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.     

Using SimBritain to Model the Geographical Impact of National Government Policies

In this article, we use a dynamic spatial microsimulation model of Britain for the analysis of the geographical impact of policies that have been implemented in Britain in the last 10 years. In particular, we show how spatial microsimulation can be used to estimate the geographical and socio-economic impact of the following policy developments: introduction of the minimum wage, winter fuel payments, working families tax credits, and new child and working credits. This analysis is carried out with the use of the SimBritain model , which is a product of a 3-year research project aimed at dynamically simulating urban and regional populations in Britain. SimBritain projections are based on a method that uses small area data from past Censuses of the British population in order to estimate small-area data for 2001, 2011, and 2021.     

The Effect on Attribute Prediction of Location Uncertainty in Spatial Data

A datum is considered spatial if it contains location information. Typically, there is also attribute information, whose distribution depends on its location. Thus, error in location information can lead to error in attribute information, which is reflected ultimately in the inference drawn from the data. We propose a statistical model for incorporating location error into spatial data analysis. We investigate the effect of location error on the spatial lag, the covariance function, and optimal spatial linear prediction (that is, kriging). We show that the form of kriging after adjusting for location error is the same as that of kriging without adjusting for location error. However, location error changes entries in the matrix of explanatory variables, the matrix of co‐variances between the sample sites, and the vector of covariances between the sample sites and the prediction location. We investigate, through simulation, the effect that varying trend, measurement error, location error, range of spatial dependence, sample size, and prediction location have on kriging after and without adjusting for location error. When the location error is large, kriging after adjusting for location error performs markedly better than kriging without adjusting for location error, in terms of both the prediction bias and the mean squared prediction error.     

Urban and Rural Estimates of Poverty: Recent Advances in Spatial Microsimulation in Australia

This paper reports on the calculation of poverty rates for small areas in Australia using a spatial microsimulation model. The spatial microsimulation methodology used involves reweighting data from confidentialised unit record files (CURFs) from surveys conducted by the Australian Bureau of Statistics (ABS) to small area census data, also from the ABS. The method is described in this paper, and then maps of poverty using poverty rates derived from this small area estimation method are shown for the eastern coast of Australia and its capital cities. Further analysis of poverty rates in capital cities is then conducted. We find that areas of higher poverty risk can be clearly identified within Sydney, Melbourne, Canberra and Brisbane. We also find that areas of high poverty are frequently ‘buffered’ by areas of moderate poverty. This is not always the case since, in some areas, we find a high poverty area neighbouring a low poverty area but, generally, there appears to be a moderate poverty ‘buffer’ in most capital cities.     

SELECTION BIAS IN SPATIAL ECONOMETRIC MODELS

ABSTRACT. The problem of spatial autocorrelation has been ignored in selection-bias models estimated with spatial data. Spatial autocorrelation is a serious problem in these models because the heteroskedasticity with which it commonly is associated causes inconsistent parameter estimates in models with discrete dependent variables. This paper proposes estimators for commonly-employed spatial models with selection bias. A maximum-likelihood estimator is applied to data on land use and values in 1920s Chicago. Evidence of significant heteroskedasticity and selection bias is found.     

The removal estimator: A ‘probable numbers’ statistic that requires no matching

The probable number of individuals (PNI) estimators all require that we be able to match left-right paired bones reliably. The problems of matching are outlined and ways of addressing them are reviewed. It is shown that archaeozoological studies in which reliable matching is difficult raise analytical problems similar to those faced by population biologists unable to use classical release-recapture methods. The removal estimator has been used to estimate the size of whale populations from incomplete census data. It can be generalized into archaeozoology to produce either a simple PNI statistic of the matching type, or a statistic that does not require reliable matching.     

A Geostatistical Linear Regression Model for Small Area Data. 一种适用于小区域数据的地统计线性回归模型

We present a new linear regression model for use with aggregated, small area data that are spatially autocorrelated. Because these data are aggregates of individual‐level data, we choose to model the spatial autocorrelation using a geostatistical model specified at the scale of the individual. The autocovariance of observed small area data is determined via the natural aggregation over the population. Unlike lattice‐based autoregressive approaches, the geostatistical approach is invariant to the scale of data aggregation. We establish that this geostatistical approach also is a valid autoregressive model; thus, we call this approach the geostatistical autoregressive (GAR) model. An asymptotically consistent and efficient maximum likelihood estimator is derived for the GAR model. Finite sample evidence from simulation experiments demonstrates the relative efficiency properties of the GAR model. Furthermore, while aggregation results in less efficient estimates than disaggregated data, the GAR model provides the most efficient estimates from the data that are available. These results suggest that the GAR model should be considered as part of a spatial analyst's toolbox when aggregated, small area data are analyzed. More important, we believe that the GAR model's attention to the individual‐level scale allows for a more flexible and theory‐informed specification than the existing autoregressive approaches based on an area‐level spatial weights matrix. Because many spatial process models, both in geography and in other disciplines, are specified at the individual level, we hope that the GAR covariance specification will provide a vehicle for a better informed and more interdisciplinary use of spatial regression models with area‐aggregated data.     

Geostatistical Smoothing of Areal Data: Mapping Employment Density with Factorial Kriging

This article summarizes area-to-point (ATP) factorial kriging that allows the smoothing of aggregate, areal data into a continuous spatial surface. Unlike some other smoothing methods, ATP factorial kriging does not suppose that all of the data within an area are located at a centroid or other arbitrary point. Also, unlike some other smoothing methods, factorial kriging allows the user to utilize an autocovariance function to control the smoothness of the output. This is beneficial because the covariance function is a physically meaningful statement of spatial relationship, which is not the case when other spatial kernel functions are used for smoothing. Given a known covariance function, factorial kriging gives the smooth surface that is best in terms of minimizing the expected mean squared prediction error. I present an application of the factorial kriging methodology for visualizing the structure of employment density in the Denver metropolitan area.     

Heterogeneity of Attribute Sampling Error in Spatial Data Sets

This paper considers the standard error of the estimate of the mean of a spatially correlated variable in the case where data are obtained by a process of random sampling. Two distinct mean estimation problems are identified: estimating the area mean and estimating the population mean. Methods are described for obtaining standard error estimates in the two cases and, within the limits of publicly available information, the methods are implemented on average household income data at the census tract scale for Syracuse, New York. The purpose of the paper is to draw attention to issues of data precision in relation to sampled geographic information on averages and in particular to consider the problems of estimating standard errors using such data. The paper also examines the extent to which standard errors vary between census tracts.     

Recursive Estimation of the Spatial Error Model

In this paper, we propose a recursive approach to estimate the spatial error model. We compare the suggested methodology with standard estimation procedures and we report a set of Monte Carlo experiments which show that the recursive approach substantially reduces the computational effort affecting the precision of the estimators within reasonable limits. The proposed technique can prove helpful when applied to real-time streams of geographical data that are becoming increasingly available in the big data era. Finally, we illustrate this methodology using a set of earthquake data.     

Unconditional Maximum Likelihood Estimation of Linear and Log-Linear Dynamic Models for Spatial Panels

This article hammers out the estimation of a fixed effects dynamic panel data model extended to include either spatial error autocorrelation or a spatially lagged dependent variable. To overcome the inconsistencies associated with the traditional least-squares dummy estimator, the models are first-differenced to eliminate the fixed effects and then the unconditional likelihood function is derived taking into account the density function of the first-differenced observations on each spatial unit. When exogenous variables are omitted, the exact likelihood function is found to exist. When exogenous variables are included, the pre-sample values of these variables and thus the likelihood function must be approximated. Two leading cases are considered: the Bhargava and Sargan approximation and the Nerlove and Balestra approximation. As an application, a dynamic demand model for cigarettes is estimated based on panel data from 46 U.S. states over the period from 1963 to 1992.     

The Local Implications of Major Job Transformations in the City: A Spatial Microsimulation Approach

The changing dynamics of regional and local labor markets during the last decades have led to an increasing labor market segmentation and socioeconomic polarization and to a rise of income inequalities at the regional, urban, and intraurban level. These problems call for effective social and local labor market policies. However, there is also a growing need for methods and techniques capable of efficiently estimating the likely impact of social and economic change at the local level. For example, the common methodologies for estimating the impacts of large firm openings or closures operate at the regional level. The best of these models disaggregate the region to the city (Armstrong 1993; Batey and Madden 1983). This paper demonstrates how spatial microsimulation modeling techniques can be used for local labor market analysis and policy evaluation to assess these impacts (and their multiplier effects) at the local level‐to measure the effects on individuals and their neighborhood services. First, we review these traditional macroscale and mesoscale regional modeling approaches to urban and regional policy analysis and we illustrate their merits and limitations. Then, we examine the potential of spatial microsimulation modeling to create a new framework for the formulation, analysis and evaluation of social and local labor market policies at the individual or household level. Outputs from a local labor market microsimulation model for Leeds are presented. We show how first it is possible to investigate the interdependencies between individual's or households labor market attributes at the microscale and to model their accessibilities to job opportunities in different localities. From this base we show how detailed what‐if microspatial analysis can be performed to estimate the impact of major changes in the local labor market through job losses or gains, including local multiplier effects.     

Modified Kaplan–Meier Estimator and Nelson–Aalen Estimator with Geographical Weighting for Survival Data

The Kaplan–Meier and Nelson–Aalen estimators are universally used methods in clinical studies. In a public health study, people often collect data from different locations of the medical services provider. When some studies need to consider survival curves from different locations, traditional estimators simply estimate the marginal survival curves using stratification. In this article, we use the idea from geographically weighted regression to add geographical weights to the observations to get modified versions of the Kaplan–Meier and Nelson–Aalen estimators which can represent the local survival curve and cumulative hazard. We use counting process methods to derive these modified estimators and to estimate their variances. In addition, we discuss some general spatial weighting functions which can be used in computing these estimators. Furthermore, we present simulation results to illustrate the performance of the modified estimators. Finally, we apply our method to prostate cancer data from the SEER cancer registry for the state of Louisiana.     

ASSESSING THE REGIONAL IMPACT OF GRANTS ON FDI LOCATION: EVIDENCE FROM U.K. REGIONAL POLICY, 1985–2005

ABSTRACT The paper implements a methodology for assessing the regional impact of investment grants on foreign direct investment (FDI) location, taking data for U.K. regional policy over the period 1985–2005. Using a Generalized Methods of Moments estimator it finds that each £25 million of grant changes the regional location of about six inward FDI projects. On average, projects have 150 jobs and each job diverted costs £27,500 (1995 prices). It also finds that the size of the area designated for grants has a positive location effect. The effect is small in relation to the overall scale of FDI, which may explain the weak grant effect found in recent plant‐based location studies.     

Gaussian Process Regression and Bayesian Model Averaging: An Alternative Approach to Modeling Spatial Phenomena

Gaussian Process Regression (GPR) is a nonparametric technique that is capable of yielding reliable out‐of‐sample predictions in the presence of highly nonlinear unknown relationships between dependent and explanatory variables. But in terms of identifying relevant explanatory variables, this method is far less explicit about questions of statistical significance. In contrast, more traditional spatial econometric models, such as spatial autoregressive models or spatial error models, place rather strong prior restrictions on the functional form of relationships, but allow direct inference with respect to explanatory variables. In this article, we attempt to combine the best of both techniques by augmenting GPR with a Bayesian Model Averaging (BMA) component that allows for the identification of statistically relevant explanatory variables while retaining the predictive performance of GPR. In particular, GPR‐BMA yields a posterior probability interpretation of model‐inclusion frequencies that provides a natural measure of the statistical relevance of each variable. Moreover, while such frequencies offer no direct information about the signs of local marginal effects, it is shown that partial derivatives based on the mean GPR predictions do provide such information. We illustrate the additional insights made possible by this approach by applying GPR‐BMA to a benchmark BMA data set involving potential determinants of cross‐country economic growth. It is shown that localized marginal effects based on partial derivatives of mean GPR predictions yield additional insights into comparative growth effects across countries.     

Wetland assessment and impact mitigation decision support framework for linear development projects: The Louis Riel Trail,Highway 11 North project,Saskatchewan, Canada

Next to agriculture, road development is one of the most significant sources of stress to wetlands in Prairie Canada. However, there currently exists limited guidance for incorporating direct, indirect, and induced effects to wetlands in impact assessment and mitigation planning for small and often routine developments, including access roads or highway improvement initiatives. Based on the Louis Riel Trail, Highway 11 North twinning project in Saskatchewan, Canada, this article demonstrates a methodological approach and decision support framework for assessing and managing direct, indirect, and induced effects to wetlands from linear developments. No regulatory‐based environmental assessment was required for the highway project; effects were deemed to be insignificant under current wetland mitigation practices. However, our results show that 1115 ha of potentially affected wetlands are located within a 500 m impact zone on either side of the proposed highway. More than 50 percent of these wetlands are seasonal, less than 1 ha in size, and typically not included in mitigation planning. An expert‐based multi‐criteria evaluation of impact and mitigation options for wetlands in the study area indicated “no net loss” as a planning priority, and a preference for a spatially ambitious mitigation plan focused on direct, indirect, and potentially induced impacts. In practice, however, mitigation is often restrictive, focused on mitigating only direct impacts within the project's right‐of‐way, in this case less than 50 ha of wetlands, resulting in the potential for significant net loss of wetland habitat and function. If the risk to wetlands is to be given due consideration in project planning and development for roads and road improvement initiatives, then structured assessment methods and decision support frameworks should be sensitive to the time and resource constraints of small projects and screening‐type assessments. This requires also that wetland mitigation policies are developed and implementation plans formulated as part of project planning and assessment initiatives for linear developments.     

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.     

Modeling Strategies for Categorical Data: Examples from Housing and Tenure Choice

Models to investigate categorical data can be divided into preprocessing, limited parameterization, and formal logit models. To illustrate the advantages of preprocessing and limited parameterization models they are applied to a data set of tenure and type of housing choice before the data are examined with hierarchical logit and nested logit models. The preprocessing approaches are useful in selecting optimal subsets of independent variables with respect to the dependent variable. The ease of application and interpretation of a limited parameterization approach extends the clarity of the results from the preprocessing approaches. Because some variables are only relevant at specific levels of other independent variables, nonstandard (nested) logit models are necessary to understand the nested relationships.     

A Selection Bias Approach to Destination Choice

Research on consumer search behavior commonly envisages destination choice as a two-step process: (1) delineate the search set, and (2) evaluate choices therein. However, much of the empirical work in destination choice—including logit and nested logit formulations—models only the latter, and not the set delineation itself. In the presence of correlation between error terms in set delineation and choice selection, statistical estimators are biased, a problem that Heckman and others have called selection bias. In this paper, an alternative two-stage method is proposed to estimate the parameters of models of set delineation and choice selection. Monte Carlo simulation is used to explore the properties of these two-stage estimators, and to show the magnitude of bias inherent in traditional methods of estimation.     

A SPATIAL CLIFF‐ORD‐TYPE MODEL WITH HETEROSKEDASTIC INNOVATIONS: SMALL AND LARGE SAMPLE RESULTS*

ABSTRACT In this paper, we specify a linear Cliff‐and‐Ord‐type spatial model. The model allows for spatial lags in the dependent variable, the exogenous variables, and disturbances. The innovations in the disturbance process are assumed to be heteroskedastic with an unknown form. We formulate multistep GMM/IV‐type estimation procedures for the parameters of the model. We also give the limiting distributions for our suggested estimators and consistent estimators for their asymptotic variance‐covariance matrices. We conduct a Monte Carlo study to show that the derived large‐sample distribution provides a good approximation to the actual small‐sample distribution of our estimators.