PDF Ebook Rational Expectations in Urban Economics
Canonical analysis of the classical general equilibrium model demonstrates the existence of an open and dense subset of standard economies that possess fully revealing rational expectations equilibria. This paper shows that the analogous result is not true in urban economies. An open subset of economies where none of the rational expectations equilibria fully reveal private information is found. There are two important pieces. First, there can be information about a location known by a consumer who does not live in that location in equilibrium, and thus the equilibrium rent does not reflect this information. Second, if a consumer’s utility depends only on information about their (endogenous) location of residence, perturbations of utility naturally do not incorporate information about other locations conditional on their location of residence. Existence of a rational expectations equilibrium is proved. Space can prevent housing prices from transmitting information from informed to uninformed households, resulting in an inefficient outcome.
People can never fully comprehend the quality and the circumstances of a city until they experience a significant part of their life living in that city. Information on physical amenities of a city (i.e., weather, parks, museums, crime, traffic jams) is easily acquired by both consumers and researchers, so there is institutional and academic work on the quality of life in cities.1 However, people cannot completely ensure that they choose the right city or location within the city for their family before they start experiencing life there. For example, there could be uncertainty about the quality of schools, congestion of commuting routes contingent on resident and business location, or even major highway closures. Current occupants of the city, or people with friends living in the city, might have information that others don’t have. Moreover, even though the current environment of the city can be understood, it is not surprising that the future developments of cities are not known with certainty, but might be known better by current occupants.
On the one hand, information about life in a city is reflected in the demand for and thus the price of housing in the city.3 Since people are rational in understanding and using the relationship associating a specific state of nature with a specific equilibrium price, depending on what model people have in mind for how equilibrium prices are determined, the price of housing can be a signal for people in choosing a city best suited to their life style. Recall that the concept of rational expectations equilibrium requires agents to use models that are not obviously controverted by their observations of the market. Therefore, the question of whether the price of housing can play a significant role in transmitting information from informed people to uninformed people not only addresses the question of the efficiency of housing
markets, but is also related to the issue of the existence of rational expectations equilibrium in urban economics.
Available information is utilized by agents in a rational expectations equilibrium, especially the information conveyed by equilibrium prices. Radner (1979) shows that in a particular asset trading model, if the number of states of initial information is finite then, generically, rational expectations equilibria exist where all traders’ private initial information is revealed. In contrast to Radner’s model, that fixes state-dependent preferences and then focuses on the information concerning traders’ conditional probabilities of various events, Allen (1981) considers a space of economies that is defined by statedependent preferences and confirms Radner’s conclusion in that context. When state space is infinite, Allen (1981) shows that the generic existence of fully-revealing rational expectations equilibria depends on the condition that the price space must have at least as high a dimension as the state space. Jordan (1980) considers a model where information revealed by endogenous variables can be affected by expectations, and then characterizes the data that allow the generic existence of rational expectations equilibria. Jordan concludes that unless the public prediction is based on a very narrow class of data, a statistically correct expectation may fail to exist even for otherwise well-behaved economies.
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