ECON734: Spatial Econometrics – Lab 2 Term I, 2018-2019 Yang Zhenlin zlyang@smu.edu.sg http://www.mysmu.edu/faculty/zlyang/

Boston House Price The Boston house-price data of Harrison, D., Rubinfeld, D. L. (1978): Hedonic prices and the demand for clean air, J. Environ. Economics & Management, Vol. 5, 81-102. Used in Belsley, Kuh & Welsch: “Regression diagnostic ...”, Wiley, 1980. Various transformations are used in the table on pages 244-261. Augmented with latitude-longitude coordinates by: Gilley, O.W., and R. Kelley Pace. (1996). On the Harrison and Rubinfeld Data. Journal of Environmental Economics and Management, Vol. 31, 403-405. It contains 506 census tracts. See boston_readme.txt for more details on the data. The file boston.dat contains the augmented data, and the file boston.xy generates the spatial with matrix based on the latitude-longitude coordinates.

Boston House Price Variables (in columns) order in the augmented data file boston.dat: CRIM per capita crime rate by town ZN proportion of residential land zoned for lots over 25,000 sq.ft. INDUS proportion of non-retail business acres per town CHAS Charles River dummy variable (= 1 if tract bounds river; 0 o.w.) NOX nitric oxides concentration (parts per 10 million) RM average number of rooms per dwelling AGE proportion of owner-occupied units built prior to 1940 DIS weighted distances to five Boston employment centres RAD index of accessibility to radial highways TAX full-value property-tax rate per $10,000 PTRATIO pupil-teacher ratio by town B 1000(Bk - 0.63)^2 where Bk is the proportion of blacks by town LSTAT % lower status of the population MEDV Median value of owner-occupied homes in $1000's latt Lattitude coordinates long Longitude coordinates

Boston House Price The model: MEDV = 0 + 1Crime + 2ZN + . . . + The spatial weight matrix is constructed using the Euclidean distance in terms of longitude and latitude by boston.xy. A threshold distance, e.g., 0.05, is chosen, which gives a Wn matrix with 19.08% non-zero elements. The model: MEDV = 0 + 1Crime + 2ZN + . . . + 13Lstat + error + spatial terms where the spatial terms may contain SED, SLD, S-Durbin, SED+SLD, S-Durbin+SED, SLD+S-Durbin, etc.

Fitting house price data with SED model The key Matlab commands in the main program Boston_Qmle_SED.m: load boston.dat; % Harrison-Rubinfeld data [n p] = size(boston); % no. of rows and columns in data y = boston(:,p-2); % median house values latt = boston(:,p-1); % lattitude coordinates long = boston(:,p); % longitude coordinates x = [ones(n,1) boston(:,1:p-3)]; vnames = char('hprice','constant','crime','zoning','industry', ... 'charlesr','noxsq','rooms2','houseage','distance','access','taxrate', ... 'pupil/teacher','blackpop','lowclass'); beth0 = pinv(x*’x)*x’*y; % OLS regression of y on x rhoh = SED_ML(y,x,W); % returns the QMLE of rho

Fitting house price data with SED model The generic m-function SED_ML.m, called by the main program Boston_Qmle_SED.m, produces the following results. (Q)MLE se_MLE t_MLE se_QMLE t_QMLE Const 29.6250 5.4956 5.3907 5.4956 5.3907 CRIM -0.1318 0.0276 -4.7693 0.0276 -4.7693 ZN 0.0379 0.0141 2.6887 0.0141 2.6887 Indus -0.0139 0.0729 -0.1909 0.0729 -0.1909 Chas -0.4975 0.8794 -0.5658 0.8794 -0.5658 NOX -19.2666 5.2686 -3.6568 5.2686 -3.6568 RM 4.2812 0.3643 11.7516 0.3643 11.7516 Age -0.0259 0.0139 -1.8604 0.0139 -1.8604 DIS -1.6095 0.3021 -5.3276 0.3021 -5.3276 RAD 0.3174 0.0767 4.1407 0.0767 4.1407 TAX -0.0130 0.0036 -3.6137 0.0036 -3.6137 PTRATIO -0.6143 0.1523 -4.0344 0.1523 -4.0344 B 0.0106 0.0031 3.4261 0.0031 3.4261 Lstat -0.4270 0.0514 -8.2999 0.0514 -8.2999 SED 0.6947 0.0420 16.5461 0.0420 16.5332 2 14.9219 0.9697 15.3874 1.7700 8.4306