A Simple Test of σ-Convergence in U.S. Housing Prices across BEA Regions

Abstract

Abstract. This study probes the convergence of housing prices at the regional and the state levels. Regional classification follows the Bureau of Economic Analysis (BEA) designation of eight regions using quarterly data from 1975:1 to 2012:3. The statistical approach employed is Iƒ-convergence, where regional and state variances are computed for testing the hypotheses. The results indicate that housing prices in nine states converge to the overall U.S. housing prices while the remaining forty-one states fail to do so. At the regional level, housing prices in the Great Lakes, Plains, Southeast, Rocky Mountains, and Southwest regions diverge from overall U.S. housing prices, while housing prices in New England, Mideast, and Far West tend to converge.(ProQuest: ... denotes formulae omitted.)1. IntroductionConvergence, according to Angulo et al. (2001), is the tendency toward equalization, for instance, among countries, regions, or states. Tools devised to measure convergence rely on measures known as absolute ?-convergence, which is based on regres- sion analysis, and Iƒ-convergence, which is based on dispersion analysis. Other competing hypotheses of convergence, as pointed out by Galor (1996), are conditional ?-convergence and club convergence. In the former case, entities with identical structural characteristics converge to one another over time, irrespective of their initial conditions. In the latter case, entities converge to one another provided that their initial conditions are the same. In a broader sense, as Doyle (1997) and O'Leary (1997) state, con- vergence implies a process by which economic vari- ables display narrow dispersion (Iƒ-convergence). Hotelling (1933) argues that the tendency towards convergence is consistent with the diminution of variance, unlike what Friedman (1992) calls the con- vergence through regression fallacy.The focus of this study is to investigate Iƒ- convergence to determine whether housing prices across the states and economic regions (as defined by the Bureau of Economic Analysis, BEA) converge based on the conjecture that the rise or collapse of the housing market may affect U.S. states and eco- nomic regions differently. Indeed, in the aftermath of the housing market collapse, as noted by Santos (2012), the number of homes with outstanding mortgage balances reached 55 million, amounting to some $9.5 trillion. Housing prices declined in the range of 20 percent to 40 percent due to the recent recession (i.e., the so-called Great Recession), caus- ing some 10 million borrowers to default on their home loans. Additionally, about 22 percent of homeowners owe more on their homes than the homes are worth (underwater). And, although in- terest rates are low by historical standards, due to expansionary monetary policies, the housing market has been relatively slow to recover. Focusing on the period immediately leading up to the housing mar- ket collapse, Cohen et al. (2012) find that housing prices rose substantially on the east and west coasts, due in large measure to the appreciation in land values rather than the physical housing structure, much more so than the interior region of the U.S. For instance, in Los Angeles, San Diego, and Miami, housing prices tripled. In the bust, the decline in Las Vegas, Phoenix, and Miami was 50 percent or more.While there have been a number of studies inves- tigating the convergence of U.S. regional housing prices, as the following literature review will show, we undertake a straightforward analysis of variance approach that examines the variance of housing prices at the state level within regions defined by the Bureau of Economic Analysis (BEA) in testing for Iƒ-convergence across BEA regions. In other words, we explore whether states partitioned in accordance with the BEA classifications converge or diverge from the national trends.Section 2 discusses the literature with respect to U.S. studies on regional housing price convergence. …