Testing a hazard model for the housing market in New Orleans

I The Setting IT IS WIDELY ACCEPTED that operation of housing markets in New Orleans can be characterized by the following two facts: (1) real estate markets have identifiable normal or "structural" vacancy rates that differ between areas and seem related to market growth or levels of activity; (2) movements in vacancy around a market's structural rate determined by either supply or demand determine the "vacancy duration" for units that are for sale, which seems to trigger significant movements in market prices. The empirical research on which such observations might rest has been growing in recent years. Kaserman, Trimble, and Johnson (1989) and Guasch and Marshall (1985) have examined the duration of vacancy and its relationship to price determination. Mortensen (1982) studied the gradual "disequilibrium" that evolves between units and occupants, which leads the majority of market transactions that involve turnover of unit. What seems missing in the current literature is a perspective that may explain the relationship between "probability" of sale and market duration in a housing market. A search model from the labor market would seem particularly applicable to housing, and this is the objective of the present article. An assumption in matching models of fixed jobs and workers, for example, nicely fits the housing market's "stock-flow" character, in which prices adjust in the short run to equate demand to a fixed stock. This article employs a Weibull hazard model to examine the relationship between uncertainty in sale and market duration in the housing market and presents estimates of it on the basis of data from the housing market in New Orleans. The objective here is neither to contribute to search theory nor, except incidentally and in a limited way, to test it, but rather to contribute to the study of an efficient way to interpret duration data in the light of search theory. My goal is to promote our understanding of the housing market by constructing a formal model of the search-and-vacancy nexus. A real estate or a housing market cannot be adequately explained by standard economic theory that assumes certainty in sale. This study employs a search-theoretic approach to examining the housing market transactions in New Orleans and explains why the attributes that are important determinants of housing prices are not necessarily the important determinants of the probability of a sale. Empirical analysis of housing markets has so far focused on the heterogeneous nature of housing and the resulting consequences for price determination. Taking cue from the labor literature, the basic questions we ask are: How much time does a seller spend in making a sale of his house? How does the market duration of a house vary across individuals? We might specify a model, for example, in which every day that the seller looks for a buyer, he has the same probability, [lambda], of finding one. That is, conditional on not being able to find a buyer yesterday, the probability of finding a buyer today is [lambda]. Thus the sequence of conditional probabilities is constant. The probability that the seller will not find a buyer in exactly 100 days is f(100) = [lambda](1 - [lambda]) (99). Now, the assumption is strong that the probability of finding a buyer is the same every day. It seems probable that the conditional probability will vary due to increased search intensity or to a change in the reservation price acceptable to the seller. So the hazard probability for our model is the conditional probability a house is sold at time t, given that it has not sold prior to t. Thus, the hazard function summarizes the relationship between current market duration and probability of sale. Hazard functions specification emphasizes the conditional probabilities, while specification in terms of a probability distribution would emphasize unconditional probability. (1) The article is organized as follows: Section II considers the implications of a search theory for specification of hazard models; Section III describes the data and provides maximum likelihood estimates of the hazard model; and Section IV concludes the article with some policy implications. …