Predicting urban land prices: a comparison of four approaches/ Zemes kainy miestuose prognozes: keturiv metody palyginimas.

ABSTRACT. This paper investigates forecasting accuracy of four different hedonic approaches, when vacant urban land prices are predicted in local markets. The investigated hedonic approaches are: 1) ordinary least squares estimation, 2) robust MM-estimation, 3) structural time series estimation and 4) robust local regression. Post-sample predictive testing indicated that more accurate predictions are obtained if the unorthodox methods of this paper are used instead of the conventional least squares estimation. In particular, the predictive unbiassness can significantly be improved when using the unconventional hedonic methods of the study. The paper also studied the structure of urban land prices. The most important attribute variables in explaining land prices were permitted building volume, house price index, northing and easting. The influence of parcel size variable and different indicator variables on land prices were much weaker.

KEYWORDS: Land price; Hedonic model; Prediction; Robustness; Flexibility

SANTRAUKA

Nagrinejama, kokiu tikslumu keturi skirtingi hedonistiniai metodai prognozuoja laisvu zemes plotu kainas vietinese miestu rinkose. Nagrineti tokie hedonistiniai metodai: 1) maziausiuju kvadratu metodas, 2) daugybiniq modeliu vertinimas, 3) struktoriniu laiko eiluciu vertinimas, 4) lokaline regresine analize. Post-sample prognostinis testas parode, kad tikslesnes prognozes gaunamos taikant netradicinius siame darbe nurodytus metodus, o ne iprasta maziausiuju kvadratu metoda. Taikant netradicinius hedonistinius tyrimo metodus, gali gerokai padideti prognoziu nesaliskumas. Darbe nagrineta ir zemes kainu mieste struktura. Aiskinant zemes kainas is budingu kintamuju svarbiausi buvo leidziamas pastato dydis, busto kainu indeksas, sklypo padetis. Sklypo dydzio kintamasis ir ivairiu rodikliu kintamieji zemes kainoms turejo daug mazesne itaka.

1. INTRODUCTION

Hedonic methods are often advocated in complex land valuation assignments in order to objectively minimise the systematic valuation error and in order to produce the necessary quality-adjustments, which stem from the differentiated nature of separate land parcels, validly and reliably. However, the use of hedonic models is plagued with some fundamental problems imposing serious threats to their empirical adequacy. These fundamental dilemmas include: (1) the temporal variability of land prices, (2) the spatial variability of land prices, (3) the model specification dilemma and (4) outlying and influential observations.

When investigating the temporal dimension of land prices it is important to understand that the behaviour of land prices is generally nonstationary. This is a typical characteristic of many economic time series, which means that the data-generating process that produces the observables is itself transient in time. The effect of time is also multidimensional: Often we can legitimately separate from each other the price trend, the price cycle, seasonal variation and random variation. Traditionally, when modelling temporal land price movements, the effect of time has been tried to reduce to the variation of cost-of-living index or house price index, which have subsequently been used as explanatory variables in a hedonic regression. Also the indicator variable technique (i.e. by using yearly time dummy variables) has been a very popular approach when analysing the temporal dimension of land prices. These approaches contain problems mainly because the influence of time can only be estimated in a manner, which is not very accurate in practice. Structural time series models, on the other hand, usually provide a more accurate description about temporal movements.

The spatial variation of land prices can be divided to the spatial heterogeneity and spatial dependency. Spatial heterogeneity implies that functional forms and parameters vary with location and are not homogeneous throughout the data set, whereas spatial dependence implies that the variation is a function of distance. The spatial dependency problem can usually be solved by including location or some distance variables into a hedonic regression as explanatory variables. The spatial heterogeneity problem is usually more problematic: One natural solution would be to narrow the analyses into reasonably small submarkets, which homogenises the data. However, in practise this operation is not typically feasible due to the scarcity of observations for the hedonic modelling purposes. Adaptive modelling techniques, such as local regression, usually provide a better solution to the spatial heterogeneity problem in that they possess a spatial adaptation property and thus explicitly address the spatial heterogeneity problem.

The model specification dilemma can be solved by three different ways: (1) parametrically, (2) semiparametrically and (3) nonparametrically. Parametric modelling is the classical approach in the hedonic modelling of land prices, which is theory-laden because pre-specified functional forms are used in the analysis. Nonparametric techniques are on the other hand data-driven, very flexible tools and semiparametric techniques combine features from parametric and nonparametric approaches. The exact research problem determines what approach should be used. Generally, nonparametric methods are useful when associations between variables are complex (i.e. highly nonlinear) and theoretically unknown. Parametric models apply well to a less complex setting where there exists valid prior knowledge about model's functional form. Irrespective of a chosen approach the model specification dilemma contains the choice of a hedonic model's functional form, the selection of relevant study variables and an error distribution assumption. And it should be noted that the result depends on the chosen scale, which is often, however, implicit.

Parametric models that represent data modelling culture (Breiman, 2001) have formed the conventional dogma of hedonic pricing methods in land price studies, where prespecified global models are estimated by means of ordinarily least squares or some modification thereof. Benefits of parametric approaches undeniably include: simplicity, interpretability, parsimony and comprehensive statistical theory. The fundamental obstacle, however, under-lying the general use of parametric models is their inflexibility, i.e. inability to learn genuine structure about the hedonic relationship from the evidence in such decision-making settings, where theoretically unknown nonlinearity is expected. This is the typical case when the effects of variables representing location and time are considered (McMillen and Thorsnes, 2003). The conventional result is that even the best parametric model tends to impose restrictions that substantially reduce the explanatory and predictive power of hedonic equation (Pace, 1993 and 1995; Anglin and Gencay, 1996; inter alia). Unless the theory-laden parametric model coincides with the data-generating process, profound mis-specification errors may result imposing serious threats to their empirical validity.

Semiparametric and nonparametric approaches are representative of algorithmic modelling culture (Breiman, 2001) that emphasise aspects of learning the complex structure from the available facts and adaptability to the features underlying the data. Semiparametric estimators are, more precisely, an intermediate strategy between theory-laden and data-driven estimators that have restricted learning ability, i.e. semiparametric estimators can approximate functions only within some prespecified classes. Their practical relevance is mainly in balancing the dual goals of low specification error and high efficiency (Pace, 1995; Anglin and Gencay, 1996) and in enchaining the interpretability of results. Nonparametric estimators are by their nature highly flexible and, thus, capable of approximating very general classes of functions (e.g. smooth functions, square integrable functions) that does not require any restrictive, unwarranted prespecification of the functional form of mean response function (nor any specific error distribution assumption). This renders nonparametric estimators to be powerful data-driven tools, albeit highly sensitive to the problem of undersmoothing or overfitting, if local estimation is implemented unduly.

Outlying and influential observations are very common in the land value studies, which may be genuine, faultless values, generated under conditions of some untypical factors or they can contain different errors (such as recording and measurement error; wrong population, etc.). Traditional hedonic modelling techniques, especially the ordinary least squares technique, are sensitive to outlying observations; even a single outlier can drastically change the results and misguide the inferences. In fact, a single sufficiently deviating data point can cause that the least squares estimator breaks down and generates results that are utterly unreliable and uninformative. Robust methods such as MM-estimation, on the contrary, are not sensitive to outliers or influential observations and, therefore, can tolerate a certain amount of bad observations without the fear that the estimator breaks down and produces completely useless results.

2. THE RESEARCH PROBLEM