestión, de forma que no se supone a priori que el signo de las interdependencias que proceden de la localización sea positivo. El principal resultado es que el término cuadrático es prácticamente nunca estadísticamente diferente de cero en todos los sectores italianos observados en la escala de zonas de desplazamientos al trabajo, de modo que parece que los efectos externos localizados están bien aproximados mediante una especificación lineal.

KEYWORDS:

• firm localization
• externalities
• non-linearities

关键词:

• 厂商在地化
• 外部性
• 非线性

MOTS-CLÉS:

• localisation des entreprises
• externalités
• non linéarités

SCHLÜSSELWÖRTER:

• Firmenlokalisierung
• Externalitäten
• Nichtlinearitäten

PALABRAS CLAVES:

• localización de empresas
• efectos externos
• no linealidad

JEL:

• C12
• C16
• C51
• R30

ACKNOWLEDGMENTS

The authors express their gratitude to three anonymous referees for their excellent and stimulating comments, which provided an important guidance in shaping the final version of the paper.

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the authors.

ORCiD

Giulio Bottazzi http://orcid.org/0000-0003-2565-4732

Notes

1. Differently from the analytical solution of the model, the numerical approach does not require that the Markov chain is reversible and does not exploit the detailed balance condition.

2. The use of maximum likelihood might appear as more appropriate. However, it poses enormous numerical difficulties as the simulation length necessary to assign reliable probabilities to all system configurations soon becomes unfeasible with the increase of the number of locations and firms. This problem is efficiently overcome by considering a binned statistics and reverting to chi-square minimization. Dubious readers are reminded that chi-square minimization in general possesses an efficient asymptotic behaviour and, in any case, it is not more severely affected by small sample biases than maximum likelihood.

3. The Monte Carlo techniques adopted here are characterized by very poor performances when a maximum likelihood approach is adopted. The problem arises every time the attractiveness of two locations is similar. In this case any redistribution of firms across locations generates a variation in the likelihood function which is, however, spurious. Washing away this spurious effect requires a computation time which is unfeasible for practical applications. For more details, see Bottazzi and Vanni (2014).

4. To guarantee the convergence of the algorithm and improve its speed, the initial search interval should be tuned on the initial values of the parameters and . Essentially, one has to avoid that the search algorithm probes the objective function outside its domain of definition. For more details, see Bottazzi and Vanni (2014).

5. The precision is, however, limited by the finite computation time. As a robustness check, a minimization algorithm based on successive parabolic interpolations was also employed, obtaining consistent results.