2017/11/29

outline

Introduction

  • Problems
  • Difficulties
  • Modelling strategy

Brief literature review

  • Hedonic pricing method(HPM)
  • Spatial issues in HPM
  • Locational attributes and attributes about neighborhood effects
  • Dealing with spatial patterns

Methodology

  • Spatial regression modelling
  • Multilevel modeling
  • Motivation of applying the spatial multilevel model

Empirical analysis

  • Data
  • Descriptive statistics
  • Regression analysis

Preliminary results

Introduction

  • Ajaccio is the largest and most important city in Corsica.
  • There are a lot of inhabitants, meanwhile, jobs attract non-local workers.
  • The inhabitants and non-local workers make Ajaccio as the densest zone in Corsica with 840 persons per \(km^{2}\)
  • The population growth rate is stable, about 1% per year.
  • however…
  • The house supply faces the pressure from holiday cottages
  • The limited house supply faces an incresing number of inhabitants and renters.
  • Ajaccio has been a “hotspot” area of house prices throught the period from 2006-2013 according to a previous study.
  • Last but not least there seem to be only few econometric studies on the housing market in Ajaccio.

Problem

  • We would like to know the determinants of dwelling prices with considering time change and space change.

Difficulties

  • Housing data structure

Our modelling strategy

Brief literature review

Hedonic pricing method(HPM)-a linkage between house attributes and house prices

  • the hedonic price model regards the good as a bundle of differential attributes
  • the most common reduced-form of HPM (Sheppard, 1999) \[lnP_{i}=X_{ij}\beta +\varepsilon\]
  • In early years, housing attributes include merely some structural attributes which describe the characteristics of the apartment itself, (Sirmans, 2005) such as square footage, storey, property age, garage, and bathrooms.
  • Sirmans(2006) The composition of hedonic pricing models
  • Garrod and Willis(1992) Valuing goods characteristics: An application of the hedonic price method to environmental attributes

  • Dubin Estimation of Regression Coefficientsin the Presence of Spatially Autocorrelated Error Terms.

Spatial issues in HPM

  • Since we study dwelling prices in Ajaccio, we can not ignore a crucial housing attribute location.
  • A theoretical motivation: everything happens somewhere (Logan, 2012)
  • A practical motivation: All social data are spatial data (Darmofal, 2015)

Locational attributes and attributes about neighborhood effects

  • Follain and Jimenez(1985) Estimating the demand for housing characteristics: A survey and critique

  • Can(1992) Specification and estimation of hedonichousing price models
  • Duranton and Puga(2004) Micro-foundations of urban agglomeration economies
  • Anselin(1988) Lagrange Multiplier Test Diagnosticsfor Spatial Dependence and Spatial Heterogeneity

Dealing with spatial patterns

  • Spatial regression models (spatial autoregressive model, spatial error model, spatial lag X model, spatial Durbin model, etc.)
  • Another way to deal with spatial patterns is applying multilevel model (MLM), other names includes hierarchical linear model, mixed model, etc. Goodman and Thibodeau (1998) Housing Market Segmentation Le Gallo and Chasco (2013) The Impact of Objectiveand Subjective Measures of Air Quality and Noise on House Prices: A MultilevelApproach for Downtown Madrid

Methodology

  • Spatial regression modelling
  • Spatial autoregressive model(SAR)
  • \[y=\rho Wy+X\beta+\varepsilon\]
  • Spatial error model(SEM)
  • \[y=X\beta + u\]
  • \[u=\rho Wu+\varepsilon\]

  • Multilevel modeling
  • Two level multilevel (no random slope, no cross-interaction )
  • \[y_{ij}=\alpha _{(i)j}+x_{ij}\beta +\varepsilon _{ij}\]
  • \[\alpha _{(i)j}=\alpha +z_{j}\gamma +u_{j}\]
  • \[y_{ij}= x_{ij}\beta+z_{j}\gamma +\alpha+u_{j} +\varepsilon _{ij}\]
  • \[\varepsilon _{ij}\sim \mathbb{N}(0,\sigma_{\varepsilon }^{2})\]
  • \[u _{j}\sim \mathbb{N}(0,\sigma_{u}^{2})\]

  • Motivation of applying the spatial multilevel model

Empirical analysis

  • Data
  • Descriptive statistics

Distribution of dwelling prices

Moran test on dependent variable

  • Dependent variable: unit price
  • Moran statistic = 0.14128
  • p-value = 0.001
  • Dependent variable: total price
  • Moran statistic = 0.082626
  • p-value = 0.001

Regression analysis

  • A worker is known by his tools. A shovel for a man who digs. An ax for a woodsman. The econometrician runs regressions —- Mastering Metrics: The Path from Cause to Effect
  • Base Model 1
  • Model 3
  • Model 4

  • Model 6
  • Model 7
  • Model 8 (SAR)

  • Model 9 (SAR)

  • Regression results