THE ECONOMICS OF AIR TRAVEL GRAVITY MODELS*

Starting with the aggregate demand model of economics, a model of demand for intercity air travel is developed which contains the gravity model as a less general submodel. The more general model is referred to as the alternative opportunities model since it takes account of alternative destinations open to travelers, not just origin and destination as does the gravity model. The demand model approach has the virtue of providing a theoretical basis for understanding and analyzing the gravity model. The gains from treating alternative locations and demand motivation variables are a substantial increase in explanatory power over that yielded by the gravity model, the identification of statistically significant determinants of air travel, and better measurement of the coefficients of population and distance by taking account of these other variables and somewhat better forecasts. A shortcoming of procedures used here is aggregation of air trips with different purposes and thus lack of clear specification of the size of effects of different variables on different types of travel. Overcoming this difficulty must await origin-destination data listed by trip purpose.     

GRAVITY AND SPATIAL STRUCTURE: THE CASE OF INTERSTATE MIGRATION IN MEXICO*

ABSTRACT The estimation of gravity models of internal (aggregate) place‐to‐place migration is plagued with endogeneity (omitted‐variable) biases if the unobserved effects of spatial structure are not accounted for. To address this econometric problem, this paper presents a more general specification of the gravity model, which allows for (bilateral) parameter heterogeneity across individual migration paths—along with (unilateral) origin‐ and destination‐specific effects. The resultant “three‐way fixed‐effects” (3FE) model is applied for an analysis of interstate migration in Mexico based on cross‐sectional data. To overcome parameter‐dimensionality problems (due to limited or incomplete information), the 3FE model is estimated using the Generalized Maximum Entropy (GME) estimator. The empirical implications of this new modeling strategy are illustrated by contrasting the 3FE‐GME estimates with those for the traditional and two‐way fixed‐effects (2FE) models. The former are far more plausible and intuitively interpretable than their traditional and 2FE counterparts, with parameter estimates changing in expected directions. The (average) effect of the migrant stock is markedly smaller than usually estimated, providing a more realistic measure of network‐induced migration. Migration outflows from centrally located origins have significantly steeper distance decay. Path‐specific distance effects exhibit directional asymmetries and spatial similarities.     

INTERPRETING SPATIAL ECONOMETRIC ORIGIN‐DESTINATION FLOW MODELS

Spatial interaction or gravity models have been used to model flows that take many forms, for example population migration, commodity flows, traffic flows, all of which reflect movements between origin and destination regions. We focus on how to interpret estimates from spatial autoregressive extensions to the conventional regression‐based gravity models that relax the assumption of independence between flows. These models proposed by LeSage and Pace ( 2008 , 2009 ) define spatial dependence involving flows between regions. We show how to calculate partial derivative expressions for these models that can be used to quantify these various types of effect that arise from changes in the characteristics/explanatory variables of the model.     

Net migration estimation in an extended,multiregional gravity model

A multi-regional framework is developed in order to analyze net migration over time to all 10 Canadian provinces within an integrated system of equations. "An extended gravity model is the basis for the equation specification and the use of constrained econometric estimation techniques allows for the provincial interdependence of the migration decision while at the same time ensuring that an important system-wide requirement is respected." The model is estimated using official Canadian data for the 1960s and 1970s. "The results suggest the predominance of the push factor for interprovincial migration for most provinces, although net migration to the Atlantic provinces is also shown to be subject to pull forces from the rest of the country." The effects of wage rate variables, unemployment, and political disturbances in Quebec on inter-provincial migration are noted.     

Models for Spatial Weights: A Systematic Look

General properties of spatial weights models, in particular Markovian properties, are systematically investigated. The role of stationary spatial distribution, interpretable as an importance-centrality or prominence index, is emphasized. Spatial interaction models, and among them the gravity model, are classified with respect to the time reversal and aggregation invariance properties obeyed by the associated spatial weights. Nine examples, involving connectivity, flows and distance decay analysis, integral geometry, and Dirichlet-Voronoi tessellations illustrate the main concepts, with a particular geometrical emphasis, and show how traditional, heuristic ingredients aimed at defining spatial weights can be recovered from general models.     

An Empirically Based Implementation and Evaluation of a Hierarchical Model for Commuting Flows. 一种基于经验的层状通勤流模型实现与评估

This article provides an empirical evaluation of a hierarchical approach to modeling commuting flows. As the gravity family of spatial interaction models represents a benchmark for empirical evaluation, we begin by reviewing basic aspects of these models. The hierarchical modeling framework is the same that Thorsen, Ubøe, and Nævdal (1999) used. However, because some modifications are required to construct a more workable model, we undertake a relatively detailed presentation of the model, rather than merely referring to the presentation in Thorsen, Ubøe, and Nævdal (1999) . The model uses a hierarchical specification of a transportation network and the individual search procedure. Journeys to work are determined by the effects of distance deterrence and of intervening opportunities, and by the location of potential destinations relative to alternatives at subsequent levels in a transportation network. The model calibration uses commuting data from a region in western Norway. The estimated parameter values are reasonable, and the explanatory power is very satisfactory when compared with the results of a competing destinations approach.     

TESTING THE SPATIAL SCALE AND THE DYNAMIC STRUCTURE IN REGIONAL MODELS (A CONTRIBUTION TO SPATIAL ECONOMETRIC SPECIFICATION ANALYSIS)*

This article addresses the problem of specification uncertainty in modeling spatial economic theories in stochastic form. It is ascertained that the traditional approach to spatial econometric modeling does not adequately deal with the type and extent of specification uncertainty commonly encountered in spatial economic analyses. Two alternative spatial econometric modeling procedures proposed in the literature are reviewed and shown to be suitable for analyzing systematically two sources of specification uncertainty, viz., the level of aggregation and the spatio-temporal dynamic structure in multiregional econometric models. The usefulness of one of these specification procedures is illustrated by the construction of a simple multiregional model for The Netherlands.     

Gravity waves from O2 nightglow during the AIDA '89 campaign II: numerical modeling of the emission rate/temperature ratio, η

The dependence of η, the ratio of emission rate fluctuation to temperature fluctuation, on the gravity wave parameters and chemical parameters is developed using a model for the O₂ airglow's response to a gravity wave. The model is in the Eulerian frame of reference using the traditional linearization and perturbation method. Two photochemical mechanisms, the three-body recombination mechanism and the two-step transfer mechanism and two kinds of waves, evanescent and internal, are separately discussed in detail. Results of the model are compared with other existing models of η(O₂) and found to be in agreement. The predictions of this model agree fairly well with the available gravity wave measurements in the magnitude of η, but the predicted phases are somewhat larger than those normally observed.     

Theoretical Underpinnings of the Gravity Hypothesis

Various theoretical rationalizations of the gravity hypothesis for spatial interaction are examined. Deterministic utility theory cannot account for variability in individual behavior. Choice models based on Luce's axiom contain some inconsistencies. Random utility theory provides a probabilistic formulation that is internally consistent, and also solves the aggregation problem. However, investigation reveals that, although this provides a theoretical justification for gravity-like behavior, the assumptions made are sufficiently unrealistic to cast doubt on the empirical validity of the gravity hypothesis.     

Comprehensive meteorological modelling of the middle atmosphere: a tutorial review

This paper reviews the current state of comprehensive, three-dimensional, time-dependent modelling of the circulation in the middle and upper atmosphere from a meteorologist's perspective. The paper begins with a consideration of the various components of a comprehensive model (or general circulation model, GCM), including treatments of processes that can be explicitly resolved and those that occur on scales too small to resolve (and that must be parameterized). The typical performance of GCMs in simulating the tropospheric climate is discussed. Then some important background on current ideas concerning the general circulation of the stratosphere and mesosphere is presented. In particular, the transformed-Eulerian mean flow formalism, the role of vertically-propagating internal gravity waves in driving the large-scale circulation, and the notion of a stratospheric surf zone are all briefly reviewed. Using this background as a guide, some middle atmospheric GCM results are discussed, with a focus on simulations made recently with the GFDL ‘SKYHI’ troposphere-stratosphere-mesosphere GCM. The presentation attempts to emphasize the interaction between theory and comprehensive modelling. Many theoretical notions cannot be confirmed in detail from observations of the real atmosphere due to the various limitations in the observational methods, but can be very completely examined in GCMs in which every atmospheric variable is known perfectly (within the limits of the numerical methods). It will be shown that our understanding of both the role of gravity waves in the general circulation and the nature of the stratospheric surf zone has benefited from analysis of GCM results.From the point of view of the upper atmosphere, one of the most interesting aspects of GCMs is their ability to generate a self-consistent field of upward-propagating gravity waves. This paper concludes with a discussion of the gravity wave field in the middle atmosphere of GCMs. Comparisons of the explicitly-resolved gravity wave field in the SKYHI model with observations are quite encouraging, and it seems that the model is capable of producing a gravity wave field with many realistic features. However, the simulated horizontal spectrum of the eddy momentum fluxes associated with the waves is quite shallow, suggesting that much of the spectrum that is important for maintaining the mean circulation is not explicitly resolvable in current GCMs. A brief discussion of current efforts at parameterizing the mean flow effects of the unresolvable gravity waves is presented.     

不同模型在镇域空间相互作用中的应用与比较分析——以湖北省大冶市为例

镇域尺度的空间相互作用研究对促进城乡统筹和城镇体系规划具有重要意义。本文借鉴最新研究成果,从理论及实践层面对镇域空间相互作用研究进行了探索,提出一种基于空间可达性的辐射模型,并与传统重力模型进行比较分析。以大冶市16个乡镇为例进行实例研究,结果表明:1辐射模型与实测数据的相似度较高,可以更好地反映镇域空间相互作用的客观规律;2两种模拟方法在体现空间相互作用的方向性以及结构特征方面具有显著差异;3辐射模型中影响范围的引入以及空间可达性对区域异质性的体现是其与重力模型的主要区别。     

PUBLIC CAPITAL, REGIONAL OUTPUT, AND DEVELOPMENT: SOME EMPIRICAL EVIDENCE

ABSTRACT The goal of our paper is to provide direct estimates of the association between public capital and regional output. This is made possible by the construction of a data series which measures public capital at the state level.
The relation between public capital and other productive factors is tested using a translog production function. Our results show that labor and public capital are complementary inputs, and that public capital exhibited diminishing returns. We also consider restrictions on the translog formulation. Linear homogeneity is rejected in all cases, and the Cobb-Douglas specification is rejected for the manufacturing and all sectors categories.     

A Comparison of Spatially Varying Regression Coefficient Estimates Using Geographically Weighted and Spatial‐Filter‐Based Techniques

Geographically weighted regression (GWR) is a technique that explores spatial nonstationarity in data‐generating processes by allowing regression coefficients to vary spatially. It is a widely applied technique across domains because it is intuitive and conforms to the well‐understood framework of regression. An alternative method to GWR that has been suggested is spatial filtering, which it has been argued provides a superior alternative to GWR by producing spatially varying regression coefficients that are not correlated with each other and which display less spatial autocorrelation. It is, therefore, worthwhile to examine these claims by comparing the output from both methods. We do this by using simulated data that represent two sets of spatially varying processes and examining how well both techniques replicate the known local parameter values. The article finds no support that spatial filtering produces local parameter estimates with superior properties. The results indicate that the original spatial filtering specification is prone to overfitting and is generally inferior to GWR, while an alternative specification that minimizes the mean square error (MSE) of coefficient estimates produces results that are similar to GWR. However, since we generally do not know the true coefficients, the MSE minimizing specification is impractical for applied research.     

A Bi‐objective Optimization Model for Designing Safe Walking Routes for School Children

This study uses a mathematical optimization approach to design safe walking routes from school to home for children. Children are thought to be safer when walking together in groups rather than alone. Thus, we assume that the risk of walking along a given road segment in a group is smaller than that of walking the same segment alone. At the same time, the walking route between school and home for each child should not deviate substantially from the shortest route. We propose a bi‐objective model that minimizes both the total risk (particularly, the total distance walked alone) and the total walking distance for all children. We present an integer programming formulation of the proposed problem and apply this formulation to two instances based on actual road networks. We obtain Pareto optimal solutions using a mathematical programming solver and analyze the characteristics of the solutions and their potential applicability to real situations. The results show that the proposed model produces much better solutions compared with the solution where each child walks along the shortest path from school to home. In some optimal solutions, only a small deviation from the shortest path results in a dramatic reduction of the risk objective.     

A Generalization of the Utility Theory Approach To the Problem of Spatial Interaction

The derivation of the gravity model from utility theory is reformulated and generalized in order to show (1) how both the number of trips to individual destinations and the total travel budget may be determined simultaneously, and (2) how the effect of both distance and destination quality on trip distribution and total budget may be analyzed. Results are compared with the revealed space preference approach and are found to be superior in dealing theoretically with trip frequency and the effects of spatial context. For empirical applications, however, the revealed preference approach is advantageous.     

De-democratising the Irish planning system

This paper examines the practices deployed to de-democratise elements of the Irish planning system. It does so through scrutinizing the processes by which a new streamlined planning procedure for large scale residential developments was institutionalized. The paper investigates how a development lobby group successfully prompted the institutionalization of this streamlined procedure by momentarily capturing the policy formulation agenda surrounding a housing crisis. It demonstrates how this was achieved by defining problems regarding the democratic character of the planning system and accruing agency through solution specification and resonance with the ideologies and rationalities of pertinent political and senior civil servant decision makers. The paper undertakes this analysis by situating a discourse analytical approach within the Multiple Streams Framework. In doing so, the paper provides an original contribution to academic scholarship through novelty of theoretical application on a disquieting aspect of neoliberalism in a planning context that as yet has received limited attention.     

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.     

我国人口与社会经济重心的动态演变

本文利用区域重心的概念及其模型,计算了1978-2002年我国逐年的人口重心和社会经济重心,得到人口重心和社会经济重心的动态演变轨迹,分析了人口和社会经济发展区域差异的动态变化及其驱动因子,并对人口重心和社会经济发展重心的动态演变趋势进行了对比分析。     

Exogenous Workplace Choice in Residential Location Models: Is the Assumption Valid?

This paper examines the assumption implicit in most models of residential location that the choice of workplace is exogenously determined. Monocentric models have generally made this assumption, but it has come under increasing scrutiny. A nested logit model of workers' choices of workplace, residence, and housing tenure within the Dallas-Fort Worth metropolitan area is developed to provide a test. A unique dataset that includes the workplace and residence census tracts of workers in Dallas-Fort Worth, and their demographic and socioeconomic characteristics, is used to estimate the model. The results confirm that a joint choice specification better represents actual choice behavior in a multinodal metropolis.     

Multiple Allocation Hub Location Model with Fixed Arc Costs

This article formulates a model to analyze the role of fixed costs in the design of optimal transportation hub networks. The primary purpose of this article is to better model costs in hub networks, an issue that has attracted considerable attention. This article allows particular versions of hub networks to emerge from the cost structure, rather than by imposing a rigid predefined connectivity protocol. The article integrates modeling approaches from an environmental hub location model with the three‐index formulation of Ernst and Krishnamoorthy to produce a hub location model with fixed and variable costs for all arcs. Our goal is to demonstrate how the inclusion of a richer cost model in transportation hub location can generate a wide range of different network types, depending on the relative magnitudes of the cost elements. While the existence of special case network solutions is well known and has been exploited in optimization, the current research provides added insight to the cost of flow in a more, or less, connected hub network. Eight fundamental prototype networks are derived as special cases, and some additional unanticipated network types also emerge. The results are illustrated with a standard CAB25 data set.