Semi-nonparametric varying coefficient regression : methodology, theory and application in urban economics

Abstract

This thesis presents three classes of semi-nonparametric varying coefficient regression for modelling spatial heterogeneity with cross-sectional data, panel data, and functional data, respectively, in the urban context. Chapter 2 presents a selective review of the nonparametric and semi-parametric methodologies. We first examine the estimation of a nonparametric regression using the kernel and the series methods, high lighting the cost of using the nonparametric methods. Next, we review the estimation of a varying coefficient regression and stress its relationship with the popular geographical weighted regression. Finally, we discuss the estimation of a functional linear regression, where the independent variable itself is a function. The functional principal component and Tikhonov regularisation are introduced subsequently to estimate the model. Chapter 3 considers a spatially varying coefficient regression model over irregularly shaped areas. We develop a novel methodology that combines local polynomials and a non-Euclidean metric, called geodesic distance, to achieve both coefficient smoothing and spatial prediction over complex regions. We implement a series of Monte Carlo simulation studies to test the proposed methodology. The results suggest that our method performs better in the estimated coefficients as well as the prediction than alternative methods. Finally, we apply the method to the housing market in Aveiro, Portugal, a coastal area separated by lagoons and rivers. The results highlight the importance of modelling spatial heterogeneity and dependence in a hedonic regression. Chapter 4 presents a spatiotemporally varying coefficient regression model which extends the spatially varying coefficient regression model into the temporal dimension. A three-dimensional local polynomial method is applied to estimate the coefficient. The Monte-Carlo simu lations show that the proposed methodology outperforms the existing geographical and temporal weighted regression. Empirically, we apply the methodology to study the relationship between human activities and consumption amenities in Beijing. To measure the human activi ties and the distribution of the consumption amenities, we collect two unique datasets, a high-resolution mobile phone positioning dataset from Wechat, a mobile social-networking application, and a point-of-interest(POI) dataset from Meituan-Dianping, a crowd-sourcing review website. The results show that the spatial configurations for the consumption amenities play a significant role in attracting human activities, after controlling for a wide range of location-specific characteristics. However, the effects vary substantially over space and a 24-hour time span. The results provide insights into the geographic contextual uncertainties of local amenities in shaping the rise and fall in the city liveliness. Chapter 5 proposes a novel methodology called sieve continuum generalised method of moments to estimate a functional linear regression model. The methodology uses the sieve method to achieve dimension reduction and the continuum generalised method of moments to exploit all the moment conditions. It provides a general framework for estimating a functional linear regression with exogenous regressors as well as a functional instrumental variable regression. The proposed estimator has a closed-form which makes it easy to implement and intuitively appealing. Finally, we derive the optimal rate of convergence for the estimator. Chapter 6 concludes with the summaries, the limitations of the thesis, as well as the directions for future researches.