Abstract
This paper applies a time-varying parameter vector autoregressive approach to estimate the relative effects of housing and stock returns on the growth rate of US consumption over time. We use annual data from 1890 to 2012 and find that at the 1- and 2-year horizons and over time, generally the housing return positively affects consumption growth while the stock return negatively affects it. For the 3- to 6-year horizons, the two return shocks generally exert a negative, but small, effect on consumption growth. These opposite responses to changes in housing and stock returns suggest different mechanisms through which wealth affects consumption. Further, the housing return effect generally increases after 1980. The sub-period from 1980 to 2012 includes the 1997/2002 asset price boom/bust where house prices continued to rise moderately as stock prices fell. These findings suggest that the magnitude of the relative return effects differs with both time and horizons and also depends on whether prices increase or decrease.
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Notes
This discussion in Ludwig and Sløk (2001) considers the effects of changes in stock and housing prices on consumption. Our empirical analysis examines the effects of house and stock returns, or the logarithmic differences in prices, on the growth rate of per capita real consumption.
See Aye et al. (2013) for a detailed discussion in this regard.
http://www.econ.yale.edu/~shiller/data.htm. A referee suggested that the Shiller data may exhibit some reliability issues. As a robustness check, we also collected annual data on the Standard and Poor’s 500 and Dow Jones Industrial Average indexes as well as per capita consumption data from the Federal Reserve Bank of St. Louis FRED® database from 1929 to 2012, where all data are deflated by the CPI. We redid our analysis with this shorter annual sample and report the results in the text. The findings differ between the two different stock price measures.
We use standard unit-root tests, namely, Augmented Dickey and Fuller (1981), Phillips and Perron (1988) Dickey and Fuller with Generalised Least Squares detrending (DF-GLS), and the Ng and Perron (2001) modified version of the PP (NP-MZt) to confirm that the log-levels of the three variables under consideration are integrated of order 1, i.e., I (1). Given nonstationary data, we also conducted the Johansen (1988, 1991) tests of cointegration. Both the Trace and Maximum Eigenvalue tests, however, do not reject the null of no cointegration, which, in turn, implies that our VAR in first differences does not need to account for error correction, and hence, is not misspecified. The unit-root and cointegration tests are available on request from the authors.
We find that all roots of the constant parameter VAR lie within the unit circle, implying stability.
The MCMC method assesses the joint posterior distributions of the parameters of interest based on certain prior probability densities that are set in advance. This paper adopts the following priors as found in Nakajima (2011): Σ β ∼ IW(25, 0.01I), (Σ a ) − 2 i ∼ G(4, 0.02), (Σ h ) − 2 i ∼ G(4, 0.02), where (Σ a ) − 2 i and (Σ h ) − 2 i are the ith diagonal of elements of Σ a and Σ h , respectively. IW and G denote the inverse Wishart and the Gamma distributions, respectively. We use flat priors to set initial values of time-varying parameters such that: \( {\mu}_{\beta_0}={\mu}_{a_0}={\mu}_{h_0}=0 \) and \( {\varSigma}_{\beta_0}={\varSigma}_{a_0}={\varSigma}_{h_0}=10\times I. \)
Geweke (1992) suggests comparing the first n 0 draws to the last n 1 draws, dropping out the middle draws, to check for convergence in the Markov chain. We compute the CD statistics as follows: \( CD=\left({\overline{x}}_0-{\overline{x}}_1\right)/\sqrt{{\widehat{\sigma}}_0^2/{n}_0+{\widehat{\sigma}}_1^2/{n}_1} \), where \( {\overline{x}}_j=\left(1/{n}_j\right){\displaystyle {\sum}_{i={m}_j}^{m_j+{n}_j-1}{x}^{(i)}} \), x (i) is the i th draw, and \( {\widehat{\sigma}}_j^2/{n}_j \) is the standard error of \( {\overline{x}}_j \) respectively for j = 0, 1. If the sequence of the MCMC sampling is stationary, it converges to a standard normal distribution. We set m 0 = 1, n 0 = 10,000, m 1 = 50,001, and n 1 = 50,000. \( {\widehat{\sigma}}_j^2 \) is computed using a Prazen window with bandwidth (B m ) = 500. The inefficiency factor is defined as 1 + 2 \( {\displaystyle {\sum}_{s=1}^{B_m}{\rho}_s} \), where ρ s is the sample autocorrelation at lag s and is computed to measure how well the MCMC chain mixes.
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Acknowledgments
We acknowledge an anonymous referee, Christiane Baumeister, and Jouchi Nakajima for many helpful comments. The usual disclaimer applies.
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Simo-Kengne, B.D., Miller, S.M., Gupta, R. et al. Time-Varying Effects of Housing and Stock Returns on U.S. Consumption. J Real Estate Finan Econ 50, 339–354 (2015). https://doi.org/10.1007/s11146-014-9470-3
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DOI: https://doi.org/10.1007/s11146-014-9470-3