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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.

Baltagi and Li (2001) derived Lagrangian multiplier tests to jointly test for functional form and spatial error correlation. This companion paper derives Lagrangian multiplier tests to jointly test for functional form and spatial lag dependence. In particular, this paper tests for linear or log-linear models with no spatial lag dependence against a more general Box-Cox model with spatial lag dependence. Conditional LM tests are also derived which test for (i) zero spatial lag dependence conditional on an unknown Box-Cox functional form, as well as, (ii) linear or log-linear functional form given spatial lag dependence. In addition, modified Rao-Score tests are also derived that guard against local misspecification. The performance of these tests are investigated using Monte Carlo experiments.

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 study aims to examine the effect of proximity and spatial dependence on the house price index for the nascent market Dar es Salaam, Tanzania. Despite the ongoing housing market transactions, there is no single house price index that takes into account proximity and spatial dependence. The proximity considerations in question are proximal to arterial roads, public hospitals, an airport and food markets. Previous studies on sub-Saharan Africa have focused on the ordinary least squares (OLS)-based hedonic model for the index and ignored spatial and proximity considerations.

Using the OLS and spatial econometric approach, the paper tests for the significance of the two effects – proximity and spatial dependence in the hedonic price model with year dummy variables from 2010 to 2019. The paper then compares the three indices in the following configurations: without the two effects, with proximity factors only, and with both effects, i.e. proximity and spatial dependence.

The inclusion of proximity factors and spatial dependence – spatial autocorrelation – seems to improve the hedonic price model but does not significantly improve the house price index. However, further research should be called for on account of the nascent nature of the market.

The paper brings new knowledge by demonstrating that it may not be necessary to take into account proximity factors and spatial dependence for the Dar es Salaam house price index.

Portfolios of mortgage loans played an important role in the Great Recession and continue to compose a material part of bank assets. This chapter investigates how cross-sectional dependence in the underlying properties flows through to the loan returns, and thus, the risk of the portfolio. At one extreme, a portfolio of foreclosed mortgage loans becomes a portfolio of real estate whose returns exhibit substantial cross-sectional and spatial dependence. Near the other extreme, almost all loans perform and yield constant returns, which do not correlate with other performing loan returns. This suggests that loan performance effectively censors the random returns of the underlying properties. Following the statistical properties of the correlations among censored variables, the authors build off this foundation and show how the loan return correlations will rise as economic conditions deteriorate and the defaulting loans reveal the underlying housing correlations. In this chapter, the authors (1) adapt tools from spatial statistics to document substantial cross-sectional dependence across house price returns and examine the spatial structure of this dependence, (2) investigate the nonlinear nature of correlations among loan returns as a function of the default rate and the underlying house price correlations, and (3) conduct a simulation exercise using parameters from the empirical data to show the implications for holding a portfolio of mortgages.

This paper investigates the impact of governance on economic growth, considering the spatial dependence between countries.

The study employs spatial regression models to estimate the impact of governance on economic growth in a sample of 116 countries worldwide in 2017.

The findings imply that the influence of governance on economic growth is statistically significant. Moreover, if all other economic control variables are constant, 1% increase in governance raises the economic growth on average by 1% at 10%, 5% and 1% significance levels, respectively. Furthermore, each country's rise in economic growth favorably and substantially influences the economic growth of its bordering nations. The unobserved characteristics or similar unobserved environments in adjacent countries also affect its economic growth.

This study adds to the discussion and investigation of the influence of governance on economic growth by considering the spatial dependence between countries, which is lacking in the literature.

Does the standard of living vary from region to region in Portugal and are spatial units in Portugal converging in income? We observe spatial error dependence between municipalities and estimate spatial econometric models to test convergence. For conditional convergence we conclude that primary sector employment, activity rate, and percentage of active population with higher education are important to distinguish the “steady state” of the regional economies, reflecting the labor market at regional level.

The purpose of this paper is to examine the relationship between the quality of different dimensions of institutional and economic growth in a panel of 15 member ECOWAS.

The study adopts Driscoll and Kraay′s nonparametric covariance matrix estimator, and the spatial error model to account for cross-section dependency, cross-country heterogeneity and spatial dependence inherent in empirical modelling, which has largely been ignored in previous studies. This is because, the likelihood that corruption and human capital cluster in space is very high because factors that affect these phenomena disperse across borders. Similarly, to test the threshold effect, the study adopts the more refined and more appropriate dynamic panel data which models a nonlinear asymmetric dynamics and cross-sectional heterogeneity, simultaneously, in a dynamic threshold panel data framework.

The empirical evidence supports findings by previous researchers that better-quality political and economic institutions can have positive effects on economic growth. Similarly, our results support a nonlinear relationship between political institutions and economic institution, confirming the “hierarchy of institution hypothesis” in ECOWAS. Specifically, the findings show that economic institutions will only have the desired economic outcome in ECOWAS, only when political institution is above a certain threshold.

Unlike previous studies which assume cross-sectional and spatial independence, the authors account for cross-section dependency and cross-country heterogeneity inherent in empirical modelling.

The peer review history for this article is available at: https://publons.com/publon/10.1108/IJSE-10-2019-0630

The purpose of this paper is to investigate the effects of crop insurance premiums being determined by small samples of yields that are spatially correlated. If spatial autocorrelation and small sample size are not properly accounted for in premium ratings, the premium rates may inaccurately reflect the risk of a loss.

The paper first examines the spatial autocorrelation among county-level yields of corn and soybeans in the Corn Belt by calculating Moran's I and the effective spatial degrees of freedom. After establishing the existence of spatial autocorrelation, copula models are used to estimate the joint distribution of corn yields and the joint distribution of soybean yields for a group of nine counties in Illinois. Bootstrap samples of the corn and soybean yields are generated to estimate copula models with the purpose of creating sampling distributions.

The estimated bootstrap confidence intervals demonstrate that the copula parameter estimates and the premium rates derived from the parameter estimates can vary greatly. There is also evidence of bias in the parameter estimates.

Although small samples will always be an issue in crop insurance ratings and assumptions must be made for the federal crop insurance program to operate at its current scale, this analysis sheds light on some of the issues caused by using small samples and will hopefully lead to the mitigation of these small sample issues.