SPATIAL ECONOMETRICS AND HOUSE PRICE MODELS

This is the doctoral thesis project of Linda Gerkman. The thesis focuses on spatial econometrics as a subset of spatial data analysis, i.e. the spatial aspects of the data are dealt with from an econometric perspective. The attempted contribution of the thesis is mainly methodological, but the findings are illustrated by empirical studies on house price data. The thesis consists of an introductory chapter and four essays. The first and the fourth essay are co-authored with Niklas Ahlgren. The introductory chapter presents an overview of topics and problems in spatial econometrics. We begin by introducing spatial effects. Then spatial weights matrices and their specifications are discussed, especially, k-nearest neighbours weights matrices. We introduce various spatial econometric models, review estimation methods, and briefly touch upon the interpretation of the parameter estimates. We discuss the problem of omitted variables in spatial econometric models, and continue by some computational and empirical aspects, the bootstrap, and the spatial J-test (Kelejian 2008). Finally hedonic house price models are discussed. Essay 1: The paper studies inference in spatial autoregressive models when the data are generated by a unilateral spatial autoregressive process. The estimator of the spatial autoregressive parameter is shown to be consistent and asymptotically normal. Some simulation results to examine the finite sample properties of the estimator show that it is nearly unbiased, except at the boundary of the parameter space. In many cases in practice the weights matrix is unknown. We find that underspecifying (overspecifying) the weights matrix results in an underestimated (overestimated) spatial autoregressive parameter. An empirical application illustrates the use of unilateral spatial autoregressive models with real data. Key words: Maximum likelihood estimator, Spatial autoregressive model, Unilateral spatial autoregressive process, Weights matrix. Essay2: This paper studies to what extent a set of coordinate-based variables describing the small scale neighbourhood conditions can replace the spatial econometric structure in a house price model. We make assumptions that motivate a spatial Durbin model which has a rich spatial structure. When it is estimated without the small scale neighbourhood variables, its spatial lags are found to be significant. However, when the additional set of variables is included, the spatial lags become insignificant. Hence, the model would be reduced to a conventional non-spatial regression model. The assumptions still motivate a Spatial Error model. The spatial lag of the error term of this model is found to be highly significant. The paper gives a formal motivation for the empirical analysis and the arguments are implemented on real data for apartments sold in Helsinki in Finland, during the first quarter of 2002. In the empirical analysis we find that the new explanatory variables capture some of the small scale neighbourhood conditions, and thereby we obtain a simplified model. However, these small scale neighbourhood variables cannot entirely replace the spatial econometric structure. Key Words: House prices, Omitted variables, Small scale neighbourhood, Spatial econometrics. Essay 3: A practical issue is how to choose the weights matrices of a spatial econometric model. Focusing on k-nearest neighbours weights matrices, this paper proposes a strategy for specification search. The proposed strategy gives formal justification for the choice of the number of nearest neighbours. Applying the spatial J-test as the means of specification search, two approaches, an increasing and a decreasing number of neighbours approach, are suggested and examined. The results are clearly in favour of the increasing number of neighbours approach. We find that as long as the spatial dependence in the dependent variable is at least moderate, all false null models are rejected, and that the size of the final test equals the nominal size. House price data from Stockholm, Sweden, are used to illustrate the strategy in practice. Keywords: k-nearest neighbours; Model Specification; Spatial J-test; Weights matrix Essay 4: The weights matrix plays an important role in the specification of spatial econometric models. It contains the assumed spatial structure of the data. The problem is that there are usually several alternative formulations. An important practical issue is therefore how to choose the weights matrix. This paper studies the properties of the spatial J-test when it is applied to discriminate between spatial models with different k-nearest neighbours weights matrices. We find that the asymptotic test is oversized in small samples. The bootstrap is found to correct the size of the asymptotic test in small samples. Regarding the power of the test, we find that if the null model entertains an underspecified weights matrix, the power of the test is high. If the null model entertains an overspecified weights matrix, the test has low power. Keywords: Bootstrap, k-nearest neighbours; Spatial J-test; Weights matrix.