Error correction models are widely used in the housing literature to model US house price dynamics. Examples include Abraham and Hendershott (1996), Malpezzi (1999), and Capozza, Hendershott, and Mack (2004). Abraham and Hendershott (1996) use annual data for 30 metropolitan areas over the period 1977–1992 to investigate the determinants of real house price appreciation. The explanatory variables consist of three parts: the change in fundamental price, the lagged real house price appreciation with its coefficient called the “bubble builder,” and the deviation of house price from its equilibrium level in the previous period with its coefficient called the “bubble burster.” They find a positive bubble builder coefficient and a negative bubble burster coefficient. Moreover, the absolute values of these coefficients are higher for the coastal city group than for the inland city group.

Capozza, Hendershott, and Mack (2004) empirically study which variables explain the significant difference in the geographic patterns of the bubble builder and the bubble burster coefficients found in Abraham and Hendershott’s (1996) error correction specification. Using a panel dataset of 62 MSAs from 1979 to 1995, they find that higher real income growth, higher population growth, and a higher level of real construction costs increase the bubble builder coefficient, while higher real income growth, a larger population, and a lower level of real construction costs increase the absolute value of the bubble burster coefficient.

Abraham and Hendershott (1996) and Capozza, Hendershott, and Mack (2004) do not provide formal unit root and cointegration tests results to justify the existence of a long run equilibrium relationship among house prices and fundamental variables, which should be a prerequisite for the validity of error correction models.

Malpezzi (1999) uses a dataset which includes 133 MSAs and covers 18 years from 1979 through 1996 and states that short run real house price changes are well modeled by an error correction formulation. The panel unit root test of Levin, Lin, and Chu (2002, LLC test) is applied to real house price changes, the house-price-to-income ratio, and the residuals of the regression of real house prices on real per capita incomes. The first two are the dependent variables in Malpezzi’s error correction model. A unit root is rejected for price changes, but cannot be rejected for the price-to-income ratio. Moreover, a unit root is rejected for the residuals of the regression of real house prices on real per capita incomes, and hence Malpezzi concludes that real house prices and real incomes are cointegrated. This cointegration test procedure suffers from several shortcomings. First, before applying the cointegration test, Malpezzi does not examine if real house prices and income have a unit root, respectively. Second, critical values of the LLC panel unit root test have not been shown to work for residuals from the first stage regression, so the claim that house prices and incomes are cointegrated based on the LLC critical values could be misleading. Third, the LLC test does not allow cross-sectional dependence in the regression errors, hence the test result may be biased.

The 2000s’ US housing boom, which reached its peak in 2006, raises the question of whether US real house prices are supported by fundamentals; that is, whether real house prices and the fundamental economic variables such as income have a long run equilibrium relationship. The housing literature formalizes this argument by discussing the cointegration relationship among real house prices and the fundamental variables. Thus far, the results are mixed. Some papers such as Gallin (2006) and Mikhed and Zemcik (2009) apply cointegration tests and claim that there is no long run equilibrium relationship, which cast doubts on the validity of applying error correction models to US real house prices. Other papers argue that there is a cointegration relationship, such as Holly, Pesaran, and Yamagata (2010).

Gallin (2006) tests for the existence of a long run relationship among US house prices and economic fundamental variables by applying cointegration tests to both national level data and city level panel data. The augmented Engle-Granger cointegration test is applied to national level house prices, per capita income, population, construction wage, user cost of housing, and the Standard and Poor’s 500 stock index. No cointegration relationship is found. He also applies panel cointegration tests to city level house prices, per capita income, and population, for 95 MSAs over 23 years from 1978 to 2000. The panel cointegration tests he uses are Pedroni (1999) and Maddala and Wu (1999). He also applies a bootstrapped version of the tests to take into account cross-sectional dependence. The null hypothesis of no cointegration cannot be rejected, neither by the original tests nor the bootstrapped version. To test for a unit root, Gallin applies the ADF unit root test to the national level real house prices and a unit root is not rejected. But he does not provide panel unit root test result for the city level panel data.

Mikhed and Zemcik (2009) also examines if US house price and fundamental factors are cointegrated. The innovation in their paper is that they include more fundamental variables to avoid the possibility that the omission of potential demand and supply shifters cause the lack of cointegration relationships. The fundamentals included are house rent, a building cost index, per capita income, population, mortgage rate, and the Standard and Poor’s 500 stock index. Their sample includes 22 MSAs over 1978–2007, and they examine several different time periods (1978–2007, 1978–2006, 1978–2005, 1997–2007, 1978–1996). They apply the CIPS panel unit root tests to real house prices and the fundamental variables for all periods, setting the time lag in the CIPS test to 1 year. For real house prices, a unit root is rejected at the 5% level for 1978–2007 and rejected at the 10% level for 1978–2006, but cannot be rejected for other periods. The authors interpret this as a correction of the house price bubble around 2006. They further investigate the cointegration relationship of house prices and fundamentals for periods prior to 2005 when a unit root cannot be rejected in house prices. They apply the Pedroni (1999, 2004) panel cointegration test and bootstrap the critical values for possible cross-sectional dependence. No evidence of cointegration relationships is found in any of the cases. Hence they claim that US real house price dynamics are not explained by fundamentals, and this is evidence of housing bubbles in those subsamples.

Holly, Pesaran, and Yamagata (2010) study the determination of US real house prices using a panel of state level data (48 states, excluding Alaska and Hawaii and they include the District of Columbia) over 29 years from 1975 to 2003. Unlike Gallin (2006) and Mikhed and Zemcik (2009), Holly et al. find that real house prices and real income are cointegrated. The innovation of Holly et al. is that they apply the common correlated effects (CCE) estimators of Pesaran (2006) to study a panel of real house prices. They first use an asset non-arbitrage model to show that the ratio of real house price and real income should be stationary, hence the log of real house price and the log of real income should be cointegrated with a cointegration vector of (1, −1). Then they empirically find such a cointegration relationship and estimate a panel error correction model for the dynamics of adjustment of real house prices to real incomes.

Most of the above papers use time periods that end before 2006 and thus they do not include the recent US housing bust period in their sample. An exception is Mikhed and Zemcik (2009), which reports unit root tests for periods ending after 2006, and a unit root is rejected at the 5% level over 1978–2007 for real house prices. The authors then apply cointegration tests to the subperiods ending before 2006 where a unit root is not rejected. This is an ad hoc solution that does not address the issue of whether real house prices have a unit root or are stationary.

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