Spatial econometric methods deal with the incorporation of spatial interaction and spatial structure into regression analysis. The field has seen a recent and rapid growth spurred both by theoretical concerns as well as by the need to be able to apply econometric models to emerging large geocoded data bases. The review presented in this chapter outlines the basic terminology and discusses in some detail the specification of spatial effects, estimation of spatial regression models, and specification tests for spatial effects.

This paper reviews a number of conceptual issues pertaining to the implementation of an explicit “spatial ” perspective in applied econometrics. It provides an overview of the motivation for including spatial effects in regression models, both from a theory-driven as well as from a data-driven perspective. Considerable attention is paid to the inferential framework necessary to carry out estimation and testing and the different assumptions, constraints and implications embedded in the various specifications available in the literature. The review combines insights from the traditional spatial econometrics literature as well as from geostatistics, biostatistics and medical image analysis.

One important goal of this study is to develop a methodology of inference for a widely used Cliff-Ord type spatial model containing spatial lags in the dependent variable, exogenous variables, and the disturbance terms, while allowing for unknown heteroskedasticity in the innovations. We first generalize the generalized moments (GM) estimator suggested in Kelejian and Prucha (1998,1999) for the spatial autoregressive parameter in the disturbance process. We prove the consistency of our estimator; unlike in our earlier paper we also determine its asymptotic distribution, and discuss issues of efficiency. We then define instrumental variable (IV) estimators for the regression parameters of the model and give results concerning the joint asymptotic distribution of those estimators and the GM estimator under reasonable conditions. Much of the theory is kept general to cover a wide range of settings. We note the estimation theory developed by Kelejian and Prucha (1998, 1999) for GM and IV estimators and by Lee (2004) for the quasi-maximum likelihood estimator under the assumption of homoskedastic innovations does not carry over to the case of heteroskedastic innovations. The paper also provides a critical discussion of the usual specification of the parameter space.

In this paper we consider a panel data model with error components that are both spatially and time-wise correlated. The model blends specifications typically considered in the spatial literature with those considered in the error components literature. We introduce generalizations of the generalized moments estimators suggested in Kelejian and Prucha (1999) for estimating the spatial autoregressive parameter and the variance components of the disturbance process. We then use those estimators to define a feasible generalized least squares procedure for the regression parameters. We give formal large sample results for the proposed estimators. We emphasize that our estimators remain computationally feasible even in large samples.

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We suggest a nonparametric heteroscedasticity and autocorrelation consistent (HAC) estimator of the variance-covariance (VC) matrix for a vector of sample moments within a spatial context. We demonstrate consistency under a set of assumptions that should be satisfied by a wide class of spatial models. We allow for more than one measure of distance, each of which may be measured with error. Monte Carlo results suggest that our estimator is reasonable in finite samples. We then consider a spatial model containing various complexities and demonstrate that our HAC estimator can be applied in the context of that model.

This paper considers the statistical analysis of large panel data sets where even after conditioning on common observed effects the cross section units might remain dependently distributed. This could arise when the cross section units are subject to unobserved common effects and/or if there are spill over effects due to spatial or other forms of local dependencies. The paper provides an overview of the literature on cross section dependence, introduces the concepts of time-specific weak and strong cross section dependence and shows that the commonly used spatial models are examples of weak cross section dependence. It is then established that the Common Correlated Effects (CCE) estimator of panel data model with a multifactor error structure, recently advanced by Pesaran (2006), continues to provide consistent estimates of the slope coefficient, even in the presence of spatial error processes. Small sample properties of the CCE estimator under various patterns of cross section dependence, including spatial forms, are investigated by Monte Carlo experiments. Results show that the CCE approach works well in the presence of weak and/or strong cross sectionally correlated errors. We also explore the role of certain characteristics of spatial processes in determining the performance of CCE estimators, such as the form and intensity of spatial dependence, and the sparseness of the spatial weight matrix.

This paper considers the specification and estimation of social interaction models with network structures and the presence of endogenous and contextural e¤ects. With macro group settings, group fixed effects are also incorporated. Networks provide information on the identification of endogenous, exogenous and unobserved interactions among specific peers. We consider the identification and estimation of such a model. Empirical applications are provided to illustrate the usefulness of such a model. In addition to asymptotic properties of estimators, Monte Carlo studies provide evidence on finite sample performance of the estimation methods.

In this paper we consider a simultaneous system of spatially interrelated cross sectional equations. Our speci…cation incorporates spatial lags in the endogenous and exogenous variables. In modelling the disturbance process we allow for both spatial correlation as well as correlation across equations. The data set is taken to be a single cross section of observations. The model may be viewed as an extension of the widely used single equation Cli¤-Ord model. We suggest computationally simple limited and full information instrumental variable estimators for the parameters of the system and give formal large sample results. JEL classi…cation: C31

Government agencies in urbanizing areas are increasingly utilizing purchase and transfer of devel-opment rights programs to preserve farmland and protect local farm economies.This article tests the effect of development restrictions imposed by permanent easement sales on farmland sales prices, using Maryland data. We correct for selectivity bias due to the voluntary nature of these programs in estimating hedonic sales equations. Although preserved parcels ’ actual land values are lower, the effect of the restrictions is not statistically significant. These findings may encourage additional par-ticipation in preservation programs or justify reductions in the easement prices paid by agencies. Key words: farmland preservation, farmland prices, hedonic models, land values, sample selection. More than fifteen state and thirty-four local governments permanently preserve farmland by purchasing development rights or by allowing the transfer of development rights among landowners (American Farmland Trust). Particularly in metropolitan areas, agencies use these purchase of development