A two-step approach to account for unobserved spatial heterogeneity

ABSTRACT

A two-step approach to account for unobserved spatial heterogeneity. Spatial Economic Analysis. Empirical analysis in economics often faces the difficulty that the data are correlated and heterogeneous in some unknown form. Spatial econometric models have been widely used to account for dependence structures, but the problem of directly dealing with unobserved spatial heterogeneity has been largely unexplored. The problem can be serious particularly if we have no prior information justified by economic theory. In this paper we propose a two-step procedure to identify endogenously spatial regimes in the first step and to account for spatial dependence in the second step. This procedure is applied to hedonic house price analysis.

摘要

说明未观测到的空间异质性的二阶方法。Spatial Economic Analysis. 经济学中的经验分析，经常面临数据以若干未知的形式相关且异质的困难。空间计量经济模型，被大量使用来说明依赖结构，但直接处理未观测到的空间异质性之问题，则大部份仍未被探讨。该问题可能相当严重，特别是若我们没有经济理论证明的事前信息的话。我们于本文中，提出一个二阶段步骤，第一阶段首先指认内生的空间体制，第二阶段说明空间依赖。此一步骤被运用至特徵房价分析。

RÉSUMÉ

Une approche en deux temps permettant d’expliquer une hétérogénéité spatiale non observée. Spatial Economic Analysis. Une des difficultés de l’analyse spatiale, en économie, tient au fait que les données sont corrélées et hétérogènes sous une forme inconnue. On a fait grand usage de modèles économétriques spatiaux pour expliquer des structures de dépendance, sans tenir compte toutefois du problème du traitement direct d’une hétérogénéité spatiale non observée. Le problème risque d’être grave, notamment si nous ne disposons pas d’informations antérieures justifiées par une théorie économique. Dans la présente communication, nous proposons une procédure en deux temps permettant, dans un premier temps, d’identifier des régimes spatiaux endogènes, et, dans un deuxième temps, de tenir compte de la dépendance spatiale. Cette procédure est appliquée à l’analyse hédonique du prix de l’immobilier.

RESUMEN

Un enfoque bifásico para tener en cuenta la heterogeneidad espacial no observada. Spatial Economic Analysis. El análisis empírico en economía se encuentra con frecuencia ante la dificultad de que los datos están relacionados y son heterogéneos de alguna forma desconocida. Los modelos econométricos espaciales han sido utilizados con profusión para tener en cuenta las estructuras de dependencia, pero generalmente no se ha explorado el problema de tratar directamente con la heterogeneidad espacial no observada. El problema puede ser especialmente grave si no contamos con información previa justificada por la teoría económica. En este artículo proponemos un procedimiento bifásico para identificar los regímenes espaciales endógenos en la primera fase y explicar la dependencia espacial en la segunda fase. Este procedimiento se aplica al análisis del precio hedónico de la vivienda.

KEYWORDS:

• spatial econometrics
• two step
• spatial heterogeneity
• local estimation
• hedonic house prices

关键词:

• 空间计量经济
• 二阶段
• 空间异质性
• 地方评估
• 特徵房价

MOTS-CLÉS:

• économétrie spatiale
• deux temps
• hétérogénéité spatiale
• estimation locale
• prix hédoniques de l’immobilier

PALABRAS CLAVES:

• factores econométricos espaciales
• bifásico
• heterogeneidad espacial
• estimación local
• precios hedónicos de la vivienda

JEL:

• C31
• C63
• R31

ACKNOWLEDGEMENTS

A preliminary version of the paper was presented at the 55th European Regional Science Association (ERSA) Congress held in Lisbon, Portugal, 25–28 August 2015. The authors thank all the participants, particularly those in their spatial econometrics and regional economic modelling session. They are also particularly grateful to the editor and two anonymous referees for their constructive comments that greatly improved this paper.

Notes

1 See LeSage and Pace (2014) and Getis (2007, 2009) for considerations of the spatial weight matrix and the autocorrelation coefficient.

2 Recently, both from a theoretical and a computational perspective, several excellent works on the definition of the W matrix have been proposed (Bhattacharjee & Jensen-Butler, 2013; LeSage & Pace, 2007; Qu & Lee, 2015; Seya, Yamagata, & Tsutsumi, 2013). In particular, Qu and Lee (2015) defined a particular endogenous W matrix (where the usual exogenous W matrix can be considered a particular case) and showed the effects on the estimates by considering commonly used estimators in SAR cross-sectional models when the true W is endogenous.

3 A valid alternative to the GWR approach is the NCSTAR model, as noted by Lebreton (2005).

4 The main difference pertains to the way of conceiving the distance measure. In GWRs, distance is thought of as mere geographical distance (Euclidean, great circle etc.), whereas in LWRs, an economic interpretation can be also assigned.

5 The AIC in equation (4) is not the same as that used in the empirical analysis to compare different model specifications. In the second section, criterion (4) is used to select the initial bandwidth optimal value using the package GWmodel in R (Lu, Harris, Charlton, & Brunsdon, 2014), whereas the AIC in the empirical application is the common AIC used for the evaluation of the model fitting.

6 At the end of the convergence procedure, the weights that correspond to 1 are assigned to the points that form a cluster, and 0 is used for all the other points. This is equivalent to saying that the procedure allows the weights to converge to a uniform kernel within each region.

7 The weights in the diagonal of have the role, at first, of selecting the observations that contribute to local estimations through local weighted least squares estimations, whereas the weights in permit, through the reduced form of the model, the expansion of the infinite number of cross-sectional effects in the entire system (i.e., global spillover effects).

8 For details, see the spdep package in R (Bivand & Piras, 2015).