Housing and the Great Depression

Abstract

This article considers the structural stability of the relationship between the real housing price and real GDP per capita for an annual sample that includes the Great Depression. We test for structural change in parameter values using a sample of annual US data from 1890 to 1952. The article examines the long-run and short-run dynamic relationships between the real housing price and real GDP per capita to determine whether these relationships experienced structural change over the sample period. We find that temporal Granger causality exists between these two variables only for subsamples that include the Great Depression. For the other subsample periods as well as for the entire sample period, no relationship exists between these variables.

Keywords:

• Great Depression
• real house price
• real GDP per capita
• structural change

JEL Classification:

• C32
• E32
• R31

Acknowledgements

We gratefully acknowledge the helpful comments of two referees. We are responsible for any remaining errors.

Notes

¹ Shukur and Mantalos (1997) evaluate the power and size properties of eight different Granger-noncausality tests in standard and modified forms using Monte Carlo simulations, including the modification proposed by Toda and Yamamoto (1995) and Dolado and Lütkepohl (1996). The simulations indicate that the Wald test possesses the wrong size in small- and medium-sized samples. Shukur and Mantalos (2004) demonstrate that the RB bootstrap method improves the critical values, and the true size of the test approaches its nominal value in models with one to ten equations. Mantalos and Shukur (1998) examine the properties of the RB method in VAR models with cointegrated time series, discovering that the RB critical values prove more accurate than asymptotic ones, and tests based on the RB method also prove more robust. Further, Shukur and Mantalos (2000) explore the properties of various versions of Granger-causality tests and report that LR-tests with small sample correction exhibit relatively better power and size properties, even in small samples. They also document that all standard tests not based on the RB method perform poorly when no cointegration holds, especially in small samples. Mantalos (2000) compares bootstrap, corrected-LR and Wald causality tests and finds that the bootstrap test exhibits better power and size in all cases, regardless of whether the variables are cointegrated. Hacker and Hatemi-J (2006) show that the modified Wald causality test, proposed by Toda and Yamamoto (1995) and Dolado and Lütkepohl (1996), with critical values obtained from the RB bootstrap method exhibits much smaller size distortion compared to the tests based on the asymptotic distribution. Based on these findings, we use the RB-based modified-LR-statistics to examine the causality between the real house price and real GDP per capita in the United States.

² See footnote 1 for more details and references.

³ As the F-tests are easy to interpret, we can determine a single-break date in a fixed interval and possess some certain weak optimality against single-break alternatives, they gained popularity in the last two decades and have become the most preferred structural change tests in empirical studies.

⁴ In our empirical application, we have also calculated LM versions of the F-tests and results were qualitatively the same. LM-test results are available from the authors.

⁵ The results that use window parameters 0.20 and 0.30 are available from authors. They produce qualitatively similar findings to those reported in the empirical section.

⁶ We also perform the Elliott et al. (1996) DF-GLS-test for unit roots. These tests confirm the PP-test reported in Table 1. Results are available from the authors.

⁷ We also conduct the Engle and Granger (1987) cointegration test, and the findings support the Johansen’s results reported in the test. These results are available from the authors.

⁸ Although the full-sample tests indicated no cointegration, we do not rule out the possibility of cointegration in our recursive and rolling analyses. That is, some subsamples may suggest cointegration and other subsamples may not.

⁹ We also run an analysis with a window size of 25. The qualitative results did not change, although some changes did occur in the quantitative findings. These findings are available from the authors.

¹⁰ Figure 1 only reports the significance level and mean L₂ norm test for the VAR system and not for the individual equations.

¹¹ We reject parameter stability for both individual equations and VAR system, when we use sup norm. This implies that we cannot reject a temporary, but somewhat persistent, deviation from the normal parameter levels, but we can reject it against a single-break alternative.

¹² All references to recessions and expansions come from the National Bureau of Economics (NBER) Business Cycle Dating Committee.

¹³ The 5% critical values for the individual equations in the rolling and recursive specifications equal 2.2448 and 1.5444, respectively, which are not shown in the figure.

¹⁴ To do this, we estimate the VAR model in Equation 1 for a time span of 15 years rolling through t = τ – 14, τ – 12,…, τ, τ = 1905,…, 1952. Since we estimate a VAR(1) system, we lose one observation at the beginning of the sample, which explains why the first 15-year sample runs from 1891 to 1905.

¹⁵ Recall that our first 15-year sample period runs from 1891 to 1905. We report the findings for that sample at the mid-point of 15 years from 1891 to 1905, which is 1898. In other words, the point in the Figures for 1898 reports the value for the 1891–1905, a 15-year window.

¹⁶ One might consider using fractional integration and cointegration, since fractional integration intimately relates to parameter stability (Granger and Hyung, 2004). The Toda and Yamamoto (1995) approach, however, does not require cointegration, but just I(1) variables. Lack of cointegration also highlights long-run instability. So, with the existence of short-run instability as well, our analysis of doing rolling causality is well-motivated.