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For this discussion, assume there are n sample observations of the dependent variable y at unique locations. In spatial samples, often each observation is uniquely associated with a particular location or region, so that observations and regions are equivalent. Spatial dependence arises when an observation at one location, say y i is dependent on “neighboring” observations y j, y j∈ϒi. We use ϒi to denote the set of observations that are “neighboring” to observation i, where some metric is used to define the set of observations that are spatially connected to observation i. For general definitions of the sets ϒi,i=1,…,n, typically at least one observation exhibits simultaneous dependence, so that an observation y j, also depends on y i. That is, the set ϒj contains the observation y i, creating simultaneous dependence among observations. This situation constitutes a difference between time series analysis and spatial analysis. In time series, temporal dependence relations could be such that a “one-period-behind relation” exists, ruling out simultaneous dependence among observations. The time series one-observation-behind relation could arise if spatial observations were located along a line and the dependence of each observation were strictly on the observation located to the left. However, this is not in general true of spatial samples, requiring construction of estimation and inference methods that accommodate the more plausible case of simultaneous dependence among observations.

The authors provide a way to represent spatial and temporal equilibria in terms of error correction models in a panel setting. This requires potentially two different processes for spatial or network dynamics, both of which can be expressed in terms of spatial weights matrices. The first captures strong cross-sectional dependence, so that a spatial difference, suitably defined, is weakly cross-section dependent (granular) but can be non-stationary. The second is a conventional weights matrix that captures short-run spatio-temporal dynamics as stationary and granular processes. In large samples, cross-section averages serve the first purpose and the authors propose the mean group, common correlated effects estimator together with multiple testing of cross-correlations to provide the short-run spatial weights. The authors apply this model to the 324 local authorities of England, and show that our approach is useful for modeling weak and strong cross-section dependence, together with partial adjustments to two long-run equilibrium relationships and short-run spatio-temporal dynamics. This exercise provides new insights on the (spatial) long-run relationship between house prices and income in the UK.

This paper examines the price setting behaviour over time and space in the Athens residential market. In periods of house price inflation asking prices are often based upon the last observed highest selling price achieved for a similar property in the same micro-location. However, in a falling market, prices may be rigid downwards and less sensitive to the most recent transaction prices, weakening spatial effects. Furthermore, the paper considers whether future price expectations affect price setting behaviour.

The paper employs a dataset of approximately 24,500 property values from 2007 until 2014 in Athens incorporating characteristics and locational variables. The authors begin by estimating a baseline hedonic price model using property characteristics, neighbourhood amenities and location effects. Following this, a spatio-temporal autoregressive (STAR) model is estimated. Running separate models, the authors account for spatial dependence from historic valuations, contemporaneous peer effects and expectations effects.

The initial STAR model shows significant spatial and temporal effects, the former remaining important in a falling market contrasting with previous literature findings. In the second STAR model, whilst past sales effects remain significant although smaller, contemporaneous and price expectations effects are also found to be significant, the latter capturing anchoring and slow adjustment heuristics in price setting behaviour.

As valuations used in the database are based upon comparable sales, then in the recessionary periods covered in the dataset, finding comparables may have become more difficult, and hence this, in turn, may have impacted on valuation accuracy.

In addition to past effects, contemporaneous transactions and expected future values need to be taken in consideration in analysing spatial interactions in housing markets. These factors will influence housing markets in different cities and countries.

The information content of property valuations should more carefully consider the relative importance of different components of asking prices.

This is the first paper to use transactions data over a period of falling house prices in Athens and to consider current and future values in addition to past values in a spatio-temporal context.

Most spatial econometrics work focuses on spatial dependence in the regressand or disturbances. However, Lesage and Pace (2009) as well as Pace and LeSage2009 showed that the bias in β from applying OLS to a regressand generated from a spatial autoregressive process was exacerbated by spatial dependence in the regressor. Also, the marginal likelihood function or restricted maximum likelihood (REML) function includes a determinant term involving the regressors. Therefore, high dependence in the regressor may affect the likelihood through this term. In addition, Bowden and Turkington (1984) showed that regressor temporal autocorrelation had a non-monotonic effect on instrumental variable estimators.

We provide empirical evidence that many common economic variables used as regressors (e.g., income, race, and employment) exhibit high levels of spatial dependence. Based on this observation, we conduct a Monte Carlo study of maximum likelihood (ML), REML and two instrumental variable specifications for spatial autoregressive (SAR) and spatial Durbin models (SDM) in the presence of spatially correlated regressors.

Findings indicate that as spatial dependence in the regressor rises, REML outperforms ML and that performance of the instrumental variable methods suffer. The combination of correlated regressors and the SDM specification provides a challenging environment for instrumental variable techniques.

We also examine estimates of marginal effects and show that these behave better than estimates of the underlying model parameters used to construct marginal effects estimates. Suggestions for improving design of Monte Carlo experiments are provided.

The objective of this chapter is to introduce the reader to Spatial Health Econometrics (SHE). In both micro and macro health economics there are phenomena that are characterised by a strong spatial dimension, from hospitals engaging in local competitions in the delivery of health care services, to the regional concentration of health risk factors and needs. SHE allows health economists to incorporate these spatial effects using simple econometric models that take into account these spillover effects. This improves our understanding of issues such as hospital quality, efficiency and productivity and the sustainability of health expenditure of regional and national health care systems, to mention a few.

This paper aims to investigate spillover effects of public capital stock in a production function model that accounts for spatial dependencies. In many settings, ignoring spatial dependency yields inefficient, biased and inconsistent estimates in cross country panels. Although there are a number of studies aiming to estimate the output elasticity of public capital stock, many of those fail to reach a consensus on refining the elasticity estimates. We argue that accounting for spillover effects of the public capital stock on the production efficiency and incorporating spatial dependences are crucial. For this purpose, we employ a spatial autoregressive stochastic frontier model based on a number of specifications of the spatial dependency structure. Using the data of 21 OECD countries from 1960 to 2001, we estimate a spatial autoregressive stochastic frontier model and derive the mean indirect marginal effects of public capital stock, which are interpreted as spillover effects. We found that spillover effects can be an important factor explaining variations in technical inefficiency across countries as well as in explaining the discrepancies among various levels of output elasticity of public capital stock in traditional production function approaches.

This study proposes spatial origin-destination threshold Tobit to address spatial interdependence among bilateral trade flows while accounting for zero trade volumes.

This model is designed to capture multiple forms of spatial autocorrelation embedded in “directional” trade flows. The authors apply this improved model to export flows among 32 Asian countries in 1990.

The empirical results indicate the presence of all three types of spatial dependence: exporter-based, importer-based and exporter-to-importer-based. After further considering multifaceted spatial correlation in bilateral trade flows, the authors find that the effect of conventional trade variables changes in a noticeable way.

This finding implies that the standard gravity model may produce biased estimates if it does not take spatial dependence into account.

This paper attempts to offer an improved model of the standard gravity model by taking spatial dependence into account.

The purpose of this paper is on developing and implementing a model which provides a fuller and more comprehensive reflection of the interaction of house prices at the suburb level.

The authors examine how changes in housing prices evolve across space within the suburban context. In doing so, the authors developed a model which allows for suburbs to be connected both because of their geographic proximity but also by non-spatial factors, such as similarities in socioeconomic or demographic characteristics. This approach is applied to modelling home price dynamics in Melbourne, Australia, from 2007 to 2018.

The authors found that including both spatial and non-spatial linkages between suburbs provides a better representation of the data. It also provides new insights into the way spatial shocks are transmitted around the city and how suburban housing markets are clustered.

The authors have generalized the widely used SAR model and advocated building a spatial weights matrix that allows for both geographic and socioeconomic linkages between suburbs within the HOSAR framework. As the authors outlined, such a model can be easily estimated using maximum likelihood. The benefits of such a model are that it yields an improved fit to the data and more accurate spatial spill-over estimates.

We propose a generic algorithm for numerically accurate likelihood evaluation of a broad class of spatial models characterized by a high-dimensional latent Gaussian process and non-Gaussian response variables. The class of models under consideration includes specifications for discrete choices, event counts and limited-dependent variables (truncation, censoring, and sample selection) among others. Our algorithm relies upon a novel implementation of efficient importance sampling (EIS) specifically designed to exploit typical sparsity of high-dimensional spatial precision (or covariance) matrices. It is numerically very accurate and computationally feasible even for very high-dimensional latent processes. Thus, maximum likelihood (ML) estimation of high-dimensional non-Gaussian spatial models, hitherto considered to be computationally prohibitive, becomes feasible. We illustrate our approach with ML estimation of a spatial probit for US presidential voting decisions and spatial count data models (Poisson and Negbin) for firm location choices.

This chapter proposes augmenting a simple income stock price model with spatial structures to evaluate the significance of real and financial linkages in instigating stock market contagion. The treatment is premised upon the clustering of excessive returns and volatilities during the Subprime crisis envisaged from our regime switching analysis over a long time span, and the presence of spatial autocorrelation in the baseline income stock model. With the channel factors manifested as spatial weights, this chapter explores specifications of explicit interrelated stock price returns and implicit spatial autocorrelation in the error term for the 3-year period from 2007 to 2009. Model validity is authenticated by way of model choice and spatial weight selection. The finding shows that spatial dependence in either specification is not too sizable indicating that contagion is not spreading fast in the sample period. Of the various factors considered, non-performing loans, market liquidity, and credit to deposit ratio turn out to be the most important transmission factors. Current account balance, net FDI flows, and size of GDP are among the least significant media. In sum, these suggest that financial linkages could play a more important role in facilitating shock transmission when compared to real linkages such as trade.