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A Primer on Piecewise Parabolic Multiple Regression Analysis via Estimations of Chicago CBD Land Prices

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  • Colwell, Peter F

Abstract

This article proposes a non-parametric method for estimating spatial price functions. Space is divided into squares. The independent variables are barycentric coordinates that uniquely describe the location of observations in space. The regression coefficients are estimates of the height of the function directly over the vertices of the square spatial units. Within each square the function has hyperbolic iso-price curves and parabolic sections. The price function is continuous, but not differentiable, at the boundaries between contiguous squares. This method is applied to the problem of describing the price per front foot of land in the Chicago CBD. A rather complex price surface is revealed that would be difficult to estimate using other methodologies but was easily estimated by this simple method. Copyright 1998 by Kluwer Academic Publishers

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  • Colwell, Peter F, 1998. "A Primer on Piecewise Parabolic Multiple Regression Analysis via Estimations of Chicago CBD Land Prices," The Journal of Real Estate Finance and Economics, Springer, vol. 17(1), pages 87-97, July.
    • Handle: RePEc:kap:jrefec:v:17:y:1998:i:1:p:87-97
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    Cited by:

    1. Steven C. Bourassa & Eva Cantoni & Martin Hoesli, 2005. "Spatial Dependence, Housing Submarkets, and House Prices," FAME Research Paper Series rp151, International Center for Financial Asset Management and Engineering.
    2. Enwei Zhu & Jing Wu & Hongyu Liu & Xindian Li, 2022. "Within‐City Spatial Distribution, Heterogeneity and Diffusion of House Price: Evidence from a Spatiotemporal Index for Beijing," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 50(3), pages 621-655, September.
    3. David Geltner & Anil Kumar & Alex M. Van de Minne, 2020. "Riskiness of Real Estate Development: A Perspective from Urban Economics and Option Value Theory," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 48(2), pages 406-445, June.
    4. Robert J. Hill & Alicia N. Rambaldi, 2022. "Hedonic Models and House Price Index Numbers," Springer Books, in: Duangkamon Chotikapanich & Alicia N. Rambaldi & Nicholas Rohde (ed.), Advances in Economic Measurement, chapter 0, pages 413-444, Springer.
    5. Robert J. Hill & Michael Scholz, 2014. "Incorporating Geospatial Data in House Price Indexes: A Hedonic Imputation Approach with Splines," Graz Economics Papers 2014-05, University of Graz, Department of Economics.
    6. Nichols, Joseph B. & Oliner, Stephen D. & Mulhall, Michael R., 2013. "Swings in commercial and residential land prices in the United States," Journal of Urban Economics, Elsevier, vol. 73(1), pages 57-76.
    7. Steven Bourassa & Eva Cantoni & Martin Hoesli, 2007. "Spatial Dependence, Housing Submarkets, and House Price Prediction," The Journal of Real Estate Finance and Economics, Springer, vol. 35(2), pages 143-160, August.
    8. Jamie Spinney & Pavlos Kanaroglou & Darren Scott, 2011. "Exploring Spatial Dynamics with Land Price Indexes," Urban Studies, Urban Studies Journal Limited, vol. 48(4), pages 719-735, March.
    9. W. Erwin Diewert & Chihiro Shimizu, 2022. "Residential Property Price Indexes: Spatial Coordinates Versus Neighborhood Dummy Variables," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 68(3), pages 770-796, September.
    10. Peter Colwell & Henry Munneke, 2009. "Directional Land Value Gradients," The Journal of Real Estate Finance and Economics, Springer, vol. 39(1), pages 1-23, July.
    11. Michael R. Mulhall & Joseph B. Nichols & Stephen D. Oliner, 2010. "Commercial and residential land prices across the United States," Finance and Economics Discussion Series 2010-16, Board of Governors of the Federal Reserve System (U.S.).
    12. Florenz Plassmann & T. Nicolaus Tideman, 2003. "A Framework for Assessing the Value of Downtown Land," Working Papers e07-5, Virginia Polytechnic Institute and State University, Department of Economics.
    13. JPeter F. Colwell & Henry J. Munneke, 2003. "Estimating a Price Surface for Vacant Land in an Urban Area," Land Economics, University of Wisconsin Press, vol. 79(1), pages 15-28.

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