A Spatial Hedonic Analysis of the Value of the Greenbelt in the City of Vienna, Austria

Shanaka Herath, Johanna Choumert, Gunther Maier

Introduction

Greenbelts are important features of various cities – also Vienna

Proximity to greenbelt is attractive for housing

Counter effect to proximity to the city center

What effect does proximity to the greenbelt have on housing prices in Vienna?

Spatially located observations – spatial analysis

Structure

Introduction Greenbelt in Vienna Data and variables Empirical strategy Estimation results Conclusion

Greenbelt in Vienna

Most important: Wienerwald (N – W) Over 1,000 km2 Mainly woodland In the city many trails for

hiking and mountain biking (accessible by tram or bus)

Secondary green area: Prater (2nd district) Approx. 6 km2 Mainly woods, wetlands Amusement park, sports

facilities

Data and variables

Data provided by ERES.NET GmbH based on Immobilien.net

Dec. 11, 2009 – Mar. 25, 2010 Apartment sales (1651) Only those with location information

Asking price Size # of rooms, bathrooms, toilets Condition Features (balcony, terrace, elevator, parquet flooring)

Data and variables

Geocoding of addresses via Google maps Geocoding of the boundary of Wienerwald (in

the city) and of Prater For every apartment in the dataset we calculate

the minimum distance to Wienerwald (greenbelt, dis_g) and Prater (dis_p) in addition to distance to city center (dis_c)

Empirical strategy

Standard hedonic price theory:

… vector (nx1) of housing prices … matrix (nxj) of housing characteristics

(explanatory variables) … unknown parameter vector (jx1) … vector of random error terms (nx1) If we assume to be iid distributed: standard

OLS estimation – in case of spatial correlation: inefficient and maybe biased estimates.

Empirical strategy

When iid-assumption does not hold, neighborhood relations have to be taken into account

Neighborhood characterized by W (spatial weight matrix or neighborhood matrix)

3 types of spatial model: Spatial lag model: Spatial error model: Spatial Durbin model: SDM generalizes SLM and SEM

Empirical strategy

Semi-log specification Two variants of “location in the city”:

District dummies Distance from CBD

OLS estimation LM tests for spatial autocorrelation in the

residuals – verified LM tests for different spatial weight matrices

(distance, nearest neighbors) Test of SDM against SLM and SEM

Empirical strategy

Parameters of the SLM, SDM cannot be interpreted directly or compared to those of OLS or SEM

Average effect of a marginal change: Direct effect + Indirect effect = Total effect

OLS SEM SLM SDMDistrictsDistance

Estimation results

Model Spatial weights matrix (criterion)

Moranstatistic

LM error LM lag RLM error

RLM lag

Model 1 WDHALF (0.5 km) 0.056(0.000)

17.014(0.000)

3.332(0.068)

17.552(0.000)

3.870(0.049)

  WD1 (1 km) 0.029(0.000)

9.347(0.002)

1.767(0.184)

8.969(0.003)

1.389(0.239)

  WD2 (2 km) -0.025 (1.000)

37.417(0.000)

0.592(0.442)

37.172(0.000)

0.347(0.556)

  W1 (k = 1) 0.104(0.000)

15.425(0.000)

4.089(0.043)

11.661(0.001)

0.324(0.569)

  W3 (k = 3) 0.058(0.000)

13.227(0.000)

7.730(0.005)

8.003(0.005)

2.505(0.114)

  W5 (k = 5) 0.039(0.000)

9.452(0.002)

12.819(0.000)

3.569(0.059)

6.937(0.008)

Model 2 WDHALF (0.5 km) 0.260(0.000)

370.493(0.000)

4.298(0.038)

374.046(0.000)

7.851(0.005)

  WD1 (1 km) 0.279(0.000)

847.553(0.000)

0.483(0.487)

847.937(0.000)

0.867(0.352)

  WD2 (2 km) 0.143(0.000)

1204.118(0.000)

4.187(0.041)

1210.248(0.000)

10.317(0.001)

  W1 (k = 1) 0.390(0.000)

214.472(0.000)

78.341(0.000)

145.961(0.000)

9.829(0.002)

  W3 (k = 3) 0.296(0.000)

339.875(0.000)

147.802(0.000)

224.335(0.000)

32.262(0.000)

  W5 (k = 5) 0.249(0.000)

385.522(0.000)

221.050(0.000)

231.811(0.000)

67.339(0.000)

Notes: W (row standardised) spatial weights matrix is used. p-values follow in parentheses. k denotes number of neighbours in cases where "nearest neighbours" are considered

Testing for spatial autocorrelation Verified in all cases

We need to apply a spatial model rather than just OLS

Tests also used to find the best W matrix for SLM and SEM

Estimation results

Testing the SDM against the SEM For both model specifications the SDM is superior to the

SEM

Specification…   Df LL Chi2 Prob > χ2

with district Spatial error model -> spatial Durbin model        

Spatial error model 49 281.21 -  + LOG (lagged dependent variable) 95 395.53 228.63 (Df = 46) 0.00***

with distance from the city centre

Spatial error model -> spatial Durbin model        

Spatial error model 28 129.49 -  + LOG (lagged dependent variable) 53 164.97 70.96 (Df = 25) 0.00***

Estimation results

Intrinsic characteristics expected signs generally consistent across the models

District dummies: All negative significant (relative to CBD) Show the expected pattern (attractive vs. unattractive

districts) OLS estimates seem to be inflated (upward

biased) Seem to pick up spatial effects

Estimation results

Distance to city center negative and significant

Distance to green belt negative and significant Effect is smaller than that of

distance to CBD Distance to Prater

Negative and significant in 3 of four estimations

Effect is stronger for model with district dummies (picks up some of the distance decay)

Variable OLS 1 OLS 2 SEM 1 SEM 2

LOGdis_c   -0.200***(0.015)

  -0.228***(0.027)

LOGdis_g -0.044**(0.015)

-0.150***(0.013)

-0.040***(0.012)

-0.062**(0.022)

LOGdis_p -0.084***(0.024)

-0.060***(0.012)

-0.060**(0.022)

0.012(0.023)

R2 0.90 0.85    Adj. R2 0.90 0.85    F-statistic 318.7 375.9    Prob (F-stat) 0.00 0.00    λ     -0.75 0.70LR test value     34.16*** 394.72***

Log likelihood     281.21 129.49AIC -432.26 189.75 -464.42 -202.97Breusch-Pagan test

96.89 56.58 95.61   64.90 

No. of observations

1651 1651 1651 1651

Estimation results

For the SDM no significant total effects for Model 1 The previous results are confirmed for Model 2

Distance to CBD negative and significant due to direct effect

Distance to green belt is negative and significant due to indirect effect – smaller than CBD coefficient

Distance to Prater is negative, but insignificant

Variable Specification 1 Specification 2Direct effects

Indirect effects

Total effects

Direct effects

Indirect effects

Total effects

LOGdis_c

   -0.188**(-3.149)

-0.082(-1.246)

-0.271***(-8.254)

LOGdis_g 0.083*(2.026)

-0.141(-1.245)

-0.058(-0.600)

-0.022(-0.739)

-0.097**(-2.598)

-0.120***(-5.488)

LOGdis_p -0.094*(-2.554)

0.044(0.196)

-0.049(-0.255)

0.015(0.339)

-0.025(-0.482)

-0.009(-0.437)

Notes: z values are in parenthesis.

Conclusion

The impact of proximity to the green belt is verified for the Viennese housing market (sales of apartments).

Distance to green areas in the city is of lower importance.

Natural amenities are important factors in the residential choice of households.

But, they are clearly dominated by distance to the city center.

Conclusion

Spatial effects seem to be important in residential hedonic price models.

Cannot be fully accounted for in the structural part of the model – spatial autocorrelation in residuals remains.

OLS estimates are upward biased. SDM needs special treatment for interpretation