A two-step approach to account for unobserved spatial heterogeneity

A two-step approach to account for unobserved spatial heterogeneity. Spatial Economic Analysis. Empirical analysis in economics often faces the difficulty that the data are correlated and heterogeneous in some unknown form. Spatial econometric models have been widely used to account for dependence structures, but the problem of directly dealing with unobserved spatial heterogeneity has been largely unexplored. The problem can be serious particularly if we have no prior information justified by economic theory. In this paper we propose a two-step procedure to identify endogenously spatial regimes in the first step and to account for spatial dependence in the second step. This procedure is applied to hedonic house price analysis.     

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.     

Do Neighbours Influence Value‐Added‐Tax Introduction? A Spatial Duration Analysis

The spatial survival models typically impose frailties, which characterize unobserved heterogeneity, to be spatially correlated. However, the spatial effect may not only exist in the unobserved errors, but it can also be present in the baseline hazards and the dependent variables. A new spatial survival model with these three possible spatial correlation structures is explored and used to investigate the implementation of value‐added tax (VAT) in 99 countries over the period 1970–2009. Estimation is performed by a Bayesian approach through the Markov chain Monte Carlo method. The estimation results suggest the presence of a significant spatial correlation among the VAT introductions of neighbouring countries.     

Modeling regional economic dynamics: Spatial dependence,spatial heterogeneity and nonlinearities

Spatial modeling of economic phenomena requires the adoption of complex econometric tools, which allow us to deal with important methodological issues, such as spatial dependence, spatial unobserved heterogeneity and nonlinearities. In this paper we describe some recently developed econometric approaches (i.e. Spatial Autoregressive Semiparametric Geoadditive Models), which address the three issues simultaneously. We also illustrate the relative performance of these methods with an application to the case of house prices in the Lucas County.     

Estimating the distribution of welfare effects using quantiles

This paper proposes a framework to model welfare effects that are associated with a price change in a population of heterogeneous consumers. The framework is similar to that of Hausman and Newey (Econometrica, 1995, 63, 1445–1476), but allows for more general forms of heterogeneity. Individual demands are characterized by a general model that is nonparametric in the regressors, as well as monotonic in unobserved heterogeneity, allowing us to identify the distribution of welfare effects. We first argue why a decision maker should care about this distribution. Then we establish constructive identification, propose a sample counterparts estimator, and analyze its large‐sample properties. Finally, we apply all concepts to measuring the heterogeneous effect of a change of gasoline price using US consumer data and find very substantial differences in individual effects across quantiles.     

Raising the bar (10)

This editorial summarizes the papers published in issue 14(1) so as to raise the bar in applied spatial economic research and highlight new trends. The first paper applies the Shapley-based decomposition approach to determine the impact of firm-, linkage- and location-specific factors to the survival probability of enterprises. The second paper applies Bayesian comparison methods to identify simultaneously the most likely spatial econometric model and spatial weight matrix explaining new business creation. The third paper compares the performance of continuous and discrete approaches to explain subjective well-being across space. The fourth paper applies a multiple imputation approach to determine regional purchasing power parities at the NUTS-3 level using data available at the NUTS-2 level. Finally, the last paper constructs a regional input–output table for Japan from its national counterpart using and comparing the performance of four non-survey techniques.     

Raising the bar (5)

Raising the bar (5). Spatial Economic Analysis. This editorial summarizes and comments on the papers published in this issue 12(1) so as to raise the bar in applied spatial economic research and highlight new trends. The first paper examines the impact of the level of education on the decision to migrate and finds that it is approximately twice as large if both variables are modelled simultaneously. The second paper is one of the first papers to introduce a spatial component to models of international environmental agreements and to develop an exciting overlap with New Economic Geography. The third paper provides a tool, applied to Beijing, with which urban economic planners can investigate the role of variation and selection mechanisms in cluster development and identify possible paths of growth. The fourth paper contributes to the existing literature on retail geography by examining the role of consumption possibilities as an urban amenity. The fifth paper develops a Bayesian estimator of a linear regression model with spatial lags among the dependent variable, the explanatory variables and the disturbances. Finally, the sixth paper develops a semi-parametric generalized method of moments (GMM) estimator for a spatial autoregressive model with space-varying coefficients of the explanatory variables and a spatial autoregressive coefficient common to all units.     

Do monetary subjective well-being evaluations vary across space? Comparing continuous and discrete spatial heterogeneity

Using subjective well-being estimations, this study analyzes whether compensating variations vary across space using a cross-sectional data set from Chile. To achieve this goal, it describes and compares two econometric ways of modelling unobserved spatial heterogeneity. Both approaches allow compensating variations to vary across spatial units by assuming some distribution a priori. One method assumes that the spatial heterogeneity can be represented by a discrete distribution (a group of regions that share the same coefficient) and the other that the preferences can be represented by a continuous distribution (each region has a different coefficient). The results show that focusing just on the average estimates of compensating variations, as the applied studies have done so far, masks useful local variation. More empirical studies are needed to assess the advantages and disadvantages of both econometric approaches and how their results compare across a wide range of conditions and samples.     

PANEL PROBIT WITH FLEXIBLE CORRELATED EFFECTS: QUANTIFYING TECHNOLOGY SPILLOVERS IN THE PRESENCE OF LATENT HETEROGENEITY

In this paper, we introduce a Bayesian panel probit model with two flexible latent effects: first, unobserved individual heterogeneity that is allowed to vary in the population according to a nonparametric distribution; and second, a latent serially correlated common error component. In doing so, we extend the approach developed in Albert and Chib (Journal of the American Statistical Association 1993; 88 : 669–679; in Bayesian Biostatistics, Berry DA, Stangl DK (eds), Marcel Dekker: New York, 1996), and in Chib and Carlin (Statistics and Computing 1999; 9 : 17–26) by releasing restrictive parametric assumptions on the latent individual effect and eliminating potential spurious state dependence with latent time effects. The model is found to outperform more traditional approaches in an extensive series of Monte Carlo simulations. We then apply the model to the estimation of a patent equation using firm‐level data on research and development (R&D). We find a strong effect of technology spillovers on R&D but little evidence of product market spillovers, consistent with economic theory. The distribution of latent firm effects is found to have a multimodal structure featuring within‐industry firm clustering. Copyright © 2012 John Wiley & Sons, Ltd.     

A heterogeneous coefficient approach to the knowledge production function

Past literature has used conventional spatial autoregressive panel data models to relate patent production output to knowledge production inputs. However, research conducted on regional innovation systems points to regional disparities in both regions’ ability to turn their knowledge inputs into innovation and to access external knowledge. Applying a heterogeneous coefficients spatial autoregressive panel model, we estimate region-specific knowledge production functions (KPFs) for 94 NUTS-3 regions in France using a panel covering 21 years from 1988 to 2008 and four high-technology industries. A great deal of regional heterogeneity in the KPF relationship exists across regions, providing new insights regarding spatial spillin and spillout effects between regions.     

Testing for random effects in panel models with spatially correlated disturbances

In the empirical analysis of panel data the Breusch–Pagan (BP) statistic has become a standard tool to infer on unobserved heterogeneity over the cross-section. Put differently, the test statistic is central to discriminate between the pooled regression and the random effects model. Conditional versions of the test statistic have been provided to immunize inference on unobserved heterogeneity against random time effects or patterns of spatial error correlation. Panel data models with spatially correlated error terms are typically set out under the presumption of some known adjacency matrix parameterizing the correlation structure up to a scaling factor. This paper delivers a bootstrap scheme to generate critical values for the BP statistic allowing robust inference under misspecification of the adjacency matrix. Moreover, asymptotic results are derived for the case of a finite cross-section and infinite time dimension. Finite sample simulations show that misspecification of spatial covariance features could lead to large size distortions, while the robust bootstrap procedure retains asymptotic validity.     

Employment Growth in Italian Local Labour Systems: Issues of Model Specification and Sectoral Aggregation

Abstract

In this paper we construct a model to estimate local employment growth in Italian local labour markets for the period 1991–2001. The model is constructed in a similar manner to the original models of Glaeser et al. (1992), Henderson et al. (1995) and Combes (2000). Our objective is to identify the extent to which the results estimated by these types of models are themselves sensitive to the model specification. In order to do this we extend the basic models by successively incorporating new explanatory variables into the model framework. In addition, and for the first time, we also estimate these same models at two different levels of sectoral aggregation, for the same spatial structure. Our results indicate that these models are highly sensitive to sectoral aggregation and classification and our results therefore strongly support the use of highly disaggregated data.     

环境规制与经济增长关系再研究——基于半参数空间模型

论文采用2005-2017年我国30个省份的面板数据,考虑经济增长的溢出效应,利用空间杜宾模型和半参数空间杜宾模型研究环境规制与经济增长的关系。结果表明:第一,中国经济增长存在显著的正空间相关性,在普通参数模型和空间杜宾模型中环境规制对经济增长的影响不显著。第二,半参数空间杜宾模型的拟合优度高于空间杜宾模型,同时,环境规制与经济增长存在显著的非线性关系。     

A Spatial Model of the Impact of Bankruptcy Law on Entrepreneurship

Abstract

This paper employs spatial econometrics techniques to estimate the impact of bankruptcy regulation on small firm formation. The estimation of the model is computationally challenging due to the joint appearance of a lagged endogenous variable and the unobserved heterogeneity which requires modelling of initial conditions as described in Heckman (1981). We test for the joint significance of the state dummy variables in a way that can be viewed as an interesting alternative to the Hausman procedure. This was important for our analysis since, as sometimes happens in finite samples, the estimated variance–covariance matrix was not positive semi-definite. We found that the predicted probability of starting a business is 25% higher in states with higher bankruptcy exemptions than their neighbours relative to states with lower exemptions than their neighbours.

Un modèle spatial de l'impact des lois sur la faillite sur la création d'entreprises

Résumé La présente communication emploie des techniques d’économétrie spatiale pour évaluer l'impact de la réglementation en matière de faillite sur la constitution de petites entreprises. L'estimation du modèle pose des difficultés sur le plan computationnel en raison de l'apparition conjointe d'une variable endogène décalée et de l'hétérogénéité non observée, qui rend nécessaire la modélisation de conditions initiales, de la façon décrite par Heckman (1981). Nous testons la signification conjointe des variables indicatrices de l’état d'une façon qui peut être considérée comme une alternative intéressante à la procédure de Hausman. Ceci était important pour notre analyse, car, comme nous le relevons parfois dans des échantillons finis, la matrice variance–covariance estimée n’était pas semi-définie positive. Nous en concluons que la probabilité prévisible du lancement d'une affaire est plus élevée de l'ordre de 25% dans les états qui appliquent des exemptions pour les faillites supérieures à celles des pays avoisinants, par rapport aux états qui appliquent des exemptions inférieures à celles de leurs voisins.

Un modelo espacial del impacto de la ley de bancarrotas sobre las iniciativas empresariales

Résumén Este artículo emplea técnicas de econometría espacial para estimar el impacto de las normativas de bancarrotas sobre la formación de empresas pequeñas. La valoración del modelo es computacionalmente desafiante, debido a la aparición conjunta de una variable endógena rezagada y heterogeneidad inadvertida que requieren la modelación de las condiciones iniciales, como se describe en Heckman (1981). Ensayamos la significancia conjunta de las variables de prueba estatales de una forma que puede percibirse como una alternativa interesante al procedimiento Hausman. Esto fue importante para nuestro análisis, ya que, como ocurre a veces con muestras finitas, la matriz estimada de varianza–covarianza no fue semidefinitiva positiva. Descubrimos que la probabilidad predicha de iniciar un negocio es un 25% mayor en los estados con mayores exenciones de bancarrota que sus vecinos, en relación con estados con menos exenciones que sus vecinos.

     

Comparison of Hypothesis Testing and Bayesian Model Selection

The main goal of both Bayesian model selection and classical hypotheses testing is to make inferences with respect to the state of affairs in a population of interest. The main differences between both approaches are the explicit use of prior information by Bayesians, and the explicit use of null distributions by the classicists. Formalization of prior information in prior distributions is often difficult. In this paper two practical approaches (encompassing priors and training data) to specify prior distributions will be presented. The computation of null distributions is relatively easy. However, as will be illustrated, a straightforward interpretation of the resulting p-values is not always easy. Bayesian model selection can be used to compute posterior probabilities for each of a number of competing models. This provides an alternative for the currently prevalent testing of hypotheses using p-values. Both approaches will be compared and illustrated using case studies. Each case study fits in the framework of the normal linear model, that is, analysis of variance and multiple regression.     

Inference for the two-parameter bathtub-shaped distribution based on record data

Here we consider the record data from the two-parameter of bathtub-shaped distribution. First, we develop simplified forms for the single moments, variances and covariance of records. These distributional properties are quite useful in obtaining the best linear unbiased estimators of the location and scale parameters which can be included in the model. The estimation of the unknown shape parameters and prediction of the future unobserved records based on some observed ones are discussed. Frequentist and Bayesian analyses are adopted for conducting the estimation and prediction problems. The likelihood method, moment based method, bootstrap methods as well as the Bayesian sampling techniques are applied for the inference problems. The point predictors and credible intervals of future record values based on an informative set of records can be developed. Monte Carlo simulations are performed to compare the so developed methods and one real data set is analyzed for illustrative purposes.     

Raising the bar (6)

Raising the bar (6). Spatial Economic Analysis. This editorial summarizes and comments on the papers published in issue 12(4) so as to raise the bar in applied spatial economic research and highlight new trends. The first paper addresses the question of whether ‘jobs follow people’ or ‘people follow jobs’. The second paper develops a new methodology to determine functional regions. The third paper is a major contribution to the growing literature on new modelling approaches and applications of disaster impact models. The fourth paper focuses on the costs and benefits of higher education. The fifth paper develops a two-step procedure to identify endogenously spatial regimes in the first step using geographically weighted regression, and to account for spatial dependence in the second step. Finally, the sixth paper estimates a dynamic spatial panel data model to explain house prices and to show that restricted housing supply in the city of Cambridge, UK, has some undesirable labour market effects.     

A Social Interactions Model with Endogenous Friendship Formation and Selectivity

This paper analyzes the endogeneity bias problem caused by associations of members within a network when the spatial autoregressive (SAR) model is used to study social interactions. When there are unobserved factors that affect both friendship decisions and economic outcomes, the spatial weight matrix (sociomatrix; adjacency matrix) in the SAR model, which represents the structure of a friendship network, might correlate with the disturbance term of the model, and consequently result in an endogenous selection problem in the outcomes. We consider this problem of selection bias with a modeling approach. In this approach, a statistical network model is adopted to explain the endogenous network formation process. By specifying unobserved components in both the network model and the SAR model, we capture the correlation between the processes of network and outcome formation, and propose a proper estimation procedure for the system. We demonstrate that the estimation of this system can be effectively done by using the Bayesian method. We provide a Monte Carlo experiment and an empirical application of this modeling approach on the friendship networks of high school students and their interactions on academic performance in the Add Health data. Copyright © 2015 John Wiley & Sons, Ltd.     

Fixed effects demeaning in the presence of interactive effects in treatment effects regressions and elsewhere

The present paper shows that cross-section demeaning with respect to time fixed effects is more useful than commonly appreciated, in that it enables consistent and asymptotically normal estimation of interactive effects models with heterogeneous slope coefficients when the number of time periods, T, is small and only the number of cross-sectional units, N, is large. This is important when using OLS but also when using more sophisticated estimators of interactive effects models whose validity does not require demeaning, a point that to the best of our knowledge has not been made before in the literature. As an illustration, we consider the problem of estimating the average treatment effect in the presence of unobserved time-varying heterogeneity. Gobillon and Magnac (2016) recently considered this problem. They employed a principal components-based approach designed to deal with general unobserved heterogeneity, which does not require fixed effects demeaning. The approach does, however, require that T is large, which is typically not the case in practice, and the results reported here confirm that the performance can be extremely poor in small-T samples. The exception is when the approach is applied to data that have been demeaned with respect to fixed effects.     

A Bayesian Approach to Parameter Estimation in the Presence of Spatial Missing Data

The missing data problem has been widely addressed in the literature. The traditional methods for handling missing data may be not suited to spatial data, which can exhibit distinctive structures of dependence and/or heterogeneity. As a possible solution to the spatial missing data problem, this paper proposes an approach that combines the Bayesian Interpolation method [Benedetti, R. & Palma, D. (1994) Markov random field-based image subsampling method, Journal of Applied Statistics, 21(5), 495–509] with a multiple imputation procedure. The method is developed in a univariate and a multivariate framework, and its performance is evaluated through an empirical illustration based on data related to labour productivity in European regions.