We propose a new class of models specifically tailored for spatiotemporal data analysis. To this end, we generalize the spatial autoregressive model with autoregressive and heteroskedastic disturbances, that is, SARAR(1, 1), by exploiting the recent advancements in score-driven (SD) models typically used in time series econometrics. In particular, we allow for time-varying spatial autoregressive coefficients as well as time-varying regressor coefficients and cross-sectional standard deviations. We report an extensive Monte Carlo simulation study in order to investigate the finite-sample properties of the maximum likelihood estimator for the new class of models as well as its flexibility in explaining a misspecified dynamic spatial dependence process. The new proposed class of models is found to be economically preferred by rational investors through an application to portfolio optimization.1 See Lee and Yu (2016) for identification issues in spatial Durbin panel models. 2 For the incidental parameter problem within spatial panel data models with fixed effects see Lee and Yu (2010a).

Empirical analysis in economics often faces the difficulty that the data is correlated and heterogeneous in some unknown form. Spatial parametric approaches have been widely used to account for dependence structures, but the problem of directly deal with spatially varying parameters has been largely unexplored. The problem can be serious in all those cases in which we have no prior information justified by the economic theory. In this paper we propose an algorithm-based procedure which is able to endogenously identify structural breaks in space. The proposed algorithm is illustrated by using two well known house price data sets

We exploit the information derived from geographical coordinates to endogenously identify spatial regimes in technologies that are the result of a variety of complex, dynamic interactions among site-specific environmental variables and farmer decision making about technology, which are often not observed at the farm level. Controlling for unobserved heterogeneity is a fundamental challenge in empirical research, as failing to do so can produce model misspecification and preclude causal inference. In this article, we adopt a two-step procedure to deal with unobserved spatial heterogeneity, while accounting for spatial dependence in a cross-sectional setting. The first step of the procedure takes explicitly unobserved spatial heterogeneity into account to endogenously identify subsets of farms that follow a similar local production econometric model, i.e. spatial production regimes. The second step consists in the specification of a spatial autoregressive model with autoregressive disturbances and spatial regimes. The method is applied to two regional samples of olive growing farms in Italy. The main finding is that the identification of spatial regimes can help drawing a more detailed picture of the production environment and provide more accurate information to guide extension services and policy makers. Keywords Unobserved heterogeneity • Spatial dependence • Cobb-Douglas production function • Olive production JEL codes D24 • C14 • Q12

In spatial discrete choice models the spatial dependent structure adds complexity in the estimation of parameters. Appropriate general method of moments (GMM) estimation needs inverses of n-by-n matrices and an optimization complexity of the moment conditions for moderate to large samples makes practical applications more difficult. Recently, Klier and McMillen (2008) have proposed a linearized version of the GMM estimator that avoids the infeasible problem of inverting n-by-n matrices when employing large samples. They show that standard GMM reduces to a nonlinear two-stage least squares problem. On the other hand, when we deal with full maximum likelihood (FML) estimation, a multidimensional integration problem arises and a viable computational solution needs to be found. Although it remains somewhat computationally burdensome, since the inverses of matrices dimensioned by the number of observations have to be computed, the ML estimator yields the potential advantage of efficiency. Therefore, through Monte Carlo experiments we compare GMM-based approaches with ML estimation in terms of their computation times and statistical properties. Furthermore, a comparison in terms of the marginal effects also is included. Finally, we recommend an algorithm based on sparse matrices that enables more efficient use of both ML and GMM estimators.

We propose a new spatio-temporal model with time-varying spatial weighting matrices. We allow for a general parameterization of the spatial matrix, such as: (i) a function of the inverse distances among pairs of units in space to the power of an unknown time-varying distance decay parameter, and (ii) a negative exponential function of the time-varying parameter as in (i). The filtering procedure of the time-varying unknown parameters is performed using the information contained in the score of the conditional distribution of the observables. We provide conditions for the stationarity and ergodicity of the filtered sequence of the spatial matrices as well as for the consistency and asymptotic normality of the maximum likelihood estimator (MLE). An extensive Monte Carlo simulation study to investigate the finite sample properties of the maximum likelihood estimator is reported. In the empirical part of the paper we analyze the association between eight European countries' perceived risk. Our findings suggest that the economically strong countries have their perceived risk increased due to their spatial connection with the economically weaker countries. A second empirical analysis investigates the evolution of the spatial connection between the house prices in different areas of the UK. In this case we identify periods when the usually adopted sparse weighting matrix is not sufficient to describe the underlying spatial process.