1# RECORD 00fe81644f944eeadcdbef9deb3f1be4026fb7012# TITLE: Maximum Likelihood Estimation and Lagrange Multiplier Tests for Panel Seemingly Unrelated Regressions with Spatial Lag and Spatial Errors: An Application to Hedonic Housing Prices in Paris3# YEAR: 2010.0 VENUE: Social Science Research Network DOI: 10.1016/j.jue.2010.08.0074# AUTHORS: B. Baltagi; G. Bresson5# PAGES: 48 CANDIDATE TABLE PAGES (1-based): [47, 48]6# ABSTRACT: This paper proposes maximum likelihood estimators for panel seemingly unrelated regressions with both spatial lag and spatial error components. We study the general case where spatial effects are incorporated via spatial errors terms and via a spatial lag dependent variable and where the heterogeneity in the panel is incorporated via an error component specification. We generalize the approach of Wang and Kockelman (2007) and propose joint and conditional Lagrange Multiplier tests for spatial autocorrelation and random effects for this spatial SUR panel model. The small sample performance of the proposed estimators and tests are examined using Monte Carlo experiments. An empirical application to hedonic housing prices in Paris illustrates these methods. The proposed specification uses a system of three SUR equations corresponding to three types of flats within 80 districts of Paris over the period 1990-2003. We test for spatial effects and heterogeneity and find reasonable estimates of the shadow prices for housing characteristics.789===== PAGE 1 (score 0, numeric-paren 0, table-words 0, var-words 0) =====1011D I S C U S S I O N P A P E R S E R I E S12Forschungsinstitut 13zur Zukunft der Arbeit14Institute for the Study 15of Labor 16Maximum Likelihood Estimation and Lagrange 17Multiplier Tests for Panel Seemingly Unrelated 18Regressions with Spatial Lag and Spatial Errors: 19An Application to Hedonic Housing Prices in Paris20IZA DP No. 522721September 201022Badi H. Baltagi23Georges Bresson242526===== PAGE 47 (score 53, numeric-paren 0, table-words 12, var-words 8) =====2728Table 11 - Hedonic housing price SUR Equations for Paris (N=80 quartiers , 1990-2003) (distances weight matrices W1j and W2j)(*)29ln(price per sq.meter)30Coeff.31T-stat32Coeff.33T-stat34Coeff.35T-stat36ln(price per sq.meter)37Coeff.38T-stat39Coeff.40T-stat41Coeff.42T-stat43Intercept446.367457.191465.055474.804484.704494.76250no bathroom51ref.52ref.53ref.54ref.55ref.56ref.57λj (j=1,2,3)580.7355916.102600.7566120.237620.7306316.78464one bathroom651.1786610.401671.6366812.434691.8767014.25571γj (j=1,2,3)72-0.00473-0.051740.007750.083760.008770.10378two bathrooms791.169801.037811.527823.291832.0048410.16085three bathrooms and more861.319870.257883.639893.127902.332914.65592no maid's room93ref.94ref.95ref.96ref.97ref.98ref.99one maid's room1001.4631014.8031021.2761034.7071041.2041056.803106Coeff.107T-stat108Coeff.109T-stat110two maid's rooms and more111-0.690112-0.5981131.3691141.3861151.0621162.520117σ2118µ11190.2711206.0331210.18212222.724123no garage plot124ref.125ref.126ref.127ref.128ref.129ref.130σ2131µ21320.3941335.8291340.46613522.739136one garage plot1370.2651381.098139-0.163140-0.6331410.3751421.794143σ2144µ31450.4801465.9201470.45714822.735149two garage plots150-2.005151-1.034152-1.359153-1.1861541.2421553.071156σµ121570.3311586.0991590.0891609.381161three garage plots and more1620.4901630.039164-1.842165-0.162166-1.187167-0.358168σµ131690.3551706.0761710.0191722.130173Balcony174Balcony (yes or no)175-0.590176-1.2411770.2741780.5391790.3521800.927181σµ231820.4351835.9901840.20218512.920186Floor level (0 to 3)187ref.188ref.189ref.190ref.191ref.192ref.193Floor level (4 to 7)1940.8071957.5731961.23619710.3411980.7001995.733200log-likelihood201146.710202AIC203-35.428204Floor level (8 to 11)2051.5322062.6662070.5342080.815209-0.120210-0.284211Floor level (12 and more)2120.9132130.622214-0.149215-0.119216-1.112217-1.379218ddl219p-value220Square footage (20 to 40 m2)221ref.222ref.2231.8992246.3732252.3552260.989227H0228a : [γj , λj , σµlm]' =0229122300231Square footage (41 to 60 m2)2320.5002335.825234ref.235ref.2360.0262370.082238H0239b : [γj , λj ]' =024062410242Square footage (61 to 80 m2)2430.9122444.8112450.7942467.4782471.0322487.046249H0250c : [γj ,σµlm]' =025192520253Square footage (81 to 100 m2)254-0.348255-0.6532560.9612575.3512581.0292597.818260H0261d : [λj , σµlm]' =026292630264Square footage (> 100 m2)265-1.338266-0.5852670.3892680.695269ref.270ref.271H0272e : [γj] =027332741275<18502760.7362776.8222781.1072798.3862801.84828113.907282H0283f : [λj] =0284328502861850-1913287ref.288ref.289ref.290ref.291ref.292ref.293H0294g : [σµlm] =0295629602971914-19472980.1832991.0363000.9983014.5373020.7403032.9663041948-19693050.1283060.6783070.0683080.3113090.3553101.671311(*): Regression includes time dummies3121970-1980313-0.658314-2.3623150.3043160.9723170.3503181.4333191981-20033200.8053213.0353220.8763231.7133240.0233250.049326Avenue3270.4253282.3193290.2553301.1963310.4393322.212333Boulevard3340.8363353.6873361.4123376.3003380.9303395.283340Place3410.6303421.4253431.9283443.2623450.9783461.899347Street348ref.349ref.350ref.351ref.352ref.353ref.354Dist.center.arrond.(m)355-0.0003356-5.365357-0.0006358-6.473359-0.0007360-6.953361Dist.center.quartier (m)362-0.0013363-8.325364-0.0022365-9.126366-0.0025367-10.009368Upper3690.3403703.4923710.5543723.5663730.3403742.241375Rich3760.2993773.242378-0.026379-0.1773800.3643812.460382Golden3830.2823843.7503850.5263864.3413870.6543885.397389Others390ref.391ref.392ref.393ref.394ref.395ref.396SUR with spatial lags and spatial errors (SAR)397two rooms398three rooms399more than three rooms400Time of building401Kind of street402location403Bathroom404Maid's roo405Garage plot406Floor level407Arrondisseme408Spatial dep.409σ2410v1411LM test41243486.04133208.641448806.041543402.04160.0417Square footage418SUR with spatial lags and spatial errors (SAR)419two rooms420three rooms421more than three rooms4224017.142348782.0424σv23425Error comp. Var-cov. Matrices426σ2427v2428σ2429v3430σv12431σv13432433434===== PAGE 48 (score 54, numeric-paren 0, table-words 12, var-words 8) =====435436Table 12 - Hedonic housing price SUR Equations for Paris (N=80 quartiers , 1990-2003) (contiguity weight matrices W1j and W2j)(*)437ln(price per sq.meter)438Coeff.439T-stat440Coeff.441T-stat442Coeff.443T-stat444ln(price per sq.meter)445Coeff.446T-stat447Coeff.448T-stat449Coeff.450T-stat451Intercept4527.10445314.7114546.0614559.8154565.46645710.162458no bathroom459ref.460ref.461ref.462ref.463ref.464ref.465λj (j=1,2,3)4660.57546711.9304680.63446916.2134700.57147112.448472one bathroom4731.14947410.1114751.60147612.1064772.00747815.240479γj (j=1,2,3)480-0.045481-0.769482-0.065483-1.018484-0.043485-0.817486two bathrooms4871.1664881.0274891.6394903.5464912.07549210.411493three bathrooms and more4942.4874950.4854964.0154973.4594982.5034994.959500no maid's room501ref.502ref.503ref.504ref.505ref.506ref.507one maid's room5081.5075094.9475101.3225114.8555121.1705136.582514Coeff.515T-stat516Coeff.517T-stat518two maid's rooms and more519-0.738520-0.6405211.2925221.3165231.1005242.595525σ2526µ15270.2765286.0315290.18653022.680531no garage plot532ref.533ref.534ref.535ref.536ref.537ref.538σ2539µ25400.4045415.8325420.47454322.676544one garage plot5450.3925461.610547-0.055548-0.2135490.3815501.804551σ2552µ35530.5065545.9315550.46855622.695557two garage plots558-2.175559-1.111560-1.127561-0.9855621.2585633.086564σµ125650.3375666.0835670.0965689.870569three garage plots and more5700.0185710.001572-1.714573-0.149574-1.359575-0.405576σµ135770.3675786.0655790.0265802.845581Balcony582Balcony (yes or no)583-0.695584-1.4605850.3405860.6705870.3715880.963589σµ235900.4525916.0015920.20459312.799594Floor level (0 to 3)595ref.596ref.597ref.598ref.599ref.600ref.601Floor level (4 to 7)6020.7906037.3756041.24860510.3976060.6456075.234608log-likelihood609103.730610AIC61150.534612Floor level (8 to 11)6131.4846142.5726150.4536160.693617-0.161618-0.377619Floor level (12 and more)6200.9276210.617622-0.230623-0.180624-0.942625-1.147626ddl627p-value628Square footage (20 to 40 m2)629ref.630ref.6311.8376326.1506333.3056341.376635H0636a : [γj , λj , σµlm]' =0637126380639Square footage (41 to 60 m2)6400.4806415.594642ref.643ref.6440.1216450.380646H0647b : [γj , λj ]' =064866490650Square footage (61 to 80 m2)6510.9886525.1736530.8276547.5876551.0726567.257657H0658c : [γj ,σµlm]' =065996600661Square footage (81 to 100 m2)662-0.787663-1.4686641.0466655.7906661.1116678.265668H0669d : [λj , σµlm]' =067096710672Square footage (> 100 m2)673-1.304674-0.5666750.4286760.761677ref.678ref.679H0680e : [γj] =068136820.994683<18506840.7176856.6886861.1296878.4836881.77468913.095690H0691f : [λj] =0692369306941850-1913695ref.696ref.697ref.698ref.699ref.700ref.701H0702g : [σµlm] =0703670407051914-19477060.2257071.2827080.9767094.3767100.8427113.3537121948-19697130.1977141.0547150.1367160.6247170.3787181.765719(*): Regression includes time dummies7201970-1980721-0.547722-1.9547230.3837241.2117250.3627261.4577271981-20037280.7567292.8027300.8297311.6097320.1157330.242734Avenue7350.5077362.7007370.2747381.2677390.4927402.441741Boulevard7420.9207434.0057441.4397456.2617460.9347475.204748Place7490.6787501.5377511.9517523.2447530.9477541.823755Street756ref.757ref.758ref.759ref.760ref.761ref.762Dist.center.arrond.(m)763-0.0003764-4.881765-0.0006766-5.705767-0.0007768-6.632769Dist.center.quartier (m)770-0.0013771-8.291772-0.0021773-8.582774-0.0024775-9.485776Upper7770.3567784.1047790.5627803.8237810.3957822.897783Rich7840.3547854.185786-0.035787-0.2457880.4287893.117790Golden7910.3357924.6937930.5477944.5567950.7317966.232797Others798ref.799ref.800ref.801ref.802ref.803ref.804SUR with spatial lags and spatial errors (SAR)805SUR with spatial lags and spatial errors (SAR)806two rooms807three rooms808more than three rooms809two rooms810three rooms811more than three rooms812Bathroom813Maid's roo814Garage plot815Floor level816Spatial dep.817Square footage818Error comp. Var-cov. Matrices819σ2820v1821Time of building822σ2823v2824σ2825v3826σv12827σv13828σv23829Kind of street830LM test8312297300.0832location8331268.083457351.0835Arrondisseme83651132.08370.3388383255.683947592.0840