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Faced with the problem that conventional multidimensional fixed effects models only focus on unobserved heterogeneity, but ignore any potential cross-sectional dependence due to network interactions, we introduce a model of trade flows between countries over time that allows for network dependence in flows, based on sociocultural connectivity structures. We show that conventional multidimensional fixed effects model specifications exhibit cross-sectional dependence between countries that should be modeled to avoid simultaneity bias. Given that the source of network interaction is unknown, we propose a panel gravity model that examines multiplenetwork interaction structures, using Bayesian model probabilities to determine those most consistent with the sample data. This is accomplished with the use of computationally efficient Markov Chain Monte Carlo estimation methods that produce a Monte Carlo integration estimate of the log-marginal likelihood that can be used for model comparison. Application of the model to a panel of trade flows points to network spillover effects, suggesting the presence of network dependence and biased estimates from conventional trade flow specifications. The most important sources of network dependence were found to be membership in trade organizations, historical colonial ties, common currency, and spatial proximity of countries., Series: Working Papers in Regional Science

Past focus in the panel gravity literature has been on multidimensional fixed effects specifications in an effort to accommodate heterogeneity. After introducing conventional multidimensional fixed effects, we find evidence of cross-sectional dependence in flows. We propose a simultaneous dependence gravity model that allows for network dependence in flows, along with computationally efficient Markov Chain Monte Carlo estimation methods that produce a Monte Carlo integration estimate of log-marginal likelihood useful for model comparison. Application of the model to a panel of trade flows points to network spillover effects, suggesting the presence of network dependence and biased estimates from conventional trade flow specifications. The most important sources of network dependence were found to be membership in trade organizations, historical colonial ties, common currency and spatial proximity of countries., Series: Working Papers in Regional Science

Past focus in the panel gravity literature has been on multidimensional fixed effects specifications in an effort to accommodate heterogeneity. After introducing fixed effects for each origin- destination dyad and time-period speciffic effects, we find evidence of cross-sectional dependence in flows. We propose a simultaneous dependence gravity model that allows for network dependence in flows, along with computationally efficient MCMC estimation methods that produce a Monte Carlo integration estimate of log-marginal likelihood useful for model comparison. Application of the model to a panel of trade flows points to network spillover effects, suggesting the presence of network dependence and biased estimates from conventional trade flow specifications., Series: Working Papers in Regional Science

The focus is on cross-sectional dependence in panel trade flow models. We propose alternative specifications for modeling time invariant factors such as socio-cultural indicator variables, e.g., common language and currency. These are typically treated as a source of heterogeneity eliminated using fixed effects transformations, but we find evidence of cross-sectional dependence after eliminating country-specific effects. These findings suggest use of alternative simultaneous dependence model specifications that accommodate cross-sectional dependence, which we set forth along with Bayesian estimation methods. Ignoring cross-sectional dependence implies biased estimates from panel trade flow models that rely on fixed effects., Series: Working Papers in Regional Science

Focus is on efficient estimation of a dynamic space-time panel data model that incorporates spatial dependence, temporal dependence, as well as space-time covariance and can be implemented in large N and T situations, where N is the number of spatial units and T the number of time periods. Quasi-maximum likelihood (QML) estimation in cases involving large N and T poses computational challenges because optimizing the (log) likelihood requires: 1) evaluating the log-determinant of an NT x NT matrix that appears in the likelihood, 2) imposing stability restrictions on parameters reflecting space-time dynamics, as well as 3) simulations to produce an empirical distribution of the partial derivatives used to interpret model estimates that require numerous inversions of large matrices. We set forth a Markov Chain Monte Carlo (MCMC) estimation procedure capable of handling large problems, which we illustrate using a sample of T = 487 daily fuel prices for N = 12, 435 German gas stations, resulting in N x T over 6 million. The procedure produces estimates equivalent to those from QML and has the additional advantage of producing a Monte Carlo integrated estimate of the log-marginal likelihood, useful for purposes of model comparison. Our MCMC estimation procedure uses: 1) a Taylor series approximation to the logdeterminant based on traces of matrix products calculated prior to MCMC sampling, 2) block sampling of the spatiotemporal parameters, which allows imposition of the stability restrictions, and 3) a Metropolis-Hastings guided Monte Carlo integration of the logmarginal likelihood. We also provide an efficient approach to simulations needed to produce the empirical distribution of the partial derivatives for model interpretation. Der Schwerpunkt dieser Arbeit liegt auf der effizienten Schätzung eines dynamischen Raum-Zeit-Panel Datenmodells, welches sowohl die räumliche Abhängigkeit, die zeitliche Abhängigkeit, als auch die Raum-Zeit Kovarianz beinhaltet. Dieses Modell kann unter anderem in großen N- und T- Modelkonstellationen eingesetzt werden, wobei N die Zahl von Raumeinheiten und T die Anzahl der Zeiträume beziffert. Quasi-maximum likelihood (QML) Schätzungen in Fällen mit großen N- und T-Werten stellen eine rechentechnische Herausforderung dar, da folgende Schritte zur Optimierung der (Log) -Wahrscheinlichkeit erforderlich sind: 1) Auswerten der Log-Determinante einer NT x NT-Matrix, welche mit einer bestimmten Wahrscheinlichkeit auftritt, 2) Festlegung von Stabilitätsbeschränkungen für Parameter, die die Raum-Zeit-Dynamik widerspiegeln, sowie 3) Modelssimulationen zur Erzeugung einer empirischen Verteilung von Teilderivaten, die herangezogen werden um Modellschätzungen zu interpretieren, was wiederum viele Matrixinversionen erfordert. Wir haben ein Markov Chain Monte Carlo (MCMC) Schätzverfahren entwickelt, welches es möglich macht, komplexe Daten zu analysieren. Dies verdeutlichen wir anhand einer Stichprobe von T = 487 täglichen Kraftstoffpreisen für N = 12.435 deutsche Tankstellen, was eine N x T Matrix von über 6 Millionen Werten ergibt. Das entwickelte Verfahren erstellt Schätzungen, die gleichwertig dem QML Verfahren sind, jedoch den zusätzlichen Vorteil einer integrierten Monte-Carlo-Schätzung der marginalen log-Wahrscheinlichkeit erbringen. Letzteres kann für Modelvergleiche nützlich sein. Unser MCMC-Schätzverfahren verwendet folgende Methoden: 1) eine Taylor-Reihenannäherung an die log-Determinante, basierend auf Spuren von Matrixprodukten, welche vor der MCMC-Stichprobe berechnet wurden, 2) Blockstichproben der raum-zeitlichen Parameter, die es erlauben Stabilitätseinschränkungen aufzuerlegen, und 3) eine auf Metropolis-Hastings beruhende Monte-Carlo-Integration der log-marginalen Wahrscheinlichkeit. Wir bieten zudem einen effizienten Ansatz für Simulationen, die erforderlich sind, um die empirische Verteilung der partiellen Derivate für die Modellinterpretation zu erzeugen.

The focus is on cross-sectional dependence in panel trade flow models. We propose alternative specifications for modeling time invariant factors such as socio-cultural indicator variables, e.g., common language and currency. These are typically treated as a source of heterogeneity eliminated using fixed effects transformations, but we find evidence of cross-sectional dependence after eliminating country-specific effects. These findings suggest use of alternative simultaneous dependence model specifications that accommodate cross-sectional dependence, which we set forth along with Bayesian estimation methods. Ignoring cross-sectional dependence implies biased estimates from panel trade flow models that rely on fixed effects., Series: Working Papers in Regional Science

Présenté par Corinne Autant-Bernard; International audience

We apply a heterogenous coefficient spatial autoregressive panel model from Aquaro, Bailey and Pesaran (2015) to explore competition/cooperation by Berlin fueling stations in setting prices for diesel and E5 fuel. Unlike the maximum likelihood estimation method set forth by Aquaro, Bailey and Pesaran (2015), we rely on a Markov Chain Monte Carlo (MCMC) estimation methodology. MCMC estimates as applied here with non-informative priors will produce estimates equal to those from maximum likelihood, a point we demonstrate with a Monte Carlo experiment. We explore station-level price mark-ups using over 400 fueling stations located in and around Berlin, average daily diesel and E5 fuel prices, and refinery cost information covering more than 487 days. The heterogeneous coefficients spatial autoregressive panel data model uses the large sample of daily time periods to produce spatial autoregressive model estimates for each fueling station. These estimates provide information regarding the price reaction function of each station to neighboring stations. This is in contrast to conventional estimates of price reaction functions that average over the entire cross-sectional sample of stations. We show how these estimates can be used to infer competition versus cooperation in price setting by individual stations. The empirical results reveal a mix of competitive and collusive price setting, with some evidence that stations located near others of the same brand tend toward collusion, while those located near rival brands tend toward competition. Wir nutzen ein räumliches autoregressives Panel-Datenmodell von Aquaro, Bailey und Pesaran (2015), um Wettbewerbs- bzw. Kooperationsverhalten bei der Preissetzung für Diesel und E5-Benzin von Berliner Tankstellen zu untersuchen. Es wird das Markov-Chain-Monte-Carlo-Verfahren (MCMC-Verfahren) angewandt, welches in diesem Zusammenhang die gleichen Schätzungen wie die Maximum-Likelihood-Methode von Aquaro, Bailey und Pesaran (2015) liefert. Wir nutzen Informationen über mehr als 400 Tankstellen in und um Berlin, Tagesdurchschnittspreise für Diesel und E5 und Raffineriekosten von mehr als 487 Tagen, um Preisaufschläge zu untersuchen. Das angewandte Modell schätzt die Preisreaktionsfunktion - anders als übliche Schätzungen - jeder Tankstelle auf umliegende Tankstellen. Wir zeigen, wie mit diesen Schätzungen auf das das Wettbewerbs-/ Kooperationsverhalten bei der Preissetzung einzelner Tankstellen geschlossen werden kann. Die empirischen Ergebnisse zeigen eine Mischung aus wettbewerblicher und kooperativer Preissetzung mit Evidenz, dass Tankstellen mit Tankstellen derselben Marke in der Nähe zu Kooperation tendieren und Tankstellen mit Tankstellen konkurrierender Marken in der Umgebung zu Wettbewerb tendieren.

We apply a heterogenous coefficient spatial autoregressive panel model to explore competition/cooperation by duopoly pairs of German fueling stations in setting prices for diesel and E5 fuel. We rely on a Markov Chain Monte Carlo (MCMC) estimation methodology applied with non-informative priors, which produces estimates equivalent to those from (quasi-) maximum likelihood. We explore station-level pricing behavior using pairs of proximately situated fueling stations with no nearby neighbors. Our sample data represents average daily diesel and e5 fuel prices, and refinery cost information covering more than 487 days. The heterogeneous coefficients spatial autoregressive panel data model uses the large sample of daily time periods to produce spatial autoregressive model estimates for each fueling station. These estimates provide information regarding the price reaction function of each station to its duopoly rival station. This is in contrast to conventional estimates of price reaction functions that average over the entire cross-sectional sample of stations. We show how these estimates can be used to infer competition versus cooperation in price setting by individual stations., Discussion Paper / SFB823;84, 2016

Spatial regression methodology has been around for most of the 50 years (1961-2011) that the Southern Regional Science Association has been in existence. Cliff and Ord (1969) devised a parsimonious specification for the structure of spatial dependence among observations that could be used to empirically model spatial interdependence. Later work (Cliff and Ord, 1973, 1981; Ord, 1975) further developed these ideas into basic spatial regression models, which were popularized and augmented by Anselin (1988). We discuss several issues that have arisen in recent work that attempts to extend basic models of spatial interdependence to include more types of spatial and non-spatial interdependencies. Understanding these issues should help future work avoid several pitfalls that plague current and past attempts at extensions along these lines.

An introduction to spatial econometric models and methods is provided that discusses spatial autoregressive processes that can be used to extend conventional regression models. Estimation and interpretation of these models are illustrated with an applied example that examines the relationship between commuting to work times and transportation mode choice for a sample of 3,110 US counties in the year 2000. These extensions to conventional regression models are useful when modeling cross-sectional regional observations or and panel data samples collected from regions over both space and time can be easily implemented using publicly available software. Use of these models for the case of non-spatial structured dependence is also discussed. Cet article constitue une introduction aux méthodes et modèles de l’économétrie spatiale discutant des processus spatiaux autorégressifs utilisés pour étendre les modèles traditionnels de régression. Les méthodes d’estimation et l’interprétation de ces modèles sont illustrées avec un exemple appliqué traitant de la relation entre temps de navettage et choix du mode de transport pour un échantillon de 3110 comtés américains en 2000. Ces extensions des modèles traditionnels de régression sont utiles pour la modélisation d’observations régionales en coupe transversale ou en panel et sont facilement mises en œuvre avec des logiciels disponibles au public. L’utilisation de ces modèles pour le cas d’autocorrélations qui ne sont pas spatialement structurées est également discutée.

This paper explores the contribution of knowledge capital to total factor productivity differences among regions within a regression framework. We provide an econometric derivation of the relationship and show that the presence of latent/unobservable regional knowledge capital leads to a model relationship that includes both spatial and technological dependence. This model specification accounts for both spatial and technological dependence between regions, which allows us to quantify spillover impacts arising from both types of interaction. Sample data on 198 NUTS-2 regions spanning the period from 1997 to 2002 was used to empirically test the model, to measure both direct and indirect effects of knowledge capital on regional total factor productivity, and to assess the relative importance of knowledge spillovers from spatial versus technological proximity.

This paper explores the contribution of knowledge capital to total factor productivity differences among regions within a regression framework. The dependent variable is total factor productivity, defined as output (in terms of gross value added) per unit of labour and physical capital combined, while the explanatory variable is a patent stock measure of regional knowledge endowments. We provide an econometric derivation of the relationship, which in the presence of unobservable knowledge capital leads to a spatial regression model relationship. This model form is extended to account for technological dependence between regions, which allows us to quantify disembodied knowledge spillover impacts arising from both spatial and technological proximity. A six-year panel of 198 NUTS-2 regions spanning the period from 1997 to 2002 was used to empirically test the model, to measure both direct and indirect effects of knowledge capital on regional total factor productivity, and to assess the relative importance of knowledge spillovers from spatial versus technological proximity.

Spatial interaction models of the gravity type are used in conjunction with sample data on flows between origin and destination locations to analyse international and interregional trade, commodity, migration and commuting patterns. The focus is on the classical log-normal model version and spatial econometric extensions that have recently appeared in the literature. These new models replace the conventional assumption of independence between origin-destination flows with formal approaches that allow for spatial dependence in flow magnitudes. The paper also discusses problems that arise in applied practice when estimating (log-normal) spatial interaction models. (authors' abstract)

This paper investigates the impact of knowledge capital stocks on total factor productivity through the lens of the knowledge capital model proposed by Griliches (1979), augmented with a spatially discounted cross-region knowledge spillover pool variable. The objective is to shift attention from firms and industries to regions and to estimate the impact of cross-region knowledge spillovers on total factor productivity (TFP) in Europe. The dependent variable is the region-level TFP, measured in terms of the superlative TFP index suggested by Caves, Christensen and Diewert (1982). This index describes how efficiently each region transforms physical capital and labour into output. The explanatory variables are internal and out-of-region stocks of knowledge, the latter capturing the contribution of cross-region knowledge spillovers. We construct patent stocks to proxy regional knowledge capital stocks for N=203 regions over the 1997- 2002 time period. In estimating the effects we implement a spatial panel data model that controls for the spatial autocorrelation due to neighbouring regions and the individual heterogeneity across regions. The findings provide a fairly remarkable confirmation of the role of knowledge capital contributing to productivity differences among regions, and add an important spatial dimension to the discussion, by showing that productivity effects of knowledge spillovers increase with geographic proximity. (authors' abstract)

This paper uses Bayesian model comparison methods to simultaneously specify both the spatial weight structure and explanatory variables for a spatial growth regression involving 255 NUTS 2 regions across 25 European countries. In addition, a correct interpretation of the spatial regression parameter estimates that takes into account the simultaneous feed- back nature of the spatial autoregressive model is provided. Our findings indicate that incorporating model uncertainty in conjunction with appropriate parameter interpretation decreased the importance of explanatory variables traditionally thought to exert an important influence on regional income growth rates.

We survey the literature on spatial bio-economic and land-use modelling and review thematic developments. Unobserved site-specific heterogeneity is common in almost all of the surveyed works. Heterogeneity appears also to be a significant catalyst engendering significant methodological innovation. To better equip prototypes to adequately incorporate heterogeneity, we consider a smorgasbord of extensions. We highlight some problems arising with their application; provide Bayesian solutions to some; and conjecture solutions for others.

We introduce a regression-based gravity model for commodity flows between 35 regions in Austria. We incorporate information regarding the highway network into the spatial connectivity structure of the spatial autoregressive econometric model. We find that our approach produces improved model fit and higher likelihood values. The model accounts for spatial dependence in the origin-destination flows by introducing a spatial connectivity matrix that allows for three types of spatial dependence in the origins to destinations flows. We modify this origin-destination connectivity structure that was introduced by LeSage and Pace (2005) to include information regarding the presence or absence of a major highway/train corridor that passes through the regions. Empirical estimates indicate that the strongest spatial autoregressive effects arise when both origin and destination regions have neighboring regions located on the highway network. Our approach provides a formal spatial econometric methodology that can easily incorporate network connectivity information in spatial autoregressive models.