BAYSIAN INFERENCE FOR ORDERED RESPONSE DATA WITH A DYNAMIC SPATIAL‐ORDERED PROBIT MODEL

ABSTRACT Many databases involve ordered discrete responses in a temporal and spatial context, including, for example, land development intensity levels, vehicle ownership, and pavement conditions. An appreciation of such behaviors requires rigorous statistical methods, recognizing spatial effects and dynamic processes. This study develops a dynamic spatial‐ordered probit (DSOP) model in order to capture patterns of spatial and temporal autocorrelation in ordered categorical response data. This model is estimated in a Bayesian framework using Gibbs sampling and data augmentation, in order to generate all autocorrelated latent variables. It incorporates spatial effects in an ordered probit model by allowing for interregional spatial interactions and heteroskedasticity, along with random effects across regions or any clusters of observational units. The model assumes an autoregressive, AR(1), process across latent response values, thereby recognizing time‐series dynamics in panel data sets. The model code and estimation approach is tested on simulated data sets, in order to reproduce known parameter values and provide insights into estimation performance, yielding much more accurate estimates than standard, nonspatial techniques. The proposed and tested DSOP model is felt to be a significant contribution to the field of spatial econometrics, where binary applications (for discrete response data) have been seen as the cutting edge. The Bayesian framework and Gibbs sampling techniques used here permit such complexity, in world of two‐dimensional autocorrelation.     

EVIDENCE OF POLITICAL YARDSTICK COMPETITION IN FRANCE USING A TWO‐REGIME SPATIAL DURBIN MODEL WITH FIXED EFFECTS*

ABSTRACT This research proposes a two‐regime spatial Durbin model with spatial and time‐period fixed effects to test for political yardstick competition and exclude any other explanation that might produce spatial interaction effects among the dependent variable, the independent variables, or the error term. The study also derives the maximum likelihood estimator and variance–covariance matrix of the parameters of this model. Data pertaining to welfare spending by 93 departments in France during 1992–2000 provide significant empirical evidence in support of political yardstick competition. Departments governed by a small political majority mimic neighboring expenditures on welfare to a greater extent than do departments governed by a large political majority.     

ANALYZING THE IMPACT OF PUBLIC CAPITAL STOCK USING THE NEG WAGE EQUATION: A SPATIAL PANEL DATA APPROACH

ABSTRACT This paper examines the relationship between the level of public infrastructure and the level of productivity using panel data for the Spanish provinces over the period 1985–2004, a period that is particularly relevant due to the substantial changes occurring in the Spanish economy at that time. The underlying model used for the data analysis is based on the wage equation, which is one of a handful of simultaneous equations which when satisfied correspond to the short‐run equilibrium of New Economic Geography (NEG) theory. This is estimated using various spatial panel models with either fixed or random effects to allow for individual heterogeneity. Using these models, we find consistent evidence that productivity depends directly on the public capital stock endowment of each province, but also there is evidence of negative spillover effects from changes in capital stock in neighboring provinces.     

PERSISTENCE OF REGIONAL UNEMPLOYMENT: APPLICATION OF A SPATIAL FILTERING APPROACH TO LOCAL LABOR MARKETS IN GERMANY*

ABSTRACT The geographical distribution and persistence of regional/local unemployment rates in heterogeneous economies (such as Germany) have been, in recent years, the subject of various theoretical and empirical studies. Several researchers have shown an interest in analyzing the dynamic adjustment processes of unemployment and the average degree of dependence of the current unemployment rates or gross domestic product from the ones observed in the past. In this paper, we present a new econometric approach to the study of regional unemployment persistence, in order to account for spatial heterogeneity and/or spatial autocorrelation in both the levels and the dynamics of unemployment. First, we propose an econometric procedure suggesting the use of spatial filtering techniques as a substitute for fixed effects in a panel estimation framework. The spatial filter computed here is a proxy for spatially distributed region‐specific information (e.g., the endowment of natural resources, or the size of the “home market”) that is usually incorporated in the fixed effects coefficients. The advantages of our proposed procedure are that the spatial filter, by incorporating region‐specific information that generates spatial autocorrelation, frees up degrees of freedom, simultaneously corrects for time‐stable spatial autocorrelation in the residuals, and provides insights about the spatial patterns in regional adjustment processes. We present several experiments in order to investigate the spatial pattern of the heterogeneous autoregressive coefficients estimated for unemployment data for German NUTS‐3 regions. We find widely heterogeneous but generally high persistence in regional unemployment rates.     

A Structural Equation Approach to Models with Spatial Dependence

We introduce the class of structural equation models (SEMs) and corresponding estimation procedures into a spatial dependence framework. SEM allows both latent and observed variables within one and the same (causal) model. Compared with models with observed variables only, this feature makes it possible to obtain a closer correspondence between theory and empirics, to explicitly account for measurement errors, and to reduce multicollinearity. We extend the standard SEM maximum likelihood estimator to allow for spatial dependence and propose easily accessible SEM software like LISREL 8 and Mx. We present an illustration based on Anselin's Columbus, OH, crime data set. Furthermore, we combine the spatial lag model with the latent multiple-indicators–multiple-causes model and discuss estimation of this latent spatial lag model. We present an illustration based on the Anselin crime data set again.     

ESTIMATION AND HYPOTHESIS TESTING FOR NONPARAMETRIC HEDONIC HOUSE PRICE FUNCTIONS

ABSTRACT In contrast to the rigid structure of standard parametric hedonic analysis, nonparametric estimators control for misspecified spatial effects while using highly flexible functional forms. Despite these advantages, nonparametric procedures are still not used extensively for spatial data analysis due to perceived difficulties associated with estimation and hypothesis testing. We demonstrate that nonparametric estimation is feasible for large datasets with many independent variables, offering statistical tests of individual covariates and tests of model specification. We show that fixed parameterization of distance to the nearest rapid transit line is a misspecification and that pricing of access to this amenity varies across neighborhoods within Chicago.     

Knowledge Spillovers and Total Factor Productivity: Evidence Using a Spatial Panel Data Model

This article investigates the impact of knowledge capital stocks on total factor productivity (TFP) 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 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 labor 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 annual regional knowledge capital stocks for N =203 regions during 1997–2002. In estimating the effects, we implement a spatial panel data model that controls for spatial autocorrelation as well as 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 discussions in the literature by showing that productivity effects of knowledge spillovers increase with geographic proximity.     

旅游发展会推动房价上涨吗？——基于中国分省数据的经验研究

本文基于2000年～2009年中国大陆30个省区（不包含西藏）的面板数据,综合采用混合回归（POLS）、固定效应（FE）、随机效应（RE）、系统广义矩估计法（sys—GMM）,对旅游发展与房价之间的关系进行了经验检验。研究结果表明：（1）旅游发展对房价有显著的正向影响,且该影响主要发生在当期,两者之间的跨期影响并不明显;（2）旅游发展与房价的正向关系并不依赖于地区经济发展水平,城市化在旅游发展对房价的影响中起着正向调节作用;（3）系统GMM对动态面板模型的估计结果显示,地区房价具有“自我收敛”功能,房价决定系统中存在一种“逆风向”的动态调整机制;（4）旅游发展对房价的影响呈现出区域差异,其对西部、东部、中部房价的影响强度依次递减。     

Migration and ethnic nationalism: Anglophone exit and the ‘decolonisation’ of Québec

This article explains the effects of ethnic nationalism on Anglophone and Francophone migration. The rise of Québec ethnic nationalism in the 1960s dismantled the cultural division of labour, which created new opportunities for Francophones but threatened Anglophones' traditional dominance over the Québec economy. This had negative consequences for Anglophones but positive outcomes for Francophones, which in turn accounts for differences in migration patterns. Drawing from the internal colony model as well as migration and exit‐voice theories, and using ecological census data, micro‐census data and election panel data, I find that the key variables that increase the likelihood of Anglophone out‐migration either do not explain Francophone out‐migration or have opposite effects. This is because ethnonationalist policies decreased the economic return particularly for well‐educated, higher‐earning, professional Anglophones in Québec, while increasing the economic position of Francophones and in particular well‐educated professionals.     

Semiparametric Maximum Likelihood Estimates of Spatial Dependence

We semiparametrically model spatial dependence via a combination of simpler weight matrices (termed spatial basis matrices) and fit this model via maximum likelihood. Estimation of the model relies on the intuition that bounds to the log‐determinant term in the log‐likelihood can provide penalties to overfitting both the level and pattern of spatial dependence. By relying on symmetric and doubly stochastic spatial basis matrices that reflect different weight specifications assigned to neighboring observations, we are able to derive a mathematical expression for bounds on the log‐determinant term that appears in the likelihood function. These bounds can be conveniently calculated allowing us to solve for maximum likelihood estimates at the bounds using a simple optimization over two quadratic forms that involve small matrices. An intuitively pleasing aspect of our approach is that the objective function for the bounded log‐likelihoods contains one quadratic form equal to the sum‐of‐squared errors measuring the quality of fit, and another quadratic form reflecting a penalty to overfitting spatial dependence. We apply our semiparametric estimation method to a housing model using 57,647 U.S. census tracts.     

Effects of Vaccination and the Spatio-Temporal Diffusion of Covid-19 Incidence in Turkey

This study assesses the spatio-temporal impact of vaccination efforts on Covid-19 incidence growth in Turkey. Incorporating geographical features of SARS-CoV-2 transmission, we adopt a spatial Susceptible–Infected–Recovered (SIR) model that serves as a guide of our empirical specification. Using provincial weekly panel data, we estimate a dynamic spatial autoregressive (SAR) model to elucidate the short- and the long-run impact of vaccination on Covid-19 incidence growth after controlling for temporal and spatio-temporal diffusion, testing capacity, social distancing behavior and unobserved space-varying confounders. Results show that vaccination growth reduces Covid-19 incidence growth rate directly and indirectly by creating a positive externality over space. The significant association between vaccination and Covid-19 incidence is robust to a host of spatial weight matrix specifications. Conspicuous spatial and temporal diffusion effects of Covid-19 incidence growth were found across all specifications: the former being a severer threat to the containment of the pandemic than the latter.     

An Anisotropic Model for Spatial Processes

One of the key assumptions in spatial econometric modeling is that the spatial process is isotropic, which means that direction is irrelevant in the specification of the spatial structure. On the one hand, this assumption largely reduces the complexity of the spatial models and facilitates estimation and interpretation; on the other hand, it appears rather restrictive and hard to justify in many empirical applications. In this article a very general anisotropic spatial model, which allows for a high level of flexibility in the spatial structure, is proposed. This new model can be estimated using maximum likelihood and its asymptotic properties are derived at length. When the model is applied to the well-known 1970 Boston housing prices data, it significantly outperforms the isotropic spatial lag model. It also provides interesting additional insights into the price determination process in the properties market. Finally, a Monte Carlo simulation study is used to confirm the optimal properties of the model.     

现代服务业集聚形成机理空间计量分析

在纳入空间效应前提下,构建现代服务业集聚形成机理空间面板计量模型,对我国28个省域相关数据实证研究表明:我国现代服务业集聚在省域之间有较强的空间依赖性和正的空间溢出效应。技术差异在时间维度上对现代服务业集聚促进作用显著,在空间维度上并不显著;交易费用与现代服务业集聚有显著的负相关性;知识溢出、规模经济、政府行为对现代服务业集聚促进作用显著。     

PANEL DATA MODELS WITH SPATIALLY DEPENDENT NESTED RANDOM EFFECTS

This paper focuses on panel data models combining spatial dependence with a nested (hierarchical) structure. We use a generalized moments estimator to estimate the spatial autoregressive parameter and the variance components of the disturbance process. A spatial counterpart of the Cochrane‐Orcutt transformation leads to a feasible generalized least squares procedure to estimate the regression parameters. Monte Carlo simulations show that our estimators perform well in terms of root mean square error compared to the maximum likelihood estimator. The approach is applied to English house price data for districts nested within counties.     

A Spatial Mixture Model of Innovation Diffusion

The diffusion of new product or technical innovation over space is here modeled as an event‐based process in which the likelihood of the next adopter being in region r is influenced by two factors: (i) the potential interactions of individuals in r with current adopters in neighboring regions, and (ii) all other attributes of individuals in r that may influence their adoption propensity. The first factor is characterized by a logit model reflecting the likelihood of adoption due to spatial contacts with previous adopters, and the second by a logit model reflecting the likelihood of adoption due to other intrinsic effects. The resulting spatial diffusion process is then assumed to be driven by a probabilistic mixture of the two. A number of formal properties of this model are analyzed, including its asymptotic behavior. But the main analytical focus is on statistical estimation of parameters. Here it is shown that standard maximum‐likelihood estimates require large sample sizes to achieve reasonable results. Two estimation approaches are developed which yield more sensible results for small sample sizes. These results are applied to a small data set involving the adoption of a new Internet grocery‐shopping service by consumers in the Philadelphia metropolitan area.     

Cities in a pandemic: Evidence from China

This paper studies the impact of urban density, city government efficiency, and medical resources on COVID-19 infection and death outcomes in China. We adopt a simultaneous spatial dynamic panel data model to account for (i) the simultaneity of infection and death outcomes, (ii) the spatial pattern of the transmission, (iii) the intertemporal dynamics of the disease, and (iv) the unobserved city-specific and time-specific effects. We find that, while population density increases the level of infections, government efficiency significantly mitigates the negative impact of urban density. We also find that the availability of medical resources improves public health outcomes conditional on lagged infections. Moreover, there exists significant heterogeneity at different phases of the epidemiological cycle.     

Spatial skill concentration agglomeration economies

Using the Brazilian census and administrative panel data, the present paper provides evidence that the spatial concentration of analytical skills generates positive wage externalities for all workers in the local labor market. We rely on shift‐share instrumental variables to overcome the endogeneity of skill concentrations. The observed externality is independent from the classical market size economies. The estimates are robust to geography, institutions and workers' sorting on unobservable abilities.     

Comparative Spatial Filtering in Regression Analysis

One approach to dealing with spatial autocorrelation in regression analysis involves the filtering of variables in order to separate spatial effects from the variables’ total effects. In this paper we compare two filtering approaches, both of which allow spatial statistical analysts to use conventional linear regression models. Getis’ filtering approach is based on the autocorrelation observed with the use of the G_i local statistic. Griffith's approach uses an eigenfunction decomposition based on the geographic connectivity matrix used to compute a Moran's I statistic. Economic data are used to compare the workings of the two approaches. A final comparison with an autoregressive model strengthens the conclusion that both techniques are effective filtering devices, and that they yield similar regression models. We do note, however, that each technique should be used in its appropriate context.     

Spatial Autoregressive Models for Geographically Hierarchical Data Structures

This article discusses how standard spatial autoregressive models and their estimation can be extended to accommodate geographically hierarchical data structures. Whereas standard spatial econometric models normally operate at a single geographical scale, many geographical data sets are hierarchical in nature—for example, information about houses nested into data about the census tracts in which those houses are found. Here we outline four model specifications by combining different formulations of the spatial weight matrix W and of ways of modeling regional effects. These are (1) groupwise W and fixed regional effects; (2) groupwise W and random regional effects; (3) proximity‐based W and fixed regional effects; and (4) proximity‐based W and random regional effects. We discuss each of these model specifications and their associated estimation methods, giving particular attention to the fourth. We describe this as a hierarchical spatial autoregressive model. We view it as having the most potential to extend spatial econometrics to accommodate geographically hierarchical data structures and as offering the greatest coming together of spatial econometric and multilevel modeling approaches. Subsequently, we provide Bayesian Markov Chain Monte Carlo algorithms for implementing the model. We demonstrate its application using a two‐level land price data set where land parcels nest into districts in Beijing, China, finding significant spatial dependence at both the land parcel level and the district level.