When worlds collide: Different comparative static predictions of continuous and discrete agent models with land

This paper presents a difference in the comparative statics of general equilibrium models with land when there are finitely many agents, and when there is a continuum of agents. Restricting attention to quasi-linear and Cobb–Douglas utility, it is shown that with finitely many agents, an increase in the (marginal) commuting cost increases land rent per unit (that is, land rent averaged over the consumer's equilibrium parcel) paid by the consumer located at each fixed distance from the central business district. In contrast, with a continuum of agents, average land rent goes up for consumers at each fixed distance close to the central business district, is constant at some intermediate distance, and decreases for locations farther away. Therefore, there is a qualitative difference between the two types of models, and this difference is potentially testable.     

On the use of Markovian equilibrium distributions for land use policy evaluation

Using the Markov model of land use change as a framework for analyzing the impact of alternative land use policies, comparison of Markovian equilibrium distributions resulting from constrained simulations has been promoted as a means of evaluating the scope of land use policy impacts. Previous studies have not considered the question of measuring the confidence which can be placed in the predictions contained in the equilibrium distribution vector. This paper applies a method of assessing the levels of confidence in the predictions of the equilibrium distribution vector. Results suggest that use of equilibrium distributions of land use as a measure of policy impact has limited inferential value.     

A model of population distribution,traffic congestion,and neighborhood crowding in a circular city

An idealized static equilibrium model of a circularly symmetric city is presented. The model allows one to compute the spatial distribution of residences, given certain simple and plausible assumptions about the “costs” of transport, housing and neighborhood crowding. The model is chosen so as to guarantee that in first approximation, the residential population distribution which would be considered optimal by a perfect planner is identical to the distribution reached in a push-shove, laissez-faire equilibrium. This aspect of the construction is shown to be related in a simple way to the familiar “external diseconomy” situation in which a free resource is allocated among alternative uses by equating average, rather than marginal products. The existence of an infinite class of models in which the associated planner's optimum and laissez-faire equilibria are equivalent follows naturally from the standard theory of the private and social costs of highway congestion. The model leads naturally to exponentially falling population distributions which exhibit an “urban-suburban” dichotomy, to a particular overall city size, and to an optimal allocation of land between transport and residential uses.     

Precise computation of a competitive equilibrium of the discrete land market model

This paper provides a finite algorithm to compute a competitive equilibrium of the Alonso-type discrete land market model (known as bid-rent equilibrium) without assuming any condition on the spatial configuration such as monocentricity. The existence of the finite algorithm implies that the discrete land market model is sufficiently tractable for computer simulation analysis (sensitivity analysis) even if the spatial configuration is variable. Specifically, we can evaluate numerically the effects of new routes in a transportation network upon equilibrium rents and commuting mode.     

Equilibrium models with land: A criticism and an alternative

Models of economies either of urban areas or with local public goods often involve the use of a continuum of consumers along with the use of a commodity called land; each consumer generally owns a parcel of land of positive area. The purpose of the present study is to show that such models are internally inconsistent (independent of the other assumptions employed) in that only countably many consumers can own parcels of land of non-zero area if land lies in a Euclidean space. This result applies, in particular, to monocentric city models. Moreover, it is shown that the standard justification for the use of economies with an infinity of agents, that they approximate large economies with a finite number of consumers, does not necessarily apply in the case of economies with land and a continuum of consumers. A model where land is represented by subsets of $\text{R}$² is presented as an alternative.     

Patterns and dynamics of population heterogeneity in mixtures models

Mixtures of distributions are a common modelling tool for durations of social phenomena, especially when the population is believed to be heterogeneous. We discuss heterogeneity patterns which can be captured by various mixing distributions in continuous and discrete time. Particular attention is given to recidivism data which Kaplan modeled by beta-mixtures of geometric distributions. We also investigate the dynamics of heterogeneity, measured via the variance of the mixing distribution, over the duration. It is shown that not all mixture models display decreasing heterogeneity over time.     

Urban general equilibrium models and simplicial search algorithms

This paper describes how simplicial search algorithms work, and discusses how they may be used to solve static theoretical urban models. If such algorithms are to be used, land must be treated as consisting of a number of discrete sections. It is argued that this is not a serious disadvantage, and that for many purposes such discrete models have significant advantages over models in which land is treated as continuous. In particular, it is possible to deal with several groups of people having different tastes and incomes. Several related models are described, and some interesting qualitative results are presented.     

Consistent estimation of correlations between observed interval variables with skewed distributions

Departures from multinormality due to skewness in observed distributions may result in inconsistent estimates of product-moment correlations between interval variables. Therefore, the robustness of the product-moment correlation estimator against skewness in the distributions of sample data on interval variables has been investigated. This estimator is robust against skewness of maximally about 1 in absolute value. If the observed distributions have larger skewnesses, the sample data on interval variables may be redistributed over normally distributed discrete variables with 10 categories each. The estimated polychoric correlations between these discrete variables represent consistent estimates of the product-moment correlations between the original interval variables in the population.     

On a theorem of Schmeidler

Over a decade ago D. Schmeidler (1973) introduced a concept of non-cooperative equilibrium for games with a continuum of agents and, under a restriction on the payoff functions, established the existence of an equilibrium in pure strategies. The purpose of this note is to reformalize the model and the equilibrium notion of Schmeidler in terms of distributions rather than measurable functions. We shall see how once the definitions are available we get (pure strategy) equilibrium existence theorems quite effortlessly and under general conditions. A number of remarks contain applications to, among others, incomplete information games.     

Are compact cities environmentally friendly?

There is a wide consensus among international institutions and national governments in favor of compact (i.e. densely populated) cities as a way to improve the ecological performance of the transport system. Indeed, when both the intercity and intra-urban distributions of activities are given, a higher population density makes cities more environmentally friendly because the average commuting length is reduced. However, when we account for the possible relocation of activities within and between cities in response to a higher population density, the latter may cease to hold. Indeed, an increasing-density policy affects prices, wages and land rents, which in turn incentivizes firms and households to change place. This reshapes the urban system in a way that may generate a higher level of pollution. Thus, although an increase in compactness is environmentally desirable when locations are given, compactness may not be environmentally-friendly when one accounts for the general equilibrium effects generated by such a policy.     

(Non-)Existence of Equilibria in Multicommunity Models

This paper reconsiders equilibrium existence in models with migration and voting over local public goods. We show that under some straightforward assumptions on preferences and income distributions, the basic structure of multicommunity models (i.e., perfect mobility, majority rule, single crossing property) implies that no equilibrium with jurisdictions conducting different policies can exist. Stratification equilibria—with sorting of the population according to income classes—are therefore not as natural as is sometimes suggested. Mechanisms that can serve to support stratification (i.e., tight housing markets, returns to scale in the provision of publicly consumed goods) are discussed.     

New methods for analyzing structural models of labor force dynamics

The economic theory of decision-making under uncertainty is used to produce three econometric models of dynamic discrete choice: (1) for a single spell of unemployment; (2) for an equilibrium two-state model of employment and non-employment; (3) for a general three-state model with a non-market sector. The paper provides a structural economic motivation for the continuous time Markov (or more generally ‘competing risks’) model widely used in longitudinal analysis in biostatistics and sociology, and it extends previous work on dynamic discrete choice to a continuous time setting. An important feature of identification analysis is separation of economic parameters that can only be identified by assuming arbitrary functional forms from economic parameters that can be identified by non-parametric procedures. The paper demonstrates that most econometric models for the analysis of truncated data are non-parametrically under-identified. It also demonstrates that structural estimators frequently violate standard regularity conditions. The standard asymptotic theory is modified to account for this essential feature of many structural models of labor force dynamics. Empirical estimates of an equilibrium two-state model of employment and non-employment are presented.     

Discrete-space agglomeration model with social interactions: Multiplicity,stability, and continuous limit of equilibria

This study examines the properties of equilibrium, including the stability, of discrete-space agglomeration models with social interactions. The findings reveal that while the corresponding continuous-space model has a unique equilibrium, the equilibrium in discrete space can be non-unique for any finite degree of discretization by characterizing the discrete-space model as a potential game. Furthermore, it indicates that despite the above result, any sequence of discrete-space models’ equilibria converges to the continuous-space model’s unique equilibrium as the discretization of space is refined.     

Local public goods in an equilibrium : How pecuniarv externalities matter

We study two Nash equilibria among a finite number of jurisdictions which maximize property values by providing public goods. In the first Nash equilibrium, the strategies are LPGs, financed by land taxes. We give conditions under which LPGs will be underprovided and show how this result is linked to price effects caused outside the jurisdiction. In the second Nash equilibrium, the strategies are LPGs and head taxes, with the budget balanced by land taxes. Jurisdiction-specific head taxes have incentive effects, whereas land taxes do not. In this case LPGs will be provided efficiently for the resident population.     

On Models with an Uncongestible Public Good and a Continuum of Consumers

This short note shows that models with an uncongestible or mildly congestible public good and a (non-atomic) continuum of consumers have an interesting but unfortunate property. Only an infinite level of public good provision in the continuum economy can be approximated by feasible public good levels in a sequence of economies with finite populations. We discuss the theoretical and practical problems this creates for familiar models that employ a continuum of consumers and a finite level of an uncongestible public good.     

Congestion,agglomeration, and the structure of cities

Congestion costs in urban areas are significant and clearly represent a negative externality. Nonetheless, economists also recognize the production advantages of urban density in the form of positive agglomeration externalities. The long-run equilibrium outcomes in economies with multiple correlated but offsetting externalities have yet to be fully explored in the literature. Therefore, I develop a spatial equilibrium model of urban structure that includes both congestion costs and agglomeration externalities. I then estimate the structural parameters of the model using a computational algorithm to match the spatial distribution of employment, population, land use, land rents, and commute times in the data. Policy simulations based on the estimates suggest that congestion pricing may have ambiguous consequences for economic welfare.     

Pure strategy equilibria in games with countable actions

In this paper, we extend the Radner–Rosenthal theorem with finite action spaces on the existence of a pure strategy equilibrium for a finite game to the case that the action space is countable and complete. We also prove the existence of a pure strategy equilibrium for a game with a continuum of players of finite types and with a countable and complete action space. To work with the countably infinite action spaces, we prove some regularity properties on the set of distributions induced by the measurable selections of a correspondence with a countable range by using the Bollobás–Varopoulos extension of the marriage lemma.     

Linear programming and locational equilibrium: The Herbert-Stevens model revisited

The paper reviews the early work of Herbert-Stevens in which linear programming was used to find a competitive equilibrium to an urban land market. First, it is demonstrated that a solution to the Herbert-Stevens model does not meet well-established criteria for an equilibrium. Secondly, a new linear programming model is suggested which is proven to achieve equilibrium if certain conditions are met. An iterative procedure for meeting these conditions is suggested, and an operational version of the model exhibits no problem in obtaining convergence. The revised model represents a feasible way of simulating urban land markets.