General equilibrium spatial models

This paper confirms the so called perverse effect of L?schian entry on wages regardless of the form of the labor supply curves. The form of our labor supply after firm entry is not only different from the one before entry, but also sharply different from that found by Kohlhase and Ohta [8]. However, we show that while the Kohlase-Ohta model has a convex labor supply, the Ohta-Asami-Kohlhase model has a concave labor supply as does the extended model presented here. Moreover, we find that the same perverse result is derived from either one of the two contrasting forms of the labor curve assumed, i.e., regardless of the convexity vs. concavity of the labor supply. Received: May 1999/Accepted: June 2000     

Exogenous and endogenous spatial growth models

In this paper, we investigate the impact on aggregate regional utility as a result of both exogenous growth and endogenous growth in a spatial system. We will first analyze the case of two closed regions, followed by the case of two open regions. The main instrument used in our approach to study the changes in collective regional welfare is Dynamic Programming. The traditional exogenous Solow growth model forms the basis of our paper. The analysis of this model will be extended to a comparison of two closed regions with exogenous growth. By introducing a case of a common labour market, we are able to investigate exogenous growth between two open regions. For the analysis of endogenous growth, we adopt the same structure as the one used for the investigation of exogenous growth models. In this framework, an investment in knowledge is considered as the endogenous driving force. Finally, we take a closer look at the timing of cost-reducing investments. In total, seven related but distinct cases are identified and studied in more detail.     

An assessment of the deregulation of electric power generation using network models of imperfect spatial markets

Proposals have been made to deregulate the generation of electric power. But unregulated generators would be spatial oligopolists, because transmission costs would insulate them from competition from distant producers. The purpose of this analysis is to estimate the degree to which unregulated power generators would be able to exercise market power. This is accomplished by calculating spatial price equilibria for a hypothetical deregulated power market in New York state. Two types of equilibria are calculated: Nash/Bertrand equilibria, representing a lower bound to unregulated prices, and limit pricing, defining an upper bound. Equilibria are obtained for the years 1980 and 2000.     

Network facility-location models in Stackelberg-Nash-Cournot spatial competition

A hierarchical mathematical programming approach is combined with sensitivity analysis (of variational inequalities) to formulate a facility-location model for a firm competing on a discrete network. It is assumed that the locating firm will act as the leader firm in an industry characterized by Stackelberg leader-follower(s) oligopolistic competition. The othern competitors in this industry are assumed to act as Cournot firms that each operate under the Cournot assumption of zero conjectural variation with respect to theirn — 1 Cournot competitors. It is further assumed that then Cournot firms will react to the location/production/shipping activities of the Stackelberg firm. Therefore, when the Stackelberg firm makes its location, production, and shipping decisions it takes into account the reaction of then Cournot firms to its (the Stackelberg firm's) integrated location and distribution decisions. Specifically, a Cournot reaction function is developed and imbedded in the Stackelberg firm's profit-maximizing objective function to project the anticipated reaction of the Cournot firms to the Stackelberg firm's location decision.An earlier version of this paper was presented at the 37th North American Meetings, Boston, November 1990.     

The spatial extent of producer service markets: Hierarchical models of interaction revisited

The traditional view of interaction in spatial markets has been challenged by recent studies of producer service trade in the space economy. These studies find that although city-size and distance influence the direction and spatial extent of interaction, patterns of trade oftentimes counter expectations as trade flows up the urban hierarchy and across large distances. This paper seeks to determine whether the ownership structure of establishments contributes to deviations from the traditional model of hierarchical interaction. Using trade data obtained from surveys of 547 producer service establishments, patterns of trade originating from a five-tier urban hierarchy are examined empirically and evaluated using spatial survivor functions and logit models. The results indicate that the ownership structure of establishments contributes significantly to deviations from expected patterns of interaction. Independently owned establishments have smaller spatial markets and interact more often with smaller sized cities. Nonindependently owned establishments, in contrast, trade down and up the urban hierarchy in a manner much less sensitive to distance.     

Seismic loads predicted by spatial variability models

Seismic loads that result from different expressions describing the spatial variability of the seismic ground motions at the supports of lifelines are evaluated and compared in this study. The analysis considers two spatial variability models, that are commonly used in lifeline earthquake engineering, namely the ones developed by Harichandran and Vanmarcke (J. Eng. Mech., 112 (1986)) and by Luco and Wong (Earthquake Eng. Struct. Dyn., 14 (1986)). It is shown that the models produce significantly different seismic loads for the analysis of buried and above-ground lifelines.     

Estimating standard errors in spatial panel models with time varying spatial correlation

We connect time varying spatial correlation patterns to examples in the theoretical and empirical literature. Then we use simulation experiments to compare the performance of estimation techniques that use spatial weights matrices ( W ) and those that do not. The results suggest that the pattern of time varying correlation does impact inference, but not as much as the W misspecification literature suggests. We find choosing the appropriate inferential method is less of a concern if the data generating process follows a hub‐spoke correlation structure. Finally, we confirm earlier results that the cluster robust modifications proposed by Bester et al. (2011) perform well if the group sizes are chosen appropriately.     

Nonlinear dynamic models for spatial interaction: The results of some empirical experiments

The content of this paper is related to the field of urban dynamic modelling, which has been greatly stimulated recently by the use of nonlinear methods. Some results of the application of an S.I.A. model of this kind to the Rome metropolitan area are described here. The experiments are mainly concerned with the analysis of the effects produced on the territorial diffusion of places of residence and services by variations in the mobility of the population in relation to journeys to work and journeys to services and by variations in economies of scale of consumers. The analysis is carried out for residential location and service location separately, and for the interacting Lowry-type system.     

Collapse analysis of real RC spatial structures using known failure schemes of ferro‐cement shell models

Large‐span reinforced concrete (RC) shells collapses that occurred in the last decade caused many death toll as well as significant losses to national economies. The most famous cases were the collapse of the aqua park cover in Moscow on February 2004 and the 2E terminal roof destruction at Charles de Gaulle Airport near Paris on May 2004. Following the publications of the appropriate commissions that have studied the reasons of these events, the influence of concrete creep and changes in the shell geometry on buckling of RC thin‐walled shells was not properly considered in the design. This study is focused on buckling of such shells, taking into account geometrical and physical nonlinear behaviour of compressed concrete. Other important reasons of concrete shells collapse are also analysed. The study is based on available experimental and theoretical investigations of ferro‐cement shells' models previously performed by the first author. The results of these investigations, obtained for small‐scale ferro‐cement models of thin‐walled shallow RC shells, are discussed. Behaviour of the tested models is compared with that of the above‐mentioned real shells and similar structures, which also collapsed. The critical buckling loads for the shells are obtained. It is shown that these loads are lower than the actual ones; thus, the shells buckling was unavoidable. To prevent brittle shell failure, they should be designed using other dominant failure modes that appear before the buckling. Possible failure schemes of real RC shells can be predicted using dominant failure modes obtained by laboratory testing of scaled models. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

Differences in spatial understanding between physical and virtual models

In the digital age, physical models are still used as major tools in architectural and urban design processes. The reason why designers still use physical models remains unclear. In addition, physical and 3D virtual models have yet to be differentiated. The answers to these questions are too complex to account for in all aspects. Thus, this study only focuses on the differences in spatial understanding between physical and virtual models. In particular, it emphasizes on the perception of scale. For our experiment, respondents were shown a physical model and a virtual model consecutively. A questionnaire was then used to ask the respondents to evaluate these models objectively and to establish which model was more accurate in conveying object size. Compared with the virtual model, the physical model tended to enable quicker and more accurate comparisons of building heights.     

Collusion in two models of spatial competition with quantity-setting firms

We use the linear city model and the circular city model to investigate the relationship between collusion sustainability and firms’ distance, and between collusion sustainability and transportation costs when firms can sell different quantities at each location. We find that when transportation costs are low, collusion sustainability monotonically increases with firms’ distance, while when transportation costs are high, the relationship is non-monotonic. Higher transportation costs increase collusion sustainability. Finally, in the circular city model, welfare is higher under collusion than under competition when transportation costs are high and firms are distant enough.     

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.     

Consistent price and location conjectures in spatial competition models

Remarkable advances have been made in spatial competition theory during the past three decades. Only in recent years, however, have the implications of firms' conjectural responses become well understood. Here research has largely focused on analyzing markets where prices (short run) or prices and locations (medium and long run) are exogenous. This paper examines the equilibium properties of spatial firms when prices and locations are consistent or endogenous. Price reaction equations are complemented with location reaction equations, consistency conditions are introduced, and numerical solutions are then given. While the simulations are confined to one-dimensional markets, equilibrium solutions unambiguously indicate how prices, locations, and profits are related to the costs of firms, the elasticity of consumer demand, and the presence or absence of market boundaries.     

Accounting for spatial relationships in models of interstate population migration

This study focuses on the specification of distance and space in models of state-to-state population migration. Typically, space is captured by one or two simple variables that do not adequately model the spatial relationship between states. These are particularly poor measures for states with a common border, especially those with a metropolitan area located near the border. Four models of interstate population migration are developed, with increasingly complex specifications of space. The models are estimated using 1975 to 1980 migration data for the 48 contiguous states of the United States. Common borders and bordering metropolitan areas do influence interstate population flows. Models lacking a more detailed specification of space will lose explanatory power and suffer from biases.     

Testing for spatial group-wise heteroskedasticity in spatial autocorrelation regression models: Lagrange multiplier scan tests

The aim of this paper is to develop a spatial group-wise heteroskedasticity test based on the scan approach, specifically developed for spatial autocorrelation regression models (spatial lag and spatial error models): the “scan-LM test.” Based on the Lagrange multiplier (LM) principle, its main advantage lies in its comparative ease of implementation as it is not necessary to obtain the maximum likelihood estimations for the alternative hypothesis. Moreover, when rejecting the null hypothesis, this test identifies the shape and size of the spatial clusters with different residual variance, a feature which proves very useful for specification search of the regression model. Another important benefit of the scan-LM test is that it does not require the specification of a spatial weights matrix. An extensive Monte Carlo simulation confirms the good properties of the scan-LM test in terms of size and power. This test is also robust in the presence of non-normality and other forms of a spatial heteroskedasticity. We finally propose an application on housing prices in the agglomeration of Madrid for a specific submarket: the attics.