Estimating the housing price with a search-and-matching model

Abstract

Purpose – This paper aims to pose an important starting point for the application of the search-and-matching models to real estate appraisals, thus reducing the “gap” between practitioners and academicians. Due to relevant trading frictions, the search-and-matching framework has become the benchmark theoretical model of the housing market. Starting from the large related literature, this paper develops a simplified approach to modelling the frictions that focuses on the direct relationship between house price and market tightness (a common feature only for the labour market matching models). The characterization of the equilibrium through two main variables simplifies the analysis and allows using the theoretical model for empirical purposes, namely, the real estate appraisals. Design/methodology/approach – This work is both theoretical and empirical. Theoretically, a long-run equilibrium model with a positive share of vacant houses and home seekers is determined along with price and market tightness. Also, the conditions of existence and uniqueness of the steady-state equilibrium are determined. Unlike most of the search-and-matching models in the housing literature, the out-of-the steady-state dynamics are also analyzed to show the stability of the equilibrium. Empirically, to show the usefulness of the theoretical model, a numerical simulation is performed. By using two readily available housing market data – the expected time on the market and the average number of trades – it is possible to determine the key variables of the model: price, market tightness and matching opportunities for both buyers and sellers. Although the numerical simulation concerns the Italian housing market, the proposed model is generally valid, being empirically applicable to all real estate markets characterized by non-negligible trading frictions. Indeed, the proposed model can be used to compare housing markets with different features (concerning the search and matching process), as well as analyse the same housing market in different time periods (because the efficiency of the search and matching process can change). Findings – Several important results are obtained. First, the price adjustment – i.e. the difference between the actual selling price and the price obtained in an ideal situation of frictionless housing market – is remarkable. This means that the sign and the size of the price adjustment depend on the extent of trading frictions in the housing market. Precisely, the higher the trading frictions on the demand side (more buyers and less sellers), the higher the actual selling price (the price adjustment is positive), whereas the higher the trading frictions on the supply side (less buyers and more sellers), the lower the actual selling price (the price adjustment is negative). Accordingly, the real estate appraisers should assess the trading frictions in the housing market before determining the price adjustment. Second, an increase in the number of trades affects the house price only if the time on the market varies. Also, the higher the variation in the time on the market, the larger the house price adjustment. Indeed, the expected time on the market reflects the opportunities to matching for both parties and thus the trading frictions. If the time on the market increases (decreases), the seller will receive less (more) opportunities to match; thus, the actual selling price will be driven downwards (upwards). Originality/value – As far as the authors are aware, none of the existing works in the search and matching literature has considered how to take advantage of this theoretical approach to estimate the house price in the presence of trading frictions in the housing market. Indeed, the proposed theoretical model may be a useful tool for real estate appraisers, as it is able to derive the trading frictions from the time on the market and the number of trades, thus estimating properly the house price.