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2015 | OriginalPaper | Buchkapitel

Semiparametric Spatial Autoregressive Geoadditive Models

verfasst von : Roberto Basile, Saime Kayam, Román Mínguez, Jose María Montero, Jesús Mur

Erschienen in: Complexity and Geographical Economics

Verlag: Springer International Publishing

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Abstract

Modeling regional economic dynamics requires the adoption of complex econometric tools, which allow us to deal with some important methodological issues, such as spatial dependence, spatial heterogeneity and nonlinearities. Recent developments in the spatial econometrics literature have provided some instruments (such as Spatial Autoregressive Semiparametric Geoadditive Models), which address these issues simultaneously and, therefore, are of great use for practitioners. In this paper we describe these methodological contributions and present some applications of these methodologies in the fields of regional science and economic geography.

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Vorheriges Kapitel Parametric Models in Spatial Econometrics: A Survey

Nächstes Kapitel Diffusion of Growth and Cycles in Continuous Time and Space

If the interest lies in the short-term adjustments, a spatial panel data model would be required instead (Elhorst 2012).

Although classical spatial econometric models are based on the assumption of linearity and parameter homogeneity, they allow us to assess a form of heterogeneity, called “interdependence heterogeneity” (Ertur and Koch 2011): the magnitude of spatial direct and indirect partial effects is different among regions, since it depends upon the position of the regions in space, the degree of connectivity among regions, which is governed by the \(\mathbf{W}_{n}\) matrix and the estimated model parameters.

The GWR has been extended to cross-sectional models with spatial interaction terms by Pace and LeSage (2004) and Mur et al. (2009).

Usually, a fully nonparametric model (i.e., a model where all terms are smoothly interacted with each other) cannot be applied to regional data since it would require a very large number of observations to overcome the curse of dimensionality. Additivity is therefore a valid compromise between flexibility and tractability.

Although this model is widely used in environmental studies and in epidemiology (see, i.a., Augustin et al. 2009), it is rarely considered for modeling economic data.

It is worth noticing that in expression (9), for interactive terms, the penalty matrix \(\mathbf{S}_{k}\) usually depends on both interacting variables, and the associated λ _k will have two components allowing for different degrees of smoothing.

For example, in line with Kelejian and Prucha (1997), \(\mathbf{Q}_{i}\) may contain an intercept, all exogenous terms included in the model and several orders of their spatial lags.

Both first and second step equations can be estimated by using, for example, penalized least squares estimators.

The requirement that the endogenous regressor be continuously distributed is the most important limitation of the applicability of the control function approach to estimation of nonparametric and semiparametric models with endogenous regressors.

It is important to mention that a semiparametric spatial lag model has also been proposed within a partial linear framework. For example, Su and Jin (2010) develop a profile quasi-maximum likelihood estimator for the partially linear spatial autoregressive model which combines the spatial autoregressive model and the nonparametric (local polynomial) regression model. Furthermore, Su (2012) proposes a semiparametric GMM estimator of the SAR model under weak moment conditions which allows for both heteroskedasticity and spatial dependence in the error terms.

For the sake of clarity, isotropy means that the degree of smoothness is the same for all the covariates, that is, the degree of flexibility in all of them is the same. Nevertheless, the usual situation in real cases is anisotropy, since the covariates are usually measured in different units of measure or, in the case of equal measurement units (e.g. spatial location variables), the variability of such covariates differing greatly.

Nevertheless, there are some R codes using spdep package available from Montero et al. (2012) and Mínguez et al. (2012).

This kind of heterogeneity is called interactive heterogeneity by Ertur and Koch (2011), and this is why scholars usually compute average marginal effects for parametric SAR and SDM models.

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Titel: Semiparametric Spatial Autoregressive Geoadditive Models
verfasst von: Roberto Basile
Saime Kayam
Román Mínguez
Jose María Montero
Jesús Mur
Verlag: Springer International Publishing
Buch: Complexity and Geographical Economics
Print ISBN: 978-3-319-12804-7

Electronic ISBN: 978-3-319-12805-4

Copyright-Jahr: 2015
DOI: https://doi.org/10.1007/978-3-319-12805-4_4

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