Finite sample properties of estimators of spatial autoregressive models with autoregressive disturbances

The article investigates the finite sample properties of estimators for spatial autoregressive models where the disturbance terms may follow a spatial autoregressive process. In particular we investigate the finite sample behavior of the feasible generalized spatial two-stage least squares (FGS2SLS) estimator introduced by Kelejian and Prucha (1998), the maximum likelihood (ML) estimator, as well as that of several other estimators. We find that the FGS2SLS estimator is virtually as efficient as the ML estimator. This is important because the ML estimator is computationally burdensome, and may even be forbidding in large samples, while the FGS2SLS estimator remains computationally feasible in large samples. Received: 20 January 2001 / Accepted: 31 August 2001     

Exploring relationships between semi-variogram and spatial autoregressive models

This paper seeks to continue the building of a common foundation for spatial statistics and geostatistics. Equations from the conditional autoregressive (CAR) model of spatial statistics for estimating missing geo-referenced data have been found to be exactly those best linear unbiased estimates obtained with the exponential semi-variogram model of kriging, but in terms of the inverse covariance matrix rather than the covariance matrix itself. Further articulation of such relations, between the moving average (MA) and simultaneous autoregressive (SAR) or autoregressive response (AR) models of spatial statistics, and, respectively, the linear and Gaussian semi-variogram models of kriging, is outlined. The exploratory graphical and numerical work summarized in this paper indicates the following: (a) there is evidence to pair the moving average and linear models; (b) the simultaneous autoregressive and autoregressive response model pair with a Bessel function (modified of the second kind and order one) rather than the Gaussian semi-variogram model; (c) both specification error and measurement error can give rise to the nugget effect discussed in geostatistics; (d) restricting estimation to a geographic subregion introduces edge effects that increasingly bias semi-variogram model parameter estimates as the degree of spatial autocorrelation increases toward its upper limit; and (e) the theoretical spectral density function for a simultaneous autoregressive model is a direct extension of that for the conditional autoregressive model.     

Application of Markov chains and Monte Carlo simulations for developing pavement performance models for urban network management

Existing performance models developed for interurban pavements are not applicable to urban pavements due to differences in traffic demands and deterioration trends. The objective of the study was to develop performance models for the management of urban pavement networks. Markov chains and Monte Carlo simulation were applied to account for the probabilistic nature of pavements deterioration over time, using data collected in the field. One of the advantages of this methodology is that it can be used by local agencies with scarce technical resources and historical data. Eight performance models were developed and successfully validated for asphalt and concrete pavements in humid, dry and Mediterranean climates with different functional hierarchies. The resulting models evidence the impact of design, traffic demand, climate and construction standards on urban pavements performance. Predicted service life of asphalt and concrete pavements in primary networks are consistent with design standards. However, pavements in secondary and local networks present shorter and longer service life compared to design life, respectively. Climate is a relevant factor for asphalt pavements, where higher deterioration was observed compared to that expected. Opposite to this, no relevant differences between design and performance can be attributed to climate in concrete pavements.     

ML versus IV estimates of spatial SUR models: evidence from the case of Airbnb in Madrid urban area

The Annals of Regional Science - In recent decades we have seen an increased interest in the use of seemingly unrelated regressions models (SUR) in a spatial context, with compelling case studies...     

Estimation of spatial autoregressive M-way error component panel data models

This paper considers a first order spatial autoregressive panel data model with first-order spatial autoregressive disturbances, SARAR(1,1), and M-dimensional error components. We derive generalized moments (GM) estimators for the spatial autoregressive parameter of the disturbance process and the variances of the error components and define a feasible generalized two stages least squares (FG2SLS) estimator for the regression parameters of the model. Finally, we prove consistency and derive the joint asymptotic distribution of the GM and FG2SLS estimators, enabling specification tests and a proper estimation of multi-way error component models with cross-sectionally dependent observations.     

A comparison of vector autoregressive forecasting performance: spatial versus non-spatial Bayesian priors

The Annals of Regional Science - Forecasting performance of spatial versus non-spatial Bayesian priors applied to a large vector autoregressive model that includes the 48 lower US states plus and...     

Expanded reliability-based design of piles in spatially variable soil using efficient Monte Carlo simulations

Inherent spatial variability is considered as a major source of uncertainties in soil properties, and it affects significantly the performance of geotechnical structures. However, research that considers, directly and explicitly, the inherent spatial variability in reliability-based design (RBD) of geotechnical structures is limited. This paper develops a RBD approach that integrates a Monte Carlo Simulation (MCS)-based RBD approach, namely the expanded RBD approach, with random field theory to model, both directly and explicitly, the inherent spatial variability of soil properties in RBD of drilled shafts. The proposed approach is implemented in a commonly-available spreadsheet environment to effectively remove the hurdle of reliability computational algorithms and to provide a user-friendly graphical user interface to practicing engineers. To improve the efficiency and resolution of MCS at small probability levels, the expanded RBD approach is enhanced with an advanced MCS method called “Subset Simulation”. Equations are derived for the integration of the expanded RBD approach and Subset Simulation. The proposed approach is illustrated through a drilled shaft design example, and is applied to explore the effects of inherent spatial variability (including the scale of fluctuation and correlation structure) and to evaluate systematically the equivalent variance technique that is commonly used to indirectly model inherent spatial variability in current RBD approaches. It is found that inherent spatial variability significantly affects the RBD of drilled shafts, and its effects are considered in RBD using the proposed approach in a direct and explicit manner. In addition, the results show that the indirect modeling of inherent spatial variability using the equivalent variance technique with the simplified form of variance reduction function in RBD might lead to relatively conservative designs in design practice.     

Tropical cyclone winds: Uncertainties in Monte Carlo simulation

A typical Monte Carlo modelling procedure for tropical cyclone windspeeds is applied, and the many items comprising the model are discussed in detail. From the literature, each item is found to have a range of values given for it. The extremes are not taken, but rather that range is chosen which is well substantiated at both ends.The resulting 50-year return period windspeed for a typical location is foud to have a very large range, so large as to render doubtful the usefulness of the results of simulation in this application.     

Using Bayesian posterior model probabilities to identify omitted variables in spatial regression models

LeSage and Pace (2009) consider the impact of omitted variables in the face of spatial dependence in the disturbance process of a linear regression relationship and show that this can lead to a spatial Durbin model. Monte Carlo experiments and Bayesian model comparison methods are used to distinguish between spatial error and Durbin model specifications that arise with varying levels of correlation between included and omitted variables. The Monte Carlo results suggest use of the common factor relationship developed in Burridge (1981) as a way to test for the presence of omitted variables bias influencing specific explanatory variables.     

蒙特卡洛模拟的随机性及裂隙岩体渗透张量分析

１　前　　言　*蒙特卡洛模拟法作为一种计算机模拟手段,已被广泛应用于岩体的裂隙网络模拟。但蒙特卡洛法是一种随机模拟方法,是一种通过裂隙的若干物理、几何量的统计参数来获得一个随机裂隙模型的方法。一方面,真实的岩体裂隙是满足相应的统计分布规律（包括误差规律）的一个具体的裂隙系统;另一方面,由计算机给出的裂隙模型是根据这些分布获得的另一个确定的裂隙分布形式,这两者之间的渗透性质并不一致,但两者的统计规律应具有一致性。因此,确定随机模型对渗透性的影响关系是认识蒙特卡洛法和了解真实岩体渗透性质所必需的。２　蒙特卡洛模拟岩体裂隙网络的随机性假设有一岩体,其裂隙参数见表１,根据表中所提供的参数,可生成多种岩     

Testing a polynomial relationship of the non‐parametric component in partially linear spatial autoregressive models*

A statistical test procedure is proposed to check a polynomial relationship of the non‐parametric component in partially linear spatial autoregressive models, in which a residual‐based bootstrap procedure is used to derive the p‐value of the test. Some simulations are conducted to assess the performance of the test and the results show that the bootstrap approximation to the null distribution of the test statistic is valid and the test is powerful in identifying a polynomial relationship of the non‐parametric component. Furthermore, a real‐world example is given to demonstrate the usefulness of the proposed test.     

Localisation versus globalisation: some evidence from real estate services organisations

The buying and selling of real estate is predominantly conducted through transactions agents: real estate brokers. In recent decades, there have been divergent trends in commercial and residential markets. Commercial brokerage firms have become involved in a wider range of services and have internationalised; in contrast, residential firms have remained nationally, and predominantly locally, based and still concentrate on brokerage. Economic explanations are used to understand this experience. This case study highlights a weakness of arguments that globalisation is inextricably taking over more facets of life. Higher incomes are associated with a growing preference for services, many of which are best delivered locally or in a decentralised way.

AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation

An important challenge in structural reliability is to keep to a minimum the number of calls to the numerical models. Engineering problems involve more and more complex computer codes and the evaluation of the probability of failure may require very time-consuming computations. Metamodels are used to reduce these computation times. To assess reliability, the most popular approach remains the numerous variants of response surfaces. Polynomial Chaos [1] and Support Vector Machine [2] are also possibilities and have gained considerations among researchers in the last decades. However, recently, Kriging, originated from geostatistics, have emerged in reliability analysis. Widespread in optimisation, Kriging has just started to appear in uncertainty propagation [3] and reliability [4] and [5] studies. It presents interesting characteristics such as exact interpolation and a local index of uncertainty on the prediction which can be used in active learning methods. The aim of this paper is to propose an iterative approach based on Monte Carlo Simulation and Kriging metamodel to assess the reliability of structures in a more efficient way. The method is called AK-MCS for Active learning reliability method combining Kriging and Monte Carlo Simulation. It is shown to be very efficient as the probability of failure obtained with AK-MCS is very accurate and this, for only a small number of calls to the performance function. Several examples from literature are performed to illustrate the methodology and to prove its efficiency particularly for problems dealing with high non-linearity, non-differentiability, non-convex and non-connex domains of failure and high dimensionality.     

Increasing innovation in home energy efficiency: Monte Carlo simulation of potential improvements

Despite the enormous potential for savings, there is little penetration of market-based solutions in the residential energy efficiency market. We hypothesize that there is a failure in the residential efficiency improvement market: due to lack of customer knowledge and capital to invest in improvements, there is unrecovered savings. In this paper, we model a means of extracting profit from those unrecovered energy savings with a market-based residential energy services company, or RESCO. We use a Monte Carlo simulation of the cost and performance of various improvements along with a hypothetical business model to derive general information about the financial viability of these companies. Despite the large amount of energy savings potential, we find that an average contract length with residential customers needs to be nearly 35 years to recoup the cost of the improvements. However, our modeling of an installer knowledge parameter indicates that experience plays a large part in minimizing the time to profitability for each home. Large numbers of inexperienced workers driven by government investment in this area could result in the installation of improvements with long payback periods, whereas a free market might eliminate companies making poor decisions.     

County-level determinants of local public services in Appalachia: a multivariate spatial autoregressive model approach

We develop a multivariate spatial autoregressive model of local public expenditure determination based on the maximization of a strictly quasi-concave community utility function. The existence of spatial interdependence is tested for both the spatial error and spatial lag model. The full model is estimated by efficient GMM following Kelejian and Prucha (J Real Estate Finan Econ 17(1):99?C121, 1998). The results indicate significant spillover effects among local governments with respect to spending on public services. The OLS estimates of the conventional (non-spatial) model and the corresponding maximum likelihood estimates of the spatial lag and the spatial error models are presented for comparison purposes. The GMM estimates are found to be more efficient.     

State cigarette taxes and health expenditures: Evidence from dynamic spatial lag panel models

This study explores the relationship between state cigarette taxes and state expenditures on health and hospitals. We address two major sources of endogeneity from (i) the relationship between tax rates and expenditure decisions and (ii) spatial dependence in expenditure policies by using tobacco production as an instrument for cigarette tax rates and through a dynamic spatial Durbin model. We estimate the cigarette tax rate expenditure elasticity to be 0.03 (SR) and 0.87 (LR) for state health spending and 0.05 (SR) and 0.79 (LR) for state hospital spending. Increases in cigarette taxes did not reduce state spending on health over this period.     

Random excitation of a yielding cantilever: Approximate analysis versus simulations

Random vibrations of elasto-plastic cantilever beams excited by earthquakes are studied. Distribution of mass and stiffness, as well as plastic zones spreading over the beam, are taken into account. Following a complete elastic-inelastic analogy, strain is splitted into a drift and a linear elastic portion. The linear part is derived under the condition of time-invariant stiffness and is subjected to an effective earthquake excitation. Stochastic response measures of the drift process are calculated using results of the linear analysis corresponding to this effective and updated loading. Analogously, the nonlinear deflection process is considered. Special emphasis is given to the comparison between this approximate probabilistic theory and the results of extensive simulations, using a very efficient cpu-time saving version of the deterministic theory. For practical applications, a nondimensional representation is given using a similarity complex.