Spatial Growth Regressions: Model Specification,Estimation and Interpretation

Abstract

We attempt to clarify a number of points regarding use of spatial regression models for regional growth analysis. We show that as in the case of non-spatial growth regressions, the effect of initial regional income levels wears off over time. Unlike the non-spatial case, long-run regional income levels depend on: own region as well as neighbouring region characteristics, the spatial connectivity structure of the regions, and the strength of spatial dependence. Given this, the search for regional characteristics that exert important influences on income levels or growth rates should take place using spatial econometric methods that account for spatial dependence as well as own and neighbouring region characteristics, the type of spatial regression model specification, and weight matrix. The framework adopted here illustrates a unified approach for dealing with these issues.     

Innovation and Co-location

Abstract

Here we attempt to advance the understanding of the impact of co-locative factors on regional innovation performance. The objectives are to answer what role co-location plays in explaining differences in regional innovation performance and what methodological improvements can compensate for the shortcomings of existing econometric analyses. The study is based on register data from the Business Register of Statistics Norway and the patent data from the Norwegian Patent Office for the period 1995–2003, aggregated to 161 labour market regions of Norway. A Bayesian spatial autoregressive (heteroscedastic) estimation procedure is applied. The results confirm the role of various co-locative factors in the spatial distribution of innovation.     

Space-varying Coefficient Simultaneous Autoregressive Models for the Structural Analysis of Residential Water Demand

Abstract

This study develops two space-varying coefficient simultaneous autoregressive (SVC-SAR) models for areal data and applies them to the discrete/continuous choice model, which is an econometric model based on the consumer's utility maximization problem. The space-varying coefficient model is a statistical model in which the coefficients vary depending on their location. This study introduces the simultaneous autoregressive model for the underlying spatial dependence across coefficients, where the coefficients for one observation are affected by the sum of those for the other observations. This model is named the SVC-SAR model. Because of its flexibility, we use the Bayesian approach and construct its estimation method based on the Markov chain Monte Carlo simulation. The proposed models are applied to estimate the Japanese residential water demand function, which is an example of the discrete/continuous choice model.     

Fixed Effects and Random Effects Estimation of Higher-order Spatial Autoregressive Models with Spatial Autoregressive and Heteroscedastic Disturbances

Abstract

This paper develops a unified framework for fixed effects (FE) and random effects (RE) estimation of higher-order spatial autoregressive panel data models with spatial autoregressive disturbances and heteroscedasticity of unknown form in the idiosyncratic error component. We derive the moment conditions and optimal weighting matrix without distributional assumptions for a generalized moments (GM) estimation procedure of the spatial autoregressive parameters of the disturbance process and define both an RE and an FE spatial generalized two-stage least squares estimator for the regression parameters of the model. We prove consistency of the proposed estimators and derive their joint asymptotic distribution, which is robust to heteroscedasticity of unknown form in the idiosyncratic error component. Finally, we derive a robust Hausman test of the spatial random against the spatial FE model.     

Modelling spatial regimes in farms technologies

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.     

Does Evidence on Regional Economic Convergence Depend on the Estimation Strategy? Outcomes from Analysis of a Set of NUTS2 EU Regions

Abstract

The regional economic convergence/divergence issue has been discussed extensively recently, but results obtained are not always interpretable unequivocally as a consequence of the different estimation strategies used. As it is widely recognized, the most common theoretical framework applied to measure the speed of economic convergence among countries or regions remains the β-convergence approach, linked to the neoclassical Solow model. There have been many attempts to consider variations of the basic cross-sectional specification ranging from panel data models to Bayesian spatial econometric techniques. The application of spatial econometric methodologies is an essential tool for proper statistical inference on regional data. In this context, the aim of this paper is to connect the different results obtained in the literature. More specifically, we address whether or not evidence on convergence depends upon the estimation strategy, by taking the same set of data and systematically comparing the results obtained from different estimation strategies. The results from a set of NUTS2 EU regions conclude that both the model implied by the cross-sectional analysis and the one referring to the space-time dynamics incorporated in the panel specification point to convergence. The concept of convergence implied is, however, quite different, as demonstrated throughout the paper.     

Practical Proposals for Specifying k-Nearest Neighbours Weights Matrices

Abstract

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.     

CROSS‐SECTIONAL DEPENDENCE AND SPILLOVERS IN SPACE AND TIME: WHERE SPATIAL ECONOMETRICS AND GLOBAL VAR MODELS MEET

To enhance the measurement of economic and financial spillovers, we bring together the spatial and global vector autoregressive (GVAR) classes of econometric models by providing a detailed methodological review where they meet in terms of structure, interpretation, and estimation. We discuss the structure of connectivity (weight) matrices used by these models and its implications for estimation. To anchor our work within the dynamic literature on spillovers, we define a general yet measurable concept of spillovers. We formalize it analytically through the indirect effects used in the spatial literature and impulse responses used in the GVAR literature. Finally, we propose a practical step‐by‐step approach for applied researchers who need to account for the existence and strength of cross‐sectional dependence in the data. This approach aims to support the selection of the appropriate modeling and estimation method and of choices that represent empirical spillovers in a clear and interpretable form.     

The Spatial Durbin Model and the Common Factor Tests

Abstract

The spatial Durbin model occupies an interesting position in the field of spatial econometrics. It is the reduced form of a model with cross-sectional dependence in the errors and it may be used as the nesting equation in a more general approach of model selection. Specifically, in this equation we obtain the common factor tests (of which the likelihood ratio is the best known) whose objective is to discriminate between substantive and residual dependence in an apparently misspecified equation. Our paper tries to delve deeper into the role of the spatial Durbin model in the problem of specifying a spatial econometric model. We include a Monte Carlo study related to the performance of the common factor tests presented in the paper in small sample sizes.     

Forecasting a long memory process subject to structural breaks

We develop an easy-to-implement method for forecasting a stationary autoregressive fractionally integrated moving average (ARFIMA) process subject to structural breaks with unknown break dates. We show that an ARFIMA process subject to a mean shift and a change in the long memory parameter can be well approximated by an autoregressive (AR) model and suggest using an information criterion (AIC or Mallows’ _Cp$C_p$) to choose the order of the approximate AR model. Our method avoids the issue of estimation inaccuracy of the long memory parameter and the issue of spurious breaks in finite sample. Insights from our theoretical analysis are confirmed by Monte Carlo experiments, through which we also find that our method provides a substantial improvement over existing prediction methods. An empirical application to the realized volatility of three exchange rates illustrates the usefulness of our forecasting procedure. The empirical success of the HAR-RV model can be explained, from an econometric perspective, by our theoretical and simulation results.     

Raising the bar (9)

ABSTRACT

This editorial summarizes the papers published in issue 13(4) so as to raise the bar in applied spatial economic research and highlight new trends. The first paper develops an economic geography model with trade costs in all sectors and different shares of unskilled labour in all locations. The second paper translates an economic geography model into a dynamic spatial econometric model and then estimates the unknown parameters to test for congestion spillover effects among Chinese cities. The following paper also investigates spillover effects, but of sovereign and banking risks across countries. The fourth paper empirically examines if a higher market potential results in higher average productivity and lower productivity dispersion of Italian retailers. The fifth paper demonstrates that modelling more than one spatial lag in the independent variables, using different specifications of the spatial weight matrix, can be used as a tool to correct for an omitted variable bias. The final paper develops a test for the existence of non-parametric non-linearities in a linear spatial econometric model.     

Spatial Vector Autoregressions

Abstract

A spatial vector autoregressive model (SpVAR) is defined as a VAR which includes spatial as well as temporal lags among a vector of stationary state variables. SpVARs may contain disturbances that are spatially as well as temporally correlated. Although the structural parameters are not fully identified in SpVARs, contemporaneous spatial lag coefficients may be identified by weakly exogenous state variables. Dynamic spatial panel data econometrics is used to estimate SpVARs. The incidental parameter problem is handled by bias correction rather than more popular alternatives such as generalised methods of moments (GMM). The interaction between temporal and spatial stationarity is discussed. The impulse responses for SpVARs are derived, which naturally depend upon the temporal and spatial dynamics of the model. We provide an empirical illustration using annual spatial panel data for Israel. The estimated SpVAR is used to calculate impulse responses between variables, over time, and across space. Finally, weakly exogenous instrumental variables are used to identify contemporaneous spatial lag coefficients.     

Growth in a Cross-section of Cities: Location,Increasing Returns or Random Growth?

Abstract

This article analyses empirically the main existing theories on income and population city growth: increasing returns to scale, locational fundamentals and random growth. To do this we consider a large database of urban, climatological and macroeconomic data from 1,173 US cities observed in 1990 and 2000. The econometric model is robust to the presence of spatial effects. Our analysis shows the existence of increasing returns and two distinct equilibria in per-capita income and population growth. We also find important differences in the structure of productive activity, unemployment rates and geographical location between cities in low-income and high-income regimes.     

A Generalized Method of Moments Estimator for a Spatial Panel Model with an Endogenous Spatial Lag and Spatial Moving Average Errors

Abstract

This paper proposes a new generalized method of moments (GMM) estimator for spatial panel models with spatial moving average errors combined with a spatially autoregressive dependent variable. Monte Carlo results are given suggesting that the GMM estimator is consistent. The estimator is applied to English real estate price data.     

Women in the migrant economy. A positional approach to contextualize gendered transnational trajectories

ABSTRACT

Drawing on the life histories of migrant women entrepreneurs in the Netherlands and Spain, this article explores the influence of transnational trajectories on their social positions and business strategies. A translocational positional approach enables us to research the transnational strategies of women entrepreneurs more effectively in addition to examining the changes in social positions and gendered identities between the country of origin and the country of destination. This approach contributes to scholarship on ‘context’ by offering a transnational gendered dimension in relation to the effects of social, spatial and institutional factors. Our findings demonstrate how female migrant entrepreneurs redefine their social status in different contexts by establishing a business and challenge, contest or comply with gender relations in their transnational entrepreneurial journeys.     

Consistency and asymptotic normality of least squares estimators in generalized STAR models

Space–time autoregressive (STAR) models, introduced by Cliff and Ord [Spatial autocorrelation (1973) Pioneer, London] are successfully applied in many areas of science, particularly when there is prior information about spatial dependence. These models have significantly fewer parameters than vector autoregressive models, where all information about spatial and time dependence is deduced from the data. A more flexible class of models, generalized STAR models, has been introduced in Borovkova et al. [Proc. 17th Int. Workshop Stat. Model. (2002), Chania, Greece] where the model parameters are allowed to vary per location. This paper establishes strong consistency and asymptotic normality of the least squares estimator in generalized STAR models. These results are obtained under minimal conditions on the sequence of innovations, which are assumed to form a martingale difference array. We investigate the quality of the normal approximation for finite samples by means of a numerical simulation study, and apply a generalized STAR model to a multivariate time series of monthly tea production in west Java, Indonesia.     

Raising the bar (11)

This editorial summarizes the papers published in issue 14(2) so as to raise the bar in applied spatial economic research and highlight new trends. The first paper deals with past and current challenges for regional science research. The second paper investigates whether people living in deprived neighbourhoods have less chance of succeeding in a job application. The third paper finds evidence that real estate firms can avoid price competition when market shares of their allies increase in the vicinity. The fourth paper is methodological: it considers a spatial autoregressive (SAR) model with heterogeneous coefficients and extensively analyzes the impact of this extension on the direct and indirect effects estimates. The fifth paper proposes an innovative method to estimate the elements of the spatial weight matrix in a spatial econometric model. The final paper is econometric–theoretical: it proposes a new generalized method of moments (GMM) estimator of the coefficients of a SAR model if the error terms are heteroskedastic of an unknown form.     

When the difference makes a difference – the regional embeddedness of entrepreneurship

Abstract

Regional determinants of new firm formation are of interest to researchers and policymakers. In the analysis of new firm formation, most studies use econometric approaches that mask intra-unit variations, not recognizing counterbalancing and dilution effects as a result. Recent advances in spatial statistics such as Geographically Weighted Regression (GWR) take local variations into account. However, these approaches operate only on a bivariate level, making it impossible to detect the homogenous parts of the area under examination with regard to a number of relationships between new firm formation and its determinants. Based on a sample of 412 German regions, we apply GWR and subsequent graph-partitioning clustering to identify multi-relationally homogeneous sub-areas. Being that the results suggest a four-cluster solution, ‘one size fits all’ policies and premature unit zoning can be called into question.     

A Dynamic Panel Data Approach to the Forecasting of the GDP of German Länder

Abstract

In this paper, we make multi-step forecasts of the annual growth rates of the real GDP for each of the 16 German Länder simultaneously. We apply dynamic panel models accounting for spatial dependence between regional GDP. We find that both pooling and accounting for spatial effects help to improve the forecast performance substantially. We demonstrate that the effect of accounting for spatial dependence is more pronounced for longer forecasting horizons (the forecast accuracy gain is about 9% for a 1-year horizon and exceeds 40% for a 5-year horizon). We recommend incorporating a spatial dependence structure into regional forecasting models, especially when long-term forecasts are made.     

Network management as a contingent activity. A configurational analysis of managerial behaviors in different network settings

ABSTRACT

Network managers engage in several day-to-day activities, including bridging, networking, and stabilizing relationships. Still, when should they opt for one activity or another? Our study shows that this choice needs to be taken in combination with certain network characteristics, such as network development stage, connectivity, and trust. It sheds light on four different combinations of activities and network characteristics that are simultaneously able to lead to perceived high network performance. It also suggests three approaches to network management in networks that differ in their development stage, connectivity and trust: stabilize, stabilize and connect, stabilize and develop.