Spatial Econometrics Literature Research Articles

The generalized spatial random effects model in R

We describe a user-friendly, production quality R implementation of the maximum likelihood estimator of the generalized spatial random effects (GSRE) model of Baltagi, Egger and Pfaffermayr within the well known ’splm’ package for spatial panel econometrics. We extend the maximum likelihood estimator for the GSRE to including a spatial lag of the dependent variable (SAR), and we discuss the theoretical and computational approach. This is the first implementation of the SAR+GSRE, and the second of the original GSRE. Until recently only estimators restricting the spatial structure of individual effects in an arbitrary way have been available and widely employed in applied practice. We present results from the SAR+GSRE and the restricted estimators side by side, drawing on some well-known examples from the spatial econometrics literature. The potential biases from imposing inappropriate restrictions to the spatial error process and/or from omitting the SAR term are illustrated by simulation.

Spatial Dependence in the Relationship between Climate Change and Internal Migration: Evidence from the United States

Understanding and accurately estimating the effects of climate change on migration patterns may be an important concern for future climate change adaptation and mitigation efforts. In this context, issues of spatial dependence are likely relevant but have largely been neglected by previous literature. Drawing on empirical methods developed in the spatial econometrics literature, the current paper attempts to shed some light on the role of spatial dependence in the climate-migration relationship using data for the United States for the years 2005 to 2019. I find modest evidence of spatial spillover effects of temperature and precipitation on state-level migration rates. In particular, I show that not accounting for potential spatial spillover effects leads to an overestimation of the effects of precipitation on migration rates.

Estimation and inference in spatial models with dominant units

In spatial econometrics literature estimation and inference are carried out assuming that the matrix of spatial or network connections has uniformly bounded absolute column sums in the number of units, n, in the network. This paper relaxes this restriction and allows for one or more units to have pervasive effects in the network. The linear–quadratic central limit theorem of Kelejian and Prucha (2001) is generalized to allow for such dominant units, and the asymptotic properties of the GMM estimators are established in this more general setting. A new bias-corrected method of moments (BMM) estimator is also proposed that avoids the problem of weak instruments by self-instrumenting the spatially lagged dependent variable. Both cases of homoskedastic and heteroskedastic errors are considered and the associated estimators are shown to be consistent and asymptotically normal, depending on the rate at which the maximum column sum of the weights matrix rises with n. The small sample properties of GMM and BMM estimators are investigated by Monte Carlo experiments and shown to be satisfactory. An empirical application to sectoral price changes in the US over the pre- and post-2008 financial crisis is also provided. It is shown that the share of capital can be estimated reasonably well from the degree of sectoral interdependence using the input–output tables, despite the evidence of dominant sectors being present in the US economy.

Estimation and Inference in Spatial Models with Dominant Units

In spatial econometrics literature estimation and inference are carried out assuming that the matrix of spatial or network connections has uniformly bounded absolute column sums in the number of units, n, in the network. This paper relaxes this restriction and allows for one or more units to have pervasive effects in the network. The linear-quadratic central limit theorem of Kelejian and Prucha (2001) is generalized to allow for such dominant units, and the asymptotic properties of the GMM estimators are established in this more general setting. A new bias-corrected method of moments (BMM) estimator is also proposed that avoids the problem of weak instruments by self-instrumenting the spatially lagged dependent variable. Both cases of homoskedastic and heteroskedastic errors are considered and the associated estimators are shown to be consistent and asymptotically normal, depending on the rate at which the maximum column sum of the weights matrix rises with n. The small sample properties of GMM and BMM estimators are investigated by Monte Carlo experiments and shown to be satisfactory. An empirical application to sectoral price changes in the US over the pre- and post-2008 financial crisis is also provided. It is shown that the share of capital can be estimated reasonably well from the degree of sectoral interdependence using the input-output tables, despite the evidence of dominant sectors being present in the US economy.

Determinants of labour productivity growth in Spanish and Portuguese regions: a spatial shift-share approach

This article analyses the structural changes in labour productivity in the regions of Spain and Portugal during the period 2000–2015, by business sector contribution and spatial distribution. A shift-share empirical analysis was applied to identify the components of aggregate productivity growth and to ascertain the role played by the different sectors. Both the intra-sectoral component and the presence of spatial autocorrelation were found to be statistically significant, which led us to identify two clusters: one of high productivity, corresponding to regions in the eastern half of the Iberian peninsula, and the other of low productivity, in the west. For both clusters, various model specifications that have been proposed in spatial econometrics literature were used to estimate spatial spillovers of each sector and determine the contribution made to productivity growth by each sectoral component, and to identify any spatial feedbacks that may be generated in this process. The total effect of intra-sectoral component for all sectors in both clusters is positive. The highest values are obtained by the agriculture, construction, trade and public services sectors. Moreover, the total effects are greater in the high-productivity cluster, except for the industry sector.

Estimation and Inference in Spatial Models with Dominant Units

In spatial econometrics literature estimation and inference are carried out assuming that the matrix of spatial or network connections has uniformly bounded absolute column sums in the number of units, n, in the network. This paper relaxes this restriction and allows for one or more units to have pervasive effects in the network. The linear-quadratic central limit theorem of Kelejian and Prucha (2001) is generalized to allow for such dominant units, and the asymptotic properties of the GMM estimators are established in this more general setting. A new bias-corrected method of moments (BMM) estimator is also proposed that avoids the problem of weak instruments by self-instrumenting the spatially lagged dependent variable. Both cases of homoscedastic and heteroskedastic errors are considered and the associated estimators are shown to be consistent and asymptotically normal, depending on the rate at which the maximum column sum of the weights matrix rises with n. The small sample properties of GMM and BMM estimators are investigated by Monte Carlo experiments and shown to be satisfactory. An empirical application to sectoral price changes in the US over the pre- and post-2008 financial crisis is also provided. It is shown that the share of capital can be estimated reasonably well from the degree of sectoral interdependence using the input-output tables, despite the evidence of dominant sectors being present in the US economy.

Oil Price Shocks and Economic Growth in the US

We apply both conventional and spatial techniques to panel data for US states to examine the effects of plausibly exogenous oil price shocks on economic growth. Contrary to the oil curse claims, we find that oil price shocks have numerically moderate but highly statistically significant positive direct effects on growth while the indirect effects are insignificant. We also find that positive impact of oil occurs only in states with a high value of the economic freedom index. In a technical contribution to the spatial econometrics literature we propose a procedure for estimating marginal effects of oil price shocks in a model with interaction terms. In addition, we show that the cumulative direct oil price effects on economic growth are persistent over time.

The propagation of financial turbulence: interdependence, spillovers, and direct and indirect effects

We investigate the propagation of financial turbulence via trade, capital flows, and distance channels in the pre-crisis and Global Financial Crisis periods by modeling spillover and interdependence effects, using spatial econometric techniques. Financial turbulence is proxied by the ratio of nonperforming loans to total loans in a country. Spillover effects are defined as significant changes in the linkages between countries due to a shock, and interdependence effects as strong linkages among pairs of countries independent of shocks. Using annual data of 40 countries from 2003 to 2010, we find that interdependence and spillover effects should be jointly analyzed. Furthermore, our results suggest that the capital flows channel is more important than the other two channels in capturing propagation of financial turbulence. By deriving what is known in the spatial econometrics literature as direct and indirect effect estimates, we show that the marginal effects of macroeconomic variables (like GDP growth, inflation, and credit growth) on financial turbulence take different forms during a crisis than in tranquil periods.

A spatial difference-in-differences analysis of the impact of sugarcane production on respiratory diseases

Sugarcane production represents around 10% of the agricultural area and 1% of GDP in Brazil, and has grown substantially in recent years. The traditional harvest method involves burning the field to facilitate access to the canes, resulting in well-documented negative effects on health. The existing studies do not consider the effects on health in the surrounding areas. This article presents a new variety of a spatial diff-in-diff model to control for the effects of sugarcane production in neighboring non-producing regions. This method is an addition to the Spatial Econometrics literature, as it includes spatial effects on treated and untreated regions, so that the effects on both producing and surrounding non-producing regions can be properly estimated. The results indicate that the effects on the producing regions are 78% larger than if the effects on the surrounding areas were ignored. Moreover, the effects on the surrounding areas, typically ignored in other studies, are relevant, and almost as large as the effects on the producing areas.

The public sector and convergence with spatial interdependence: empirical evidence from Spain

ABSTRACTWe propose a framework to analyse convergence between regions, incorporating the public sector and technological knowledge spillovers in the context of a Neoclassical Growth Model. Second, we apply novel estimation methods pertaining to the spatial econometrics literature introducing a spatial Durbin panel data model based on instrumental variables and maximum-likelihood estimation. Our model makes it possible to analyse, in terms of convergence, the results obtained in Spanish regions with the policies implemented during the period 1980–2011. The results support the idea that education and fiscal policies have a positive effect on regional development and cohesion. Therefore, we can conclude that it is possible to obtain better results for regional convergence with higher rates of public investment in education and tax revenues. We also obtain interesting results that confirm the existence of spillover effects in economic growth and public policies, identifying their magnitude and significance.

How to Interpret the Coefficients of Spatial Models: Spillovers, Direct and Indirect Effects

This paper briefly reviews how to derive and interpret coefficients of spatial regression models, including topics of direct and indirect (spatial spillover) effects. These topics have been addressed in the spatial econometric literature over the past 5–6 years, but often at a level sometimes difficult for students new to the field. Our goal is to overcome this handicap by carefully presenting the mathematics behind these spatial effects and clearly illustrating how they work using two small fictive datasets and one large dataset with real data. The motivation for the paper is primarily pedagogical. Theoretical and conceptual impediments associated with the application of procedures are discussed.

Race to the debt trap? — Spatial econometric evidence on debt in German municipalities

Through an intertemporal budget constraint, jurisdictions may gain advantages in tax and spending competition by ‘competing’ on debt. While the existing spatial econometric literature focuses on tax and spending competition, very little is known about spatial interaction via public debt. If jurisdictions compete for mobile capital to finance public spending, they may compete in debt levels as well as taxes. We use a theoretical model to derive the reaction of jurisdictions' debt levels to their neighbors' debts. We then estimate the spatial interdependence of public debt among German municipalities using a panel on municipalities in the two largest German states from 1999 to 2006. We find significant and robust interaction effects between debt levels of neighboring municipalities, which we compare to spatial tax and spending interactions. The results indicate that a municipality increases its per capita debt by 16–33 Euro as a reaction to an increase of 100 Euro in neighboring municipalities.

Race to the Debt Trap? - Spatial Econometric Evidence on Debt in German Municipalities

Through an intertemporal budget constraint, jurisdictions may gain advantages in tax and spending competition by 'competing' on debt. While the existing spatial econometric literature focuses on tax and spending competition, very little is known about spatial interaction via public debt. This paper estimates the spatial interdependence of public debt among German municipalities using a panel on municipalities in the two largest German states from 1999 to 2006. We find signi ficant and robust interaction effects between debt of neighboring municipalities, which we compare to spatial tax and spending interactions. The results indicate that a municipality increases its per capita debt by 16-33 Euro as a reaction to an increase of 100 Euro in neighboring municipalities.

Estimation of fixed effects panel regression models with separable and nonseparable space–time filters

This paper considers a quasi-maximum likelihood estimation for a linear panel data model with time and individual fixed effects, where the disturbances have dynamic and spatial correlations which might be spatially stable or unstable. We first consider both separable and nonseparable space–time filters for the stable model. The separable space–time filter is subject to a parametric restriction which results in relative computational simplicity. In contrast to the spatial econometrics literature, we expose economic restrictions imposed by the separable space–time filter model and explore computational tractability of the nonseparable filter model. Throughout this paper, the effect of initial observations is taken into account, which results in an exact likelihood function for estimation. This is important when the span of time periods is short. We then investigate spatial unstable cases, where we propose to apply a “spatial differencing” to all variables in the regression equation as a data transformation, which may eliminate unstable or explosive spatial components in order to achieve a robust estimator. For estimates of the parameters in both the regression part and the disturbance process, they are nT-consistent and asymptotically centered normal regardless of whether T is large or not and whether the process is stable or not.

Hedonic Valuation in an Urban High‐Rise Housing Market

This study estimates the effect of spatial heterogeneity and housing‐unit attributes on the value of apartment housing in a densely urban Chinese housing market. This paper contributes to the literature in two ways. First, high‐rise housing complexes present complications in that the vertical dimension is important in purchase decisions—yet the spatial econometric literature has focused exclusively on two dimensions. We introduce a three‐dimensional (3‐D) spatial weights matrix to capture the potential for “within project” correlation among housing units located on different floors within a project. Second, a significant proportion of the world's population lives in urban high‐rise buildings but the literature has, for the most part, completely ignored such markets. Test statistics support the use of a 3‐D weight matrix; our application of the hedonic methodology to a dense, vertical housing market shows that it can be used to value amenities located within or adjacent to housing complex amenities. In our empirical example, though, we observe little difference in marginal valuation of amenities under a 3‐D weight matrix relative to a standard 2‐D weight matrix.

Practical Proposals for Specifying k-Nearest Neighbours Weights Matrices

In this article, we introduce and evaluate testing procedures for specifying the number k of nearest neighbours in the weights matrix of a spatial econometric model. An increasing and a decreasing neighbours testing procedure are suggested. Kelejian's J-test for non-nested spatial models is used in the testing procedures. The testing procedures give formal justification for the choice of k, something which has been lacking in the classical spatial econometric literature. Simulations show that the testing procedures can be used in large samples to determine k. An empirical example involving house price data is provided.

Spatial econometric panel data model specification: A Bayesian approach

Taking a Bayesian perspective on model uncertainty for static panel data models proposed in the spatial econometrics literature considerably simplifies the task of selecting an appropriate model. A wide variety of alternative specifications that include various combinations of spatial dependence in lagged values of the dependent variable, spatial lags of the explanatory variables, as well as dependence in the model disturbances have been the focus of a literature on various statistical tests for distinguishing between these numerous specifications.A Bayesian model uncertainty argument is advanced that logically implies we can simplify this task by focusing on only two model specifications. One of these, labeled the spatial Durbin model (SDM) implies global spatial spillovers, while the second, labeled a spatial Durbin error model (SDEM) leads to local spatial spillovers. A Bayesian approach to determining an appropriate local or global specification, SDEM versus SDM is set forth here for static panel variants of these two models. The logic of the Bayesian view of model uncertainty suggests these are the only two specifications that need to be considered. This greatly simplifies the task confronting practitioners when using static panel data models.

Causality, Uncertainty and Identification: Three Issues on the Spatial Econometrics Agenda

This paper offers a personal view on recent developments in the field of spatial econometrics. The approach is subjective and certainly biased. I focus on three issues that I consider of the utmost importance and which are at the basis of the discipline, namely spatial causality, the question of identification in spatial models, and the problem of selecting the (most appropriate) spatial weighting matrix. These three topics are receiving increasing attention in the spatial econometrics literature, although there are still many issues to be resolved. They will most likely be areas of intense activity in the near future. Questo articolo offre un commento personale dei recenti sviluppi nel campo dell’econometria spaziale. L’approccio e soggettivo e senza dubbio parziale. Mi sono concentrato su tre temi che considero di primaria importanza e che costituiscono la base dell’intera disciplina: la causalita spaziale, la questione dell’identificazione nei modelli spaziali ed il problema della selezione della matrice di pesi spaziali piu appropriata. Nonostante la crescente attenzione verso questi temi rimangono numerosi punti da dibattere e chiarire, che costituiranno presumibilmente l’oggetto di un’intensa attivita di ricerca nell’immediato futuro.

Spatial Econometric Panel Data Model Specification: A Bayesian Approach

Taking a Bayesian perspective on model uncertainty for static panel data models proposed in the spatial econometrics literature considerably simplifies the task of selecting an appropriate model. A wide variety of alternative specifications that include various combinations spatial dependence in lagged values of the dependent variable, spatial lags of the explanatory variables, as well as dependence in the model disturbances have been the focus of a literature on various statistical tests for distinguishing between these numerous specifications.

Evaluating the effects of heteroscedasticity on the economic growth of EU regions

The hypothesis of homoscedasticity of errors is convenient for the simplification of the estimation procedures. Unfortunately, this assumption is rather restrictive in the case of the analysis of spatially distributed data. Spatial units, in fact, can be very different in size and in other economic characteristics. This circumstance suggests the presence of heteroscedasticity in this typology of data. In this paper we study the effects of heteroscedasticity in regional economic convergence. We use two different estimators of the coefficient of variance and covariance matrix recently introduced in spatial econometrics literature that take into account the heteroscedasticity highlighted by the error terms. This methodology can be considered a suitable alternative to the identification of convergence clubs that represents a very popular approach for the analysis of structural economic differences between regions. The empirical analysis concerns the estimate of conditional economic convergence on EU NUTS 2 regions for the period 1981-2004.