ECON734: Spatial Econometrics – Lab 4

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ECON734: Spatial Econometrics – Lab 4 Term I, 2018-2019 Yang Zhenlin zlyang@smu.edu.sg http://www.mysmu.edu/faculty/zlyang/

FE-SPD Model -- Public Capital Productivity

FE-SPD Model -- Public Capital Productivity

FE-SPD Model -- Public Capital Productivity The Data (Munnell.xls): Obs State Year Y K2 K1 L Unemp 1 1970 4.45359 4.17704 4.55381 3.00454 4.7 2 4 4.28529 4.00640 4.37265 2.73830 4.4 3 5 4.18730 3.88157 4.29556 2.72933 6 5.42149 5.10906 5.23752 3.84175 7.2 8 4.40975 4.05700 4.37493 2.87518 9 4.58973 4.20046 4.38170 3.07828 5.6 7 10 3.83651 3.62849 3.78591 2.33606 4.8 12 4.84286 4.47271 4.75723 3.33286 13 4.63453 4.26175 4.61907 3.19243 4.1 16 3.85582 3.53278 3.96389 2.31765 5.8 …

Fitting the SED Model The main m-file, SEDpanel_2way_application.m: calls ‘Munnell.xls’ for data, ‘weight_Munnell.xls’ for W, ‘FnSED.m’ to obtain QMLE of . function rhoh = FnSED(T,Y,X,M,ev,lb0,ub0) rhoh = fminbnd(@FnSed,lb0,ub0); function f = FnSed(spa) nt = length(Y); n = nt/(T-1); In = eye(n); It = eye(T-1); B = In-spa*M; Yr = kron(It,B)*Y; Xr = kron(It,B)*X; XXr = Xr'*Xr; XXIr = pinv(XXr); XY = Xr'*Yr; bet = XXIr*XY; eps = Yr-Xr*bet; sig = eps'*eps/nt; f = .5*log(sig)-sum(log(1-spa*ev))/n+log(1-spa)/n; end

Fitting the SED Model In the main file, the command X = [X kron(IT,M)*X]; % add Durbin term adds the Durbin terms QMLE, Bias-Corrected QMLEs with Durbin-SED and 2Way-FE Munnel T = 17 IID Bootstrap QMLE se t QMLE_bc se_bc t_bc SED 0.4101 0.0436 9.4120 0.4175 0.0440 9.4860 LnK2 -0.0184 0.0268 -0.6867 -0.0183 0.0274 -0.6694 LnK1 0.1662 0.0272 6.1140 0.1662 0.0276 6.0140 LnL 0.7539 0.0294 25.6309 0.7539 0.0293 25.7055 Unemp -0.0009 0.0005 -1.7158 -0.0009 0.0005 -1.6978 WLnK2 -0.0750 0.0575 -1.3044 -0.0745 0.0571 -1.3057 WLnK1 0.0901 0.0594 1.5161 0.0897 0.0613 1.4638 WLnL -0.0130 0.0507 -0.2559 -0.0142 0.0508 -0.2789 Wunemp -0.0017 0.0010 -1.7525 -0.0017 0.0010 -1.7465 Elapsed time is 2.892787 seconds.

Fitting the SLD Model The main m-file, SARpanel_2way_application.m: calls ‘Munnell.xls’ for data, ‘weight_Munnell.xls’ for W, ‘FnSAR.m’ to get QMLE of . function rhoh = FnSAR(T,Y,X,XXI,W,ev,lb0,ub0) rhoh = fminbnd(@FnSed,lb0,ub0); function f = FnSed(rhoh) nT = length(Y); n = nT/(T-1); In = eye(n); It = eye(T-1); A = In-rhoh*W; AY = kron(It,A)*Y; XAY = X'*AY; bet = XXI*XAY; eps = AY-X*bet; sig = eps'*eps/nT; f = .5*log(sig)+log(1-rhoh)/n-sum(log(1-rhoh*ev))/n; end

Fitting the SLD Model Simulation for QMLE, Bias-Corrected QMLEs with Durbin-SLD 2Way-FE Munnel T = 17 IID Bootstrap QMLE se t QMLE_bc se_bc t_bc SLD 0.4124 0.0433 9.5186 0.4231 0.0455 9.3059 LnK2 -0.0090 0.0262 -0.3420 -0.0088 0.0252 -0.3491 LnK1 0.1591 0.0266 5.9888 0.1591 0.0262 6.0686 LnL 0.7514 0.0299 25.1208 0.7515 0.0292 25.7202 Unemp -0.0006 0.0006 -1.1295 -0.0006 0.0006 -1.1287 WLnK2 -0.0567 0.0481 -1.1809 -0.0555 0.0464 -1.1954 WLnK1 0.0066 0.0476 0.1391 0.0039 0.0475 0.0826 WLmL -0.3159 0.0544 -5.8105 -0.3249 0.0555 -5.8513 WUnemp -0.0013 0.0008 -1.5365 -0.0013 0.0009 -1.4997 Elapsed time is 4.430700 seconds.

Fitting the SLE Model The main file, SARARpanel_2way_application.m: calls ‘Munnell.xls’ for data, ‘weight_Munnell.xls’ for W, ‘FnSARAR.m’ to obtain QMLEs of  and . QMLE, Bias-Corrected QMLEs with SLE 2Way-FE Munnel T = 17 IID Bootstrap QMLE se t QMLE_bc se_bc t_bc SLD 0.0270 0.0384 0.7036 0.0272 0.0367 0.7412 SED 0.4068 0.0536 7.5937 0.4112 0.0503 8.1684 LnK2 -0.0145 0.0258 -0.5599 -0.0143 0.0258 -0.5545 LnK1 0.1553 0.0265 5.8638 0.1553 0.0273 5.6805 LnL 0.7555 0.0294 25.7262 0.7555 0.0296 25.4833 Unemp -0.0012 0.0005 -2.3652 -0.0012 0.0005 -2.3577 Elapsed time is 7.288321 seconds.

Fitting the SLE Model In the main files, e.g., in ‘SARARpanel_2way_application.m’, change the part below for fitting models with only individual-specific effects by defining: FnTN= kron(FT,In); ==========================================================  % transform variables based on two-way fixed effects % (change to give individual-specific effects only) Jt = IT-jt*jt'/T; [V1,D1] = eig(Jt); FT = V1(:,2:end); Jn = In-jn*jn'/n; [V2,D2] = eig(Jn); FN = V2(:,2:end); FnTN= kron(FT,FN); % for two-way fixed effects Ytr = FnTN'*Y; Xtr = FnTN'*X; Wtr = FN'*W*FN; WT = kron(It, Wtr); Mtr = Wtr; MT = kron(It, Mtr); MM = Mtr'*Mtr;