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The spatial Durbin model occupies an interesting position in the field of spatial econometrics. It is the reduced form of a model with cross-sectional dependence in the errors and it may be used as the nesting equation in a more general approach of model selection. Specifically, in this equation we obtain the common factor tests (of which the likelihood ratio is the best known) whose objective is to discriminate between substantive and residual dependence in an apparently misspecified equation. Our paper tries to delve deeper into the role of the spatial Durbin model in the problem of specifying a spatial econometric model. We include a Monte Carlo study related to the performance of the common factor tests presented in the paper in small sample sizes.Common factor tests, spatial lag model, spatial error model, C21, C50, R15,

RESUMENIn the present paper, we construct a new, simple, consistent and powerful test for spatial independence, called the SG test, by using symbolic dynamics and symbolic entropy as a measure of spatial dependence. We also give a standard asymptotic distribution of an affine transformation of the symbolic entropy under the null hypothesis of independence in the spatial process. The test statistic and its standard limit distribution, with the proposed symbolization, are invariant to any monotonuous transformation of the data.The test applies to discrete or continuous distributions. Given that the test is based on entropy measures, it avoids smoothed nonparametric estimation. We include a Monte Carlo study of our test, together with the well-known Moran's I, the SBDS (de Graaff

This article reflects on the relevance of the concept of unit roots in the spatial context. The initial introduction of this topic in the time-series literature caused significant changes in the mainstream econometric methodology. However, the literature specialized in spatial econometric modeling has not extensively dealt with this issue. The current article continues the discussion of the concept of unit roots employed in a spatial context and presents a series of peculiarities that should be noticed. Subsequently, attention focuses on the topic of deterministic trends associated with the scale factor that intervenes in autoregressive spatial processes. The incidence of this type of trend should not be neglected. It induces the risk of finding spurious correlation that should be taken into account.

In recent years, there has been a growing interest in the problems caused by the existence of instability in cross-sectional regressions. The results about local autocorrelation measures are part of this debate, as are the proposals concerning the concept of geographically weighted regressions. This article also deals with the problem of stability (or the lack thereof), but focusing the discussion on the supposition of constancy in the parameter of spatial dependence. In most cases, this assumption is treated, with the risks that this involves, as a maintained hypothesis, which should be ascertained before continuing with the modeling exercise. In the article, we present a simple heterogeneity test for this type of parameters, based on the Lagrange Multiplier principle. To illustrate its use, we take the distribution of per capita income among the European regions as our discussion case. According to our results, there are clear signs of structural breaks in the spatial distribution of this variable and the scale factor and the autocorrelation coefficient appear to be principal actors. IntroductionThere is a quite extended consensus that heterogeneity and dependence are the fundamental characteristics of spatial data (Griffith 2003). The literature has focused mainly on the treatment of spatial dependence, with extremely relevant results. The question of heterogeneity has not received so much attention, which could be attributed to a desire to limit the complexity and uncertainty involved in the specification of any work that models spatial data. Nevertheless, there is widespread evidence that spatial behavioural relations tend to be unstable, as shown by Haining (2003, chapter 4) and previously by Cressie (1991) and Upton and Fingleton (1985), among others. The complexity appears in the different dimensions associated with this broad topic, which can hide problems of global instability in the specification (relatively little studied in the specialized literature), of nonstability in the parameters of the equation or of lack of constancy of the mechanism of spatial interaction that operates in the model.Our article focuses on the last aspect and, specifically, on the problem of ''(1) testing for the presence of spatial heterogeneity by means of appropriate diagnostics'' as Anselin (1990, p. 186) indicates. To this end, we develop a heterogeneity test for the parameter of spatial dependence, based on the principle of the Lagrange Multiplier, which is relatively simple to obtain and can be easily adapted to different situations of interest. Continuing with the reference of Anselin (1990, p. 186), we believe that the issues associated with ''(2) implementing alternative estimation techniques when needed'' are well dealt with in the articles of Brunsdon, Fotheringham, and Charlton (1998b) and Pace and Lesage (2004), which we adopt as our guidelines.To illustrate the applicability of our proposal, we take the case of the distribution of per capita income on the European continent as the element of discussion. It i...

Despite the growing economic importance of tourism, and its impact on relative water shortage, little is known about the role that water plays in the productive process of hotels and restaurants and, therefore, the possible implications of water demand management policy for this sector. This study aims to fill this gap. It is based on the microdata of 676 firms in the sector, operating in the city of Zaragoza (Spain) for a 12 year period. Based on the Translog cost function, we estimate the shadow price of water in the short run and, from a long-run perspective, its direct price elasticity, its cross elasticities relative to labor, capital, and supplies, and its elasticity with respect to the level of output. The results obtained show that water provides sector firms returns that are on average higher than its price, although in the case of hotels the margin is really narrow. This situation provides policy makers with a margin for applying price increases without affecting the sector's viability, with some caution in the case of hotels. Water demand elasticity equals 20.38 in the case of hotels, but it is not significant in the case of restaurants and bar-cafes; hence, only in hotels is there potential for influencing water use patterns, encouraging the resource's conservation through pricing policy. Moreover, capital is a substitutive factor of water, and the elasticity of water with respect to output is 0.40, all of which should also be considered by policy makers in water resource management.