1. Impact of Proximate Public Assets and Infrastructure on Sydney Residential Property Prices Andrew Chernih achernih@fastmail.fm

2. Project Objectives My thesis investigated the effect of various factors on residential property prices in Sydney The main factors considered were infrastructure, transport and environmental characteristics

3. Methodology The first stage was to collect data regarding property prices and property characteristics. This came from mapping software and other sources. Secondly, a functional form was required to relate property price to certain characteristics. This requires an understanding of the relevant issues.

4. Data The entire dataset comprised 37,676 houses that sold in Sydney in the year of 2001. Property characteristics included proximity to city, coastline, roads, bus stops, train stations, schools, levels of crime, levels of air pollution and air noise, household income and foreigner ratio.

5. Distribution of properties

6. Issues Previous studies have indicated nonlinear relationships between price and certain explanatory variables, such as income and levels of air noise. Properties are spatially correlated, because properties in closer proximity will have similar accessibility and pollution characteristics and possibly structural similarities as well.

7. Study Design Four functional forms were fitted, allowing for nonlinear relationships as well as accounting for spatial correlation. The same set explanatory variables of explanatory variables was used in all four models. The dependent variable is the natural logarithm of the sale price.

8. First Model This is just the linear regression model, the favoured functional form of previous studies of this type. Given the dependent variable Y and independent variables X 1,…, X k the equation takes the following form:

9. Second Model This is the linear regression model but including a smooth function of longitude and latitude to account for spatial correlation. Given the dependent variable Y, the independent variables X 1,…, X k, the longitude L 1 and latitude L 2 then the equation takes the following form:

10. Third Model This is an additive model, which allows nonlinear relationships between the dependent and independent variables. Given the dependent variable Y and independent variables X 1,…, X k the equation takes the following form:

11. Fourth Model This adds a smooth function fitted to longitude and latitude to the additive model. This is called a geoadditive model in Kammann and Wand (2003). Given the dependent variable Y, the independent variables X 1,…, X k, the longitude L 1 and latitude L 2 then the equation takes the following form:

12. Smooth Functions Univariate smooth functions were fitted using cubic smoothing splines. Bivariate smooth functions were fitted using thin-plate smoothing splines, the natural bivariate extension of cubic smoothing splines.

13. Variable Selection The same explanatory variables selected for the linear regression model were used for the other three functional forms. This was to permit comparability of the four models and better understand the effects of including nonlinearity and spatial dependence on variable significance and magnitude

14. Variable Selection (cont.) Factor analysis was used to separate the 45 variables into 8 categories. Criteria for selecting variables were: parsimony, interpretability, significant effects, goodness of fit and meeting assumptions. A modified form of forward selection was used – starting with several key variables such as distance from the city and lotsize

15. Results Bivariate thin-plate splines could not be fit to the entire dataset, due to computational considerations Linear regression and additive models were fit to the entire dataset All four models were fitted to a random 1000 properties and the differences were analysed

16. Complete Dataset – Linear Regression VariableEstimateVariableEstimate Intercept13.07854RailStation0.00753 LotSize0.00067Park0.00173 MainRoad-0.03748Highway0.00172 NatPark-0.01256Freeway0.00813 Income0.000459Ambulance-0.00257 PM 10 -0.03728AirNoise-0.00283 City-0.02547Factory0.00544

17. Complete Dataset – Additive model Partial Plot for LotSize Partial Plot for Income

18. Complete Dataset – Additive model (cont.) Partial Plot for Air Pollution Partial Plot for Distance to City

19. Complete Dataset – Additive model (cont.) Partial Plot for Distance to Nearest RailStation Partial Plot for Distance to Nearest Park

20. Complete Dataset – Additive model (cont.) Partial Plot for Distance to Nearest Highway Partial Plot for Distance to Nearest Freeway

21. Complete Dataset – Additive model (cont.) Partial Plot for Aircraft Noise Partial Plot for Distance to Nearest Ambulance Station

22. Complete Dataset – Additive model (cont.) Partial Plot for Distance to Nearest Factory Partial Plot for Distance to Nearest National Park

23. Complete Dataset – Additive model (cont.) Partial Plot for Distance to Nearest Main Road

24. Partial Dataset Analysis But the two fitted models do not account for spatial (auto)correlation The effect of including bivariate smoothing into both models is analysed with the random 1000 properties discussed earlier

25. Comparison of linear models VariableLin. Reg.Lin. Reg. SS% Change Intercept13.1408412.8749 Lotsize0.000670.00066-2.41 Income0.000430.00023-45.07 GPO-0.02724-0.02885.73 PM 10 -0.03691Not significant RailStation0.014170.014713.81 Highway0.021120.01676-20.64 NatPark-0.0185Not significant

26. Comparison of linear models (cont.) The addition of bivariate smoothing is highly significant (p < 0.0001) Magnitude and significance of variables is seen to be largely influenced by inclusion of this smoothing Conclusion: spatial dependence is important and affects results

27. Comparison of additive models Bivariate smoothing again highly significant The addition of bivariate smoothing also changed which variables were significant in the additive model case However for the 4 variables which are significant in the additive and geoadditive models, the effect is nearly unchanged.

28. Partial Plot for GPO in additive and geoadditive models

29. Partial Plot for Income in additive and geoadditive models

30. Partial Plot for LotSize in additive and geoadditive models

31. Partial Plot for RailStation in additive and geoadditive models

32. Conclusions Additive models provide a more natural method of incorporating nonlinearities whilst maintaining the useful additive property However further research is required in model selection and validation as well as analysis of spatial dependence and how it is best dealt with

33. Actuarial applications (Generalised) additive models provide a significant extension of generalised linear models Bivariate thin-plate splines are a new way to smooth spatial risk, which has been investigated by a number of papers, such as Fahrmeir et al. (2003)

34. Acknowledgements Thanks to … The Environment Protection Authority for financial assistance and data Transport Data Centre also supplied data under the Student Data program NRMA for use of mapping software and expertise Residex for property sale information