Factors leading to the U.S. housing bubble: a structural equation modeling approach

For the past decade, academics and practitioners have debated the existence of a housing bubble. Given the sharp declines in the housing market and the financial crisis, there is little doubt that a bubble occurred and then burst. Nevertheless, an important research question remains, what factors contributed to the creation of the bubble? This research addresses this issue by selecting well understood factors that traditionally drive the housing market and constructing a regression model to investigate the nature of the relationships. Because of the co-dependence of many of the factors, structural equation modeling (SEM) is used rather than traditional regression analysis. Using this technique addresses the difficulties presented by the high levels of multi-co-linearity present in many of the factors. Because all the variables used in our models are observable rather than latent, measurement model issues typical in most SEM analyses are not a concern. Keyword: Mortgage markets, housing bubble, financial crisis, housing market, mortgage rates Research in Business and Economics Journal Factors leading to the U.S. housing bubble, Page 2 INTRODUCTION The housing market suffered a severe decline over the past two and one-half years. Further, there is no question that values dropped anywhere from a modest ten percent in sTable markets to fifty percent in markets that were overheated. With large numbers of home owners still experiencing economic distress, more homes will undoubtedly be liquidated at below purchase prices, putting further downward pressure on housing prices. With hindsight, it is easy to conclude that housing prices have generally plummeted from lofty values, and therefore, a housing bubble must have occurred. However, the problem is more complex than that. Questions still remain as what factors created the housing bubble. Further, the answers to these questions lend insight into dynamics of one the most important consumer sectors of our economy. The authors of this paper will attempt to shed some light on these issues, using empirical data and a sophisticated methodology. Many factors have been suggested as contributing to the housing bubble, which began in approximately 1998, lasting until 2006. Consumer buying behavior was driven by forces, such as greed, the desire to live in a larger house, the need to build retirement assets, and desire to avoid “ineviTable” higher prices in the future. Market conditions also contributed to higher prices, because of pressure from increases in population, shifts in demographics, availability of easy credit, and the relaxation of lending standards. Economic factors of low inflation, rising salaries, and low interest rates also have been suggested as playing a significant role in driving up housing prices. This research addresses these issues by selecting well understood factors that traditionally drive the housing market and constructing a regression model to investigate the nature of the relationships. Because of the co-dependence of many of the factors, structural equation modeling (SEM) is used rather than traditional regression analysis. This technique deals with the high levels of correlation among the many of the factors driving the housing market. Because all of the variables used in our models are observable, measurement model issues typical in most SEM analyses are not a concern. REVIEW OF THE LITERATURE Behavior of the housing market has been the subject of a substantial research stream over the past decade. Kindleberger (1987) provided a definition of a housing bubble based on buyer’s expectation that many researchers have used as a starting point for their research. Some studies questioned the existence of the bubble, such as Himmelberg, Meyer, and Sinai (2005). Other studies, such as Mints (2007), Baker (2007), and Chambers, Carriga, and Schagenhauf (2008) and Chomsisengphet and Pennington-Cross (2006) focused on factors that drove the housing market. Case and Shiller (2003) studied what factors might cause a housing bubble and studied several diverse housing markets to validate their hypotheses. Mayer and Quigley (2003) added insights to the results of Case and Shiller (2003) and took issue with their over emphasis on the investment motive of buyers. For their research, Smith and Smith (2006) defined a bubble in financial terms rather than using Kindleberger’s approach, which focused on buyer’s expectations. A more extensive review of the literature can be found in Kohn and Bryant (2010). As discussed in Kohn and Bryant (2010), there has been considerable debate concerning the definition of a bubble, methods of detection of the bubble, and root causes of the bubble, if, in fact, it did exist. Using standard regression analysis, the authors determine that a bubble did Research in Business and Economics Journal Factors leading to the U.S. housing bubble, Page 3 occur, with significant differences between two examined periods, pre-bubble, 1988 to 1996, and bubble, 1997 to 2007. Also, there were important findings from this previous work. Using median asking prices as the dependant variable, seven independent variables were included in regression analysis. These variables were the consumer price index, housing inventory, 30-year conventional mortgage rates, personal income, population, vacancy rates, and median asking rents. Results show only two variables were retained in the pre-bubble model, personal income and vacancy rates. By comparison, the bubble-period analysis revealed only two of the seven were removed, the 30-year conventional mortgage rates and personal income. Both models exhibited high values of coefficients of determination. The authors note, however, that co-linearity was very high among independent variables in the bubble model, but not significant in the pre-bubble model. Results were clear and useable in that the research reveals that a bubble did occur and variables were significant in their effects on the housing market. As the authors state, “for research with a forecasting orientation, the strong co-linearity effects would be problematic. Since we are primarily interested in identifying indications of a housing bubble, the issue of co-linearity is not a consideration.”[1] Kohn and Bryant go on to point out that more sophisticated research techniques should be used to reduce the effects of co-linearity on model results. The current research takes that next step and uses SEM to resolve problems caused by co-linearity and to be able to confirm earlier findings. The current research takes a structural approach by modeling a set of commonly accepted factors that affect the housing market and attempt to determine what role, if any, they played in driving the housing market. By using SEM rather than traditional regression analysis, the complex nature of inter-dependencies of these variables can be more accurately analyzed. There are several indicators that can be used to reflect housing market behavior. The median asking price was used as a proxy for the house price boom, since it reflects the seller’s subjective expectations of the home’s value. In some sense, this variable also captures the element of greed that exists in all bubble situations, namely, sellers in any overheated market are driven by the prospect of substantial gains to demand even higher prices for their assets. This research will investigate the behavior of median asking prices to determine what factors did or did not play a significant role in explaining the behavior of housing prices. SEM models will also help determine if the substantial shift in the behavior of housing prices that occurred over the past two decades was reflective of a bubble. The collapse of the housing market and sharp declines in housing values may not necessarily be indicative of a housing bubble, since values of assets decline during deflationary periods. Case and Shiller (2003) suggest that a bubble “referred to a situation in which excessive public expectations of future price increases cause prices to be temporarily elevated.” Our definition of a housing bubble is based on a variation of Case and Shiller’s definition. A bubble occurs when the market price of any asset rises substantially above traditionally accepted values, as determined by historical behavior. By modeling a pre-bubble period and comparing it to a bubble period, differences between the two models can be studied to determine if they are structurally different. The pre-bubble period should reflect a more sTable market in which traditional factors contribute to a rise or fall of median asking prices. During the bubble period in which housing prices have been rising substantially, a different set of factors should influence housing prices. This structural approach may shed more light on the behavior of the housing market, and hence, whether a bubble did occur. Research in Business and Economics Journal Factors leading to the U.S. housing bubble, Page 4 HOUSING BUBBLE VARIABLES The model chosen is the same as in Kohn and Bryant (2010), since the current analysis is being used to verify and extend results. Median Asking Prices (MAP) is the dependent variable, while both supply and demand factors are used as independent variables for housing consumption. Data from the Federal Reserve, Freddie Mac, and US Census were compiled from monthly series, and quarterly data were converted to monthly values through interpolation. The following is a list of the variables and a brief explanation of their meanings: Independent variable: Median Asking Price (MAP) reflects sellers’ expectations of their homes’ values, as opposed to using a measure of final settlement price that might reflect rational market forces. Dependent variables: 1. Housing Inventory reflects the supply of housing in the market place. 2. Vacancy Rates captures unoccupied housing currently available, including new construction, which was obtained from US Census data. 3. Median Asking Rents (MAR) is used to reflect ownership as an alternative to renting. 4. On the demand side, population includes demographic effects on housing. 5. Consumer Price Index (CPI) is included as a demand variable to capture overall inflation effects. 6. Personal income (PI) is a measure of housing affordability. 7. The 30-year fixed mortgage rate is included as a variable on the demand side. HOUSING BUBBLE STRUCTURAL MODEL AND HYPOTHESES The research of Kohn and Bryant (2010) was based on the classical multiple regression model, namely one dependent variable driven by many independent variables. Typically, a central issue for this approach focuses on the correlation among the independent variables, giving rise to multi-co-linearity. In an application such as a study of the behavior of the housing market, these co-dependencies would be of paramount concern for accurately establishing the role played by each of the variables. It often becomes a central weakness of the analysis that can be partially overcome by a more thorough investigation of the correlations among independent variables. Given the variables in this study, it is not surprising to find such high levels of multi-colinearity, making traditional multiple regression analysis problematic. In fact, the very high levels of multi-co-linearity that were found in previous study of Kohn and Bryant (2010) severely limited the interpretation and implication of the regression coefficients. Problems arise from the fact that, while variables are classified as either independent or dependent, independent variables can be correlated. Further complications arise in more complex systems, because some variables play a dual role of simultaneously being dependent on one or more variables, while acting as independent variables in that they influence others. In this analysis, rather than use the term dependent and independent, we use exogenous and endogenous to signify the roles that variables can play. An exogenous variable is one that is not dependent on any other variables (though it may be correlated with another variable) and acts as the typical independent variable in regression analysis. Endogenous variables, on the other hand, have the dual role described above, simultaneously influencing and being influenced by Research in Business and Economics Journal Factors leading to the U.S. housing bubble, Page 5 other variables. This approach lays the foundation for a more realistic and complex model of system behavior. The variables that form the basis for our research fall into the categories of exogenous and endogenous, because they are highly correlated and interdependent. Using SEM allows us to more accurately represent the relationships among these variables. The robustness of this approach eliminates the issue of multi-co-linearity, because it incorporates this behavior into the structural model. Further, it allows for correlations between the variables to be represented. Thus, SEM addresses this particular weakness of multiple regression. SEM also addresses whether variables are observable or latent. An observable variable is directly measurable using an accepTable scale. Latent variables are not directly measurable and require the construction of a measurement model. This model must be tested and validated using confirmatory factor analysis before it can be used in SEM analysis. When SEM uses latent variables, another layer of analysis is needed to ensure that a sound theoretical basis exists for overall SEM analysis. In this study, no variables are latent, meaning that all the variables are directly observable. The lack of latent variables means that measurement models are not needed, and hence, the traditional issues of validation of the measurement models upon which many structural models rest is not an issue in this study. Thus for many reasons, SEM is the logical alternative to regression in dealing with the complexity and interdependence of the variables in understanding the behavior of housing prices. Another issue of primary importance in SEM analysis is the likelihood that the theory is validated by the empirical analysis. SEM is used as a confirmatory methodology for causal relationships. The use of the word “theory” in this context means a construct that has a wide acceptance as a correct explanation of the phenomenon. More specifically, causality has been demonstrated, and researchers wish to use empirical evidence as a demonstration of the theory. Much has been written about the philosophy of causality and the basis of causal models. The reader will find discussions of causality in Bolen (1989), Bullock, Harlow, and Mulaik (1994), and Hair, Anderson, Tatham, and Black (1984). This is in stark contrast to the use of traditional statistical analysis as an exploratory tool in which many proposed hypotheses might explain a set of data. Here the word “hypothesis” implies that a possible explanation has been suggested, but by no means is accepted, as the correct explanation. Causality is not assumed, and caveats are presented disclaiming cause and effect implications. Empirical data is used in conjunction with a variety of statistical tests to explore the validity of the hypothesis. Usually alpha and beta error in hypothesis testing of correlation and coefficient of determination in regression are typical measures to lend support to the likelihood of the hypothesis. SEM, on the other hand, has a large number of goodness-of-fit measures or indices to establish causality. These include chi-square goodness-of-fit, goodnessof-fit index (GFI), adjusted goodness-of-fit (AGFI), normed fit index (NFI), and root mean square residual (RMSR) to name a few. Bolen (1989) and Hair, Anderson, Tatham, and Black (1984) have extensive discussions of these measures. This research uses SEM as an exploratory methodology, since we are interested in studying the behavior of the housing market rather than confirming a proposed theory of market behavior. As such, fit indices are not useful to us. Rather we are interested in which factors can be shown to play a significant, statistically and explanatory, role in housing market behavior. Using SEM to determine which linkages belong in our models and coefficients of determination are sufficient indicators to establish how the housing market has evolved over the past 20 years. Research in Business and Economics Journal Factors leading to the U.S. housing bubble, Page 6 We based our structural model on commonly accepted relationships among the variables that influence housing prices. Generally it is accepted that Population drives Housing Inventories, Vacancy Rates, and the Median Asking Prices (MAP). The Consumer Price Index (CPI) drives Personal Income (PI), 30-Year Fixed Mortgage Rates, and MAP. Housing Inventory also drives Vacancy Rates, MAP, and Median Asking Rents (MAR). Finally, we propose that Vacancy Rates and MAR drive MAP. Population and CPI were treated as correlated variables. Thus, many of the variables are driven by one or more variables, and, in turn, drive other variables. Hence Population and CPI are exogenous while PI, Mortgage Rates, Housing Inventory, Vacancy Rates and Median Asking Rents are endogenous variables. Median Asking Prices is also endogenous but is strictly a dependent variable. These relationships result in a structural model shown in Figure 1.