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Erschienen in: The Journal of Real Estate Finance and Economics 2/2019

08.01.2018

Spatial Dependence in the Residential Canadian Housing Market

verfasst von: Yuan Zhang, Yiguo Sun, Thanasis Stengos

Erschienen in: The Journal of Real Estate Finance and Economics | Ausgabe 2/2019

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Abstract

This paper studies the spatial dependence of residential resale housing returns in ten major Canadian Census Metropolitan areas (or CMAs) from 1992Q4 to 2012Q4 and makes the following methodological contributions. Firstly, in the context of a spatial dynamic panel data model we use grid search to derive the appropriate spatial weight matrix W among different possible specifications. We select the compound W with the minimum root mean squared error formed from geographical distances and the ten CMAs’ gross domestic product. Secondly, contrary to common practice in the literature, we decompose the impacts of explanatory variables into direct and indirect impacts and proceed to derive and plot the impulse response functions of housing returns to external shocks. The empirical results suggest that Canadian residential housing markets exhibit statistically significant spatial dependence and spatial autocorrelation and that both geographical distances and economic closeness are the dominant channels of spatial interaction. Furthermore, the special feature of the Canadian housing market is that the responses to the shocks do not spread widely across regions and that they fade fast over time.

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Fußnoten
1
Canada Mortgage and Housing Corporation (or CMHC) Canadian Housing Observer 2012.
 
2
Another available housing price measure is the Multiple Listing Services (MLS\(^{{\circledR }}\)) conducted by Canadian Real Estate Association (or CREA). However, the MLS\(^{{\circledR }}\) index are not quality adjusted. Holios and Pesando (1992) discussed some shortcomings of MLS\(^{{\circledR }}\) index, including mix of units sold varies over time, so that the ’quality’ of dwelling units sold is not held constant; the short-run signals regarding price movements often diverge; and the MLS index suggests a more rapid rate of price escalation.
 
3
Detailed definition of bungalow and two-story executive can be found in Glossary of Housing Types of Royal LePage House Price Survey.
 
4
See Appendix A for the detailed list of selected 10 CMAs and their geographical locations. A CMA is a larger area than a city as it also includes municipalities adjacent to the city urban core. Geographic definitions used by Royal LePage is slightly differ from those used by Statistics Canada. However, it is the closest data available.
 
5
More specifically, we use annual CMA-level household income divided by the annual national level household income, and we assume this ratio remain constant in a given year. Then, we use this ratio multiplied by the quarterly national level income to get the quarterly CMA-level household income.
 
6
In most applied spatial econometrics, the same spatial weight matrix is used in both spatial lags of dependent variable and disturbances. We tried to estimate our model with different weight matrices in spatial lags and spatial errors, yet the results did not change much. This indicates that spatial dependence of housing returns and spatial autocorrelation in disturbances comes from a similar channel.
 
7
We thank the anonymous referee for clarifying this point.
 
8
We also tried to construct economic weight matrix using the negative exponential function. However, in those cases we ran into computational problems and as such we only use the inverse distance weighting function to construct the economic weight.
 
9
The variable movi,j includes all people lived in different address 5 years before the census year, regardless of where did they moved. While the other variable in Eq. 6migi,j only counts the number of people moved between CMA i and j specifically, and it does not include the population growth from immigrants and external migrants. These two variables are different, and we think they are both important to be used to explain the spatial dependence of housing returns.
 
10
The absolute value of eigenvalues of the matrix \(\hat {\lambda }W\) are 0.7984, 0.2289, 0.1600, 0.1548, 0.1180, 0.1010, 0.0984, 0.0712, 0.05338, and 0.0147. The absolute value of eigenvalues of the matrix \(\hat {\rho }W\) are 0.9916, 0.2843, 0.1987, 0.1922, 0.1465, 0.1254, 0.1222, 0.0885, 0.0663, and 0.0183. All absolute eigenvalues are less than 1, which ensures our spatial system is stationary. Equation 21 in Appendix C shows the overall impacts of spatial interactive relations on the housing returns.
 
11
It is worth noting that the weight matrices used in spatial models are typically assumed to be exogenous. However, the exogeneity assumption may not be reasonable. Kelejian and Piras (2014) discuss an estimation method with an endogenous weight matrix. Similarly, in Case et al. (1993), many of the weight matrices used to capture economic similarities are likely to be endogenous. In our case we also use weight matrices based on economic factors, yet the finally selected W in Eq. 12 formed by geographical distances and the real GDP levels is taken to be exogenous as geographical factors and GDP levels are taken as given. In that sense, the issue of endogeneity that we face may not be as severe. Given the complexity of our approach for arriving at the final choice of the weight matrix based on a data driven grid search method, we leave any issue of endogeneity for future research.
 
12
The magnitude of one standard deviation of population growth in each CMA is listed in last column of Table 7.
 
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Metadaten
Titel
Spatial Dependence in the Residential Canadian Housing Market
verfasst von
Yuan Zhang
Yiguo Sun
Thanasis Stengos
Publikationsdatum
08.01.2018
Verlag
Springer US
Erschienen in
The Journal of Real Estate Finance and Economics / Ausgabe 2/2019
Print ISSN: 0895-5638
Elektronische ISSN: 1573-045X
DOI
https://doi.org/10.1007/s11146-017-9623-2

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