Regression Analysis
The paper by Campell et al., (2009) tries to examine time-series fluctuations in the prices of houses as well as the housing returns by use of tools that have been proved successful in the characterization of the nature of performance in the bond and stock markets. The authors show that the ratio of house rents to house prices (called the ”rent–price ratio”) must equal the present discounted value of future expected housing service flows, as well as the future expected returns to house assets. This model is called the dynamic version of the Gordon growth model in financial literature. It improves the researcher’s assessments of the study variables and aids in making an informed conclusion.
The model applies to a housing market in 23 metropolitan areas in the United States, four census regions, and the entire nation from 1975 to 2007. The dependent variables, as in equations 18, 19, and 20, are as follows: real rate ( ), the real growth rate of rents ( ), and the housing premium ( ), respectively (where is time in years). The first lags of real rent growth rate ( ), housing premium ( ), and actual rate ( ), are the independent variables while the second lags of real per-capita income growth ( ), employment growth ( ), and population growth ( ).
In table 4 (which provides estimates of vector auto-regression (VAR) model in equations 18, 19, and 20), the coefficients in the middle panel (real growth rate of rents) are statistically significant at 5% level of significance. It means the researcher rejects the outcome by applying the Wald test of no predictability. The independent variables explain the lagged real growth rate ( ), a median of 39% of the full sample coefficient of variation ( ). In comparison, the independent variables explain the coefficient of variance in the interquartile range of between 25% and 45% of the full-samples.
Reference
Campbell, S. D., Davis, M. A., Gallin, J., & Martin, R. F. (2009). What moves housing markets: A variance decomposition of the rent–price ratio. Journal of Urban Economics, 66(2), 90-102. https://doi.org/10.1016/j.jue.2009.06.002