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Bayesian Estimation of the Hierarchical SLX Model with an Application to Housing Markets

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Abstract

Hierarchical or multilevel models have long been used in hedonic models to delineate housing submarket boundaries in order to improve model accuracy. School districts are one important delineator of housing submarkets in an MSA. Spatial hedonic models have been extensively employed to deal with unobserved spatial heterogeneity and spatial spillovers. In this paper, we develop the spatially lagged X (or SLX) hierarchical model to integrate these two approaches to better understanding local housing markets. We apply the SLX hierarchical model to housing and school district test score data from Cincinnati Ohio. Our results highlight the importance of accounting for spatial spillovers and the fact that houses are embedded in school districts which vary in quality.

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Notes

  1. Brasington and Haurin (2006) confirms this result with more recent data and using spatial statistics as an identification strategy.

  2. We are indebted to him for creating this data set and making it freely available to other researchers. The full data set is available on his webpage at: http://homepages.uc.edu/~brasindd/housing.html.

  3. Some of the more recent papers in the real estate and urban economics literature that use this data set are Leguizamon (2010), Christafore and Leguizamon (2012), Leguizamon and Ross (2012), Christafore et al. (2013), Yinger (2015), Hall (2017), and Leguizamon and Leguizamon (2017).

  4. In the 2009 (and final) edition of Top Ten Charter Communities by Market Share, National Alliance for Public Charter Schools (2009) shows that 27% of public school students in Dayton attended charter schools, while the same number for Cincinnati was 15%.

  5. This highlights another important advantage of Brasington’s data set and Ohio as an institutional setting – the high degree of institutional variation in Ohio compared to other states. It would be very difficult to conduct a study of local government structure like Brasington (2004) in the South, for example, given how local government tends to be consolidated to the county level for historical reasons (Fischel 2009).

  6. Sales transacted for less than $30,000 are not included to remove non-arms-length sales and uninhabitable homes.

  7. We follow in the steps of Hayes and Taylor (1996), Clapp et al. (2008), and Chiodo et al. (2010) in using math scores as the primary educational measure in a hedonic regression.

  8. One common question on spatial econometrics applications refers to the choice of the weight matrix. The k–nearest neighbors, is a row–normalized, meaning that the sum of the rows of the spatial weight matrix sum to unity, and thus allowing for the pre–multiplication of an explanatory variable to obtain spatially–weighted explanatory variable. Inverse distance matrix, which are common in other spatial applications, does not allow for the row-normalization of the weight matrix since it destroys the idea of distance, and thus are not used in spatial econometric models.

  9. Hierarchical models often go by different terminology in education research. Multilevel, nested, and mixed models are all different terms applied to the same set of models.

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Authors and Affiliations

  1. Department of Economics, College of Business and Economics, West Virginia University, Morgantown, WV, 26056, USA

    Joshua C. Hall

  2. Texas Tech University, Box 41210, Lubbock, TX, 79409-1210, USA

    Donald J. Lacombe

  3. Regional Economic Research Institute, Florida Gulf Coast University, Fort Myers, FL, 33965-6565, USA

    Amir Neto

  4. Washington Center for Real Estate Research, Runstad Department of Real Estate, College of Built Environments, University of Washington, Box 355726, 224 Gould Hall, Seattle, WA, 98195-5726, USA

    James Young

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  1. Joshua C. Hall
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  2. Donald J. Lacombe
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  3. Amir Neto
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  4. James Young
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Correspondence to Joshua C. Hall.

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Hall, J.C., Lacombe, D.J., Neto, A. et al. Bayesian Estimation of the Hierarchical SLX Model with an Application to Housing Markets. J Econ Finan 46, 360–373 (2022). https://doi.org/10.1007/s12197-021-09568-2

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