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Directional Land Value Gradients

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Abstract

The standard urban model supports the concept of a constant land price gradient throughout the urban area. It is a reasonable conjecture that the land price gradient would vary with direction from the CBD. The variation in the gradient could be caused by a number of factors, but the idea that the land price gradient is flatter along radial transportation routes than in other directions is widely recognized even though there is little rigorous empirical work supporting this belief. This paper will examine the structure of urban land prices with a focus on the land price gradient as a function of the direction around the center of the city using a piecewise linear function. The added flexibility in the gradient estimate gained by this approach reveals a dramatically varying directional land price gradient.

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Notes

  1. Haas (1922) has been credited with conducting the first formal empirical study related to gradients using land values using a regression analysis. Haas examined agricultural land prices with a particular focus on distance to the city center and city size using a simple linear model (see Colwell and Dilmore 1999 for further discussion of Haas’ contribution).

  2. In addition to regressing the log of unit price on the distance from the city center and the log of unit price on the log of the distance from the CBD, Mills also estimated the land price function as a linear model which is less theoretically and empirically appealing.

  3. Alperovich and Deutsch (2002) used a similar approach for estimating population densities in Tel-Aviv.

  4. Cameron (2006), within the context of measuring localized environmental disamenities, also proposed an estimation technique to analyze continuously varying directional gradient using periodic functions (similarly to Cheshire and Sheppard 1995). The author showed that within the context of a hedonic house price model failure to account for directional gradients effects can obscure the measured effect of distance. The distance portion of the hedonic house price model includes a logarithmic measure of distance (d i ), an interaction term between distance and the cosine function (d i cos(q i )), as well as an interaction term between distance and the sine function (d i sin(q i )). Note that q i is the direction from the site to the ith house site measured in radians from due east (counter clockwise). The specification results in a single period (i.e., a Dromedarian assumption); one peak and one valley (directionally) over the entire 360°. In addition, the estimated gradient increases in amplitude with increased distance from the site. While the use of a more general form of the periodic functions is discussed, the added flexibility would require non-linear estimation and suffer from many of the same problems as the simple periodic function used, as well as a few new ones. For example, if the periodic functions are rewritten to be d i cos(Kq i ) and d i cos(Kq i ), allowing for K peaks and valleys, a discontinuity at ends of the gradient function will be introduce if K is not constrained to be an integer. In addition, this modification would more than likely introduce peaks and troughs where they do not exist.

  5. For examples of kernel approaches used explaining land values, see McMillen 1996, Meese and Wallace 1991, Thorsnes and McMillen 1998, Yatchew 1998. Pace 1993, 1995 also apply kernel nonparametric regression estimators. An alternative to kernel methods is piecewise parabolic, see Colwell 1998 and Colwell and Munneke 2003.

  6. Colwell and Sirmans (1978, 1980) assert a non proportional relationship between value and lot area exists when the cost of assembling or subdividing parcels is recognized. A persistent nonlinear pricing relationship is possible when the traditional assumption of zero transaction costs is relaxed. It seems reasonable to conclude that in land markets, a developer assembling or sub-dividing parcels will suffer transaction (conversion) cost. If this developer is operating in a perfectly competitive world, these transaction costs are fully recouped leading to a non-proportional pricing relationship.

  7. There is overwhelming empirical evidence of a concave function between urban land price and parcel size over time and across different markets. For example, see Brownstone and DeVany (1991), Colwell and Munneke (1997), Colwell and Scheu (1994), Isakson and Ecker (2001), McMillen and McDonald (1989, 1991), and Munneke (1996). There is an alternative viewpoint, termed the Mickey Mouse Problem by Oi (1971), that land prices are linear with a vertical intercept reflecting the price of entry into a community. It is not clear how, if this alternative viewpoint was true, Colwell and Munneke (1999) could have found essentially linear pricing with zero intercept in downtown Chicago. It is not obvious why the price of entry into a community is not proportional to land area instead of a lump-sum.

  8. McMillen and McDonald (1991) noted that if the zoning classification of a parcel is based on the relative price of a parcel in alternative classifications, selection bias should be observed in the estimation of the land price equation. They note that this point is relatively easy to show for a simple two land use case by defining the price function for the two land uses as P 1i = ω 1 x 1i + e 1i and P 2i = ω 2 x 2i + e 2i . If the equation that determines a parcel’s land use can be written as:

    $$ \Psi _i = \delta \left( {P_{1i} - P_{2i} } \right) - \varepsilon _i $$

    and the price equations are substituted into this land use equation, the resulting reduced form equation can be written as:

    $$ \begin{array}{*{20}c} {\Psi _i = \delta \;\,\left( {\omega _1 x_{1i} - \omega _2 x_{2i} } \right) + \delta \;{\kern 1pt} \left( {e_{1i} - e_{2i} } \right) - \varepsilon _i } \\ {\Psi _i = \theta _i \;z_i - \eta _i {\kern 1pt} {\kern 1pt} .} \\ \end{array} $$

    Clearly, the error term of the reduced form equation,\(\eta _i = \varepsilon _i - \delta \left( {e_{1i} - e_{2i} } \right)\), is a function of the error terms of the price equations (i.e., selection bias is present).

  9. The idea of a sample of sold properties not representing the population of properties is not a new concept. Case et al. (1991), Gatzlaff and Haurin (1997, 1998) Haurin and Hendershott (1991), and Munneke and Slade (2000) examine the bias related to examining a sample of sold properties. The sample available to the authors does not allow for the estimation of this correction.

  10. Specifically, the data are drawn from Cook County, Illinois.

  11. This simplification is an artifact of the how the data was initially recorded, by property identification number vs street address.

  12. The definition of a high concentration of open space devoted to conservation arose from an analysis of the residential model’s error term in absence of this measure. Spatially correlated errors were found in several locations near areas of dense conservation open space. The addition of this variable to the analysis removed the measurement error.

  13. More precisely, O’Hare Airport’s location is defined as the center of the northwest quarter of section 8 of Township 40N and Range 12E.

  14. Recall that it is necessary to consider the potential for sample selection bias in the estimation of the land price equations for the individual land uses. The standard two-step procedure to consider this potential bias, outlined in Lee (1982), calls for the introduction of a selection variable (inverse Mills ratio) to the land price equation as an explanatory variable. The selection variables are constructed from the estimates of a multinomial logit model with, in our case, the dependent variable representing the three zoning classifications (residential, commercial, and industrial).

  15. See Brownstone and DeVany (1991), Colwell and Munneke (1997), Colwell and Scheu (1994), Isakson and Ecker (2001), McMillen and McDonald (1989, 1991), and Munneke (1996).

  16. For comparison, we have imposed the non-directional gradient variable specification to our data, the price gradient for the full sample is estimated to be −0.0325 and the non-directional gradients are −0.0294, −0.0392, and −0.0309 for the residential, commercial, and industrial land uses, respectively.

  17. The impact of introducing directional variability into the measurement of the gradient base on the traditional unit price model, while not directly related to this study, provides additional evidence of the impact of relaxing the proportionality assumption in the price-lot area relationship. To obtain the unit price equation, simply set g in Eq. 2 equal to one and divide both sides by lot area (A). The estimation results of this model show a substantially steeper price gradient than revealed in the unconstrained model presented in the paper. For the full sample, the significant gradient parameters range from −0.07902 to −0.16339. Each gradient parameter is statistically significant with the exception of the due north parameter. In the individual land use models, all of the gradient parameters are significant with the exception of the end point rays. The significant gradient parameters from the individual land use models range from −0.09122 to −0.16602 for residential, −0.05236 to −0.13817 for commercial, and −0.07600 to −0.20439 for industrial. The gradient magnitude is 1.5–3.0 times greater on average in the unit price model than its equivalent counterpart in the unconstrained model presented in this paper. The resulting land price surface has less variation with distance (is less star shaped) than in the unconstrained model.

  18. An alternative to the estimation of a spatial error surface is to include a spatially correlated error term in the model. Basu and Thibodeau (1998), Gelfand et al. (2004), and Ecker and Isakson (2005) are a few examples of studies implementing such an approach.

  19. It should be noted that the error model was estimated based on a five mile grid pattern. In estimating the model, the omitted vertex was chosen such that the intercept would not be significantly different from zero. Thus, if a vertex coefficient was found to be significantly different from zero, the area near the vertex was searched for clusters of correlated errors. As noted in the text, variables were then formulated to remove the error.

References

  • Alperovich, G., & Deutsch, J. (2002) An application of a switching regimes regression to the study of urban structure. Papers in Regional Science 81:83–98

    Article  Google Scholar 

  • Basu, S., & Thibodeau, T. G. (1998). Analysis of spatial correlation in house prices. Journal of Real Estate, Finance and Economics 17(1):61–85.

    Article  Google Scholar 

  • Brownstone, D., & DeVany, A. (1991). Zoning, returns to scale, and the value of undeveloped land. Review of Economics and Statistics 73(4):699–704.

    Article  Google Scholar 

  • Cameron, T. A. (2006). Directional heterogeneity in distance profiles in hedonic property value models. Journal of Environmental Economics and Management 51:26–45.

    Article  Google Scholar 

  • Case, B., Pollakowski, H., & Wachter, S. (1991) On choosing among house price index methodologies. AREUEA Journal, 19(3):286–307.

    Google Scholar 

  • Cheshire, P., & Sheppard, S. (1995). On the price of land and the value of amenities. Economica, 246(62):247–267.

    Article  Google Scholar 

  • Colwell, P. 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 , 17(1):87–97, Special Issue on Spatial Econometrics.

    Article  Google Scholar 

  • Colwell, P. F., & Dilmore, G. (1999). Who was first? An examination of an early hedonic study. Land Economics, 75:620–626.

    Article  Google Scholar 

  • Colwell, P. F., & Munneke, H. J. (1997). The structure of urban land prices. Journal of Urban Economics, 41:321–336.

    Article  Google Scholar 

  • Colwell, P. F., & Munneke, H. J. (1999). Land prices and land assembly in the CBD. Journal of Real Estate Finance and Economics, 18(2):163–180.

    Article  Google Scholar 

  • Colwell, P. F., & Munneke, H. J. (2003). Estimating a price surface for vacant land in an urban area. Land Economics, 79(1):15–28.

    Article  Google Scholar 

  • Colwell, P. F., & Scheu, T. (1994) A history of site valuation rules. Journal of Real Estate Research 9:353–68

    Google Scholar 

  • Colwell, P. F., & Sirmans, C. F. (1978). Area, time, centrality, and the value of urban land. Land Economics, 54:514–519.

    Article  Google Scholar 

  • Colwell, P. F., & Sirmans, C. F. (1980). Nonlinear urban land prices. Urban Geography, 1:141–152.

    Google Scholar 

  • Ecker, M. D., & Isakson, H. R. (2005). A unified convex-concave model of urban land values. Regional Science and Urban Economics, 35(3):265–277.

    Article  Google Scholar 

  • Gatzlaff, D., & Haurin, D. (1997). Sample selection bias and repeat-sales index estimates. Journal of Real Estate Finance and Economics, 14:33–50.

    Article  Google Scholar 

  • Gatzlaff, D., & Haurin, D. (1998). Sample selection and biases in local house value indices. Journal of Urban Economics, 43:199–222.

    Article  Google Scholar 

  • Gelfand, A. E., & Ecker, M. D., Knight, J. R., & Sirmans, C. F. (2004). The dynamics of location in home prices. The Journal of Real Estate Finance and Economics, 29(2):149–166.

    Article  Google Scholar 

  • Haas, G. (1922). Sales prices as a basis for farm land appraisal. The University of Minnesota Agricultural Experiment Station, St. Paul. Technical Bulletin 9.

  • Haurin, D., & Hendershott, P. (1991). House price indexes: Issues and results. AREUEA Journal, 19(3):259–269.

    Google Scholar 

  • Isakson, H. R., & Ecker, M. D. (2001). An analysis of the influence of location in the market for undeveloped urban fringe land. Land Economics, 77(1):30–41.

    Article  Google Scholar 

  • Kau, J. B., & Sirmans, C. F. (1979). Urban land value functions and the price elasticity of demand for housing. Journal of Urban Economics, 6(1):112–121.

    Article  Google Scholar 

  • Lee, L. F. (1982). Some approaches to the correction of selectivity bias. Review of Economic Studies, 49:355–372.

    Article  Google Scholar 

  • Lee, L. F., Maddala, G. S. & Trost, R. P. (1980). Asymptotic covariance matrices of two stage probit and two stage tobit methods for simultaneous models with selectivity. Econometrics, 48:491–503.

    Article  Google Scholar 

  • McMillen, D. P. (1996). One hundred fifty years of land values in Chicago: A Nonparametric Approach. Journal of Urban Economics, 40:100–124.

    Article  Google Scholar 

  • McMillen, D. P., & McDonald J. F. (1989) Selectivity in urban land value functions. Land Economics 65:342–351

    Google Scholar 

  • McMillen, D. P., & McDonald, J. F. (1991). Urban land value functions with endogenous zoning. Journal of Urban Economics, 29(1):14–27.

    Article  Google Scholar 

  • Meese, R., & Wallace, N. (1991). Nonparametric-estimation of dynamic hedonic price models and the construction of residential housing price indexes. AREUEA Journal, 19(3):308–332.

    Google Scholar 

  • Mills, E. S. (1971). The value of urban land. In S. PerloffH (Ed) The quality of the urban environment (pp. 231–253). Baltimore: John Hopkins University Press.

    Google Scholar 

  • Munneke, H. J. (1996). Redevelopment decisions for commercial and industrial properties. Journal of Urban Economics, 39(2):229–253.

    Article  Google Scholar 

  • Munneke, H. J., & Slade, B. A. (2000). An empirical study of sample selection bias in indices of commercial real estate. Journal of Real Estate Finance and Economics, 21(1):45–64.

    Article  Google Scholar 

  • Oi, W. (1971). A Disneyland dilemma: Two part tariffs for a Mickey Mouse monopoly. Quarterly Journal of Economics, 85(1):77–96.

    Article  Google Scholar 

  • Soderberg, B., & Janssen, C. (2001). Estimating distance gradients for apartment properties. Urban Studies, 38(1):61–79.

    Article  Google Scholar 

  • Pace, R. K. (1995). Parametric, semiparametric, and nonparametric estimation of characteristic values within mass assessment and hedonic pricing models. Journal of Real Estate Finance and Economics, 11(3):195–217.

    Article  Google Scholar 

  • Pace, R. K. (1993). Nonparametric methods with applications to hedonic models. Journal of Real Estate Finance and Economics, 7(3):185–204.

    Article  Google Scholar 

  • Thorsnes, P., & McMillen, D. P. (1998). Land value and parcel size: A semi-parametric analysis. Journal of Real Estate Finance and Economics, 17(3):233–244.

    Article  Google Scholar 

  • Yatchew, A. (1998). Nonparametric regression techniques in economic. Journal of Economic Literature, 36:669–721.

    Google Scholar 

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Acknowledgement

The authors would also like to thank participants at the 2003ASSA/AREUEA Meetings, as well as the reviewers, for their helpful comments. Any remaining errors and omissions are wholly the responsibility of the authors. Financial support for this research was provided by a Terry–Sanford Research Grant from the Terry College of Business at the University of Georgia.

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Authors and Affiliations

  1. Department of Finance, University of Illinois at Urban-Champaign, Urbana, IL, USA

    Peter F. Colwell

  2. Terry College of Business, The University of Georgia, 206 Brooks Hall, Athens, GA, 30602-6255, USA

    Henry J. Munneke

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  1. Peter F. Colwell
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  2. Henry J. Munneke
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Correspondence to Henry J. Munneke.

Appendix

Appendix

Table 6 Estimation results multinomial logit
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Colwell, P.F., Munneke, H.J. Directional Land Value Gradients. J Real Estate Finan Econ 39, 1–23 (2009). https://doi.org/10.1007/s11146-007-9104-0

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