In Search of ‘W’

Abstract

The paper discusses the standard approaches in constructing the spatial weights matrix, W, and the implications of using such approaches in terms of the potential mis-specification of W. We then look at more recent attempts to measure W in the literature, including: Bayesian (searching for 'best fit'); non-parametric techniques; the use of spatial correlation to estimate W; other iteration techniques; and alternative approaches. Lastly, an illustration is provided based on estimating spatial lag models determining establishment level R&D spending in the UK, finding that differently constructed W matrices produce different estimates of spatial spillovers.A la recherche du « W » RÉ SUMÉ La pre´sente communication se penche sur les me´thodes standards de la structure de la matrice de poids spatiale « W », et les implications de l'emploi de ces me´thodes sur le plan d'une erreur de spe´cification potentielle de W. Elle se penche ensuite sur des tentatives plus re´centes de mesure de W dans certains ouvrages, y compris des infe´rences baye´siennes (recherche de meilleure probabilite´); des techniques non parame´triques; l'emploi d'une corre´lation spatiale pour l'e´valuation de W; des techniques d'ite´ration diverses; et d'autres me´thodes en alternative. Enfin, elle contient une illustration base´e sur l'estimation de mode`les a`de´calage spatial permettant de de´terminer le niveau d'e´tablissement de de´penses en R&D au Royaume-Uni, qui conclut que des matrices W a`structure diffe´rente produisent diffe´rentes e´valuations de de´bordement spatial. En busca de 'W'EXTRACTO Este trabajo trata los planteamientos típicos al construir la matriz de ponderaciones espaciales, W, y las implicaciones de utilizar dichos planteamientos en te´rminos de la posible especificacio´n erro´nea de W. Seguidamente, examinamos intentos ma´s recientes de ponderar W en la bibliografía, incluyendo: bayesiano (búsqueda de lo que 'mejor encaja'); te´cnicas no parame´tricas; el uso de correlacio´n espacial para estimar W; otras te´cnicas de iteracio´n; y planteamientos alternativos. Finalmente, se ofrece una ilustracio´n basada en estimar modelos de retardo (lag) espacial que determinan Richard Harris (to whom correspondence should be sent), el gasto en I'D a nivel de establecimiento en el Reino Unido; se descubre que matrices W construidas de forma diferente producen estimaciones diferentes de excedentes (spillovers) espaciales.

Environmental Regulation, Economic Network and Sustainable Growth of Urban Agglomerations in China

“…Introducing spatial interaction in spatial econometric models has been advocated by previous researches [66,67]. As Harris et al [67] observed, "the standard approach using W is that spillovers are entered through the interaction between regions of the dependent or other variables in the model, weighted by W, as the proxies for spatial spillovers." Therefore, the different spatial weight matrices reflect different types of interaction among cities in the urban agglomeration.…”

The Role of Structural Change in European Regional Productivity Growth

“…Currently, there are no strong theoretical justifications for modifying the shift-share method through the inclusion of, for example, a specific spatial weights matrix. Moreover, Harris and Kravtsova (2009) warn against the standard approach in the spatial econometrics literature of imposing spatial weights matrices that use contiguous or distance-related measures to weight observations because it imposes a structure of spatial interactions that is untested and potentially misspecified.…”

Mekânsal ekonometri ve sosyal bilimlerde kullanım alanları

“…Çünkü mekânsal veriler, geleneksel ekonometrideki verilere ek olarak, uzaydaki konumlar hakkında da bilgi sağlar (Arbia, 2006). Ne var ki, Harris, Moffat ve Kravtsova (2011), bu ilişkilerin tanımlanma sürecinin genellikle belirsiz olduğunu ve modellerin sonuçlarının değişik uzaklık tanımlarına göre farklı sonuçlar verebileceğini ortaya koymaktadır. Öte yandan, Anselin (1988) konumun, bir başka deyişle gözlemler arası uzaklıkların coğrafi verilerden elde edilerek belirlenebileceği gibi, "ekonomik uzaklıklar, kişiler arası uzaklıklar" gibi soyut anlamda da tanımlanabileceğini ifade etmektedir.…”