TSP Version 4.5 (04/27/00) Windows32 128MB Copyright (C) 2000 TSP International ALL RIGHTS RESERVED 03/31/04 1:51 PM In case of questions or problems, see your local TSP consultant or send a description of the problem and the associated TSP output to: TSP International P.O. Box 61015, Station A Palo Alto, CA 94306 USA PROGRAM COMMAND *************************************************************** | 1 OPTIONS MEMORY = 128; | 2 ?************************************************************* | 2 ? * | 2 ? THIS COMPUTER PROGRAM IS FOR THE PANEL DATA * | 2 ? SPECIFICATION WHERE THE DISTURBANCES ARE BOTH * | 2 ? SPATIALLY AND TIME-WISE AUTOCORRELATED * | 2 ? * | 2 ? Y=ALPHA+X*BETA+U, U=(IT#(RHO*WEIGHTINGMATRIX))*U+E, * | 2 ? E=(eT#MU)+V * | 2 ? * | 2 ?************************************************************* | 2 ?************************************************************* | 2 ?EXPLANATION OF THE VARIABLES USED IN THE PROGRAM * | 2 ?Y.......VECTOR OF DEPENDENT VARIABLE * | 2 ?X.......VECTOR OF EXOGENOUS EXPLANATORY VARIABLE * | 2 ?U.......VECTOR OF DISTURBANCES * | 2 ?MMAT....SPATIAL WEIGHTING MATRIX(REMAINS SAME FOR ALL TIME * | 2 ?E.......VECTOR OF INNOVATIONS * | 2 ?RHO.....SPATIAL AUTOREGRESSIVE PARAMETER * | 2 ?AHOLS...OLS ESTIMATE OF ALPHA * | 2 ?AHGLS...GLS ESTIMATE OF ALPHA * | 2 ?BHOLS...OLS ESTIMATE OF BETA * | 2 ?BHGLS...GLS ESTIMATE OF BETA * | 2 ?RHOHGM..GENERAL MOMENTS ESTIMATOR OF RHOH * | 2 ?NS......NUMBER OF CROSS SECTIONAL UNITS * | 2 ?T.......NUMBER OF TIME PERIODS * | 2 ?NT......TOTAL SAMPLE SIZE * | 2 ?************************************************************* | 2 | 2 ?************************************************************* | 2 ? READ THE DATA * | 2 ?************************************************************* | 2 SET NS = 100; | 3 SET T = 4; | 4 SET NT = NS*T; | 5 SMPL 1 NT; | 6 READ (FILE='C:\TEMP\VAR3.DAT', FORMAT = FREE) Y X1 X2; | 7 SMPL 1 NS; | 8 READ (FILE='C:\TEMP\MMAT.DAT') M1-M100; | 9 MMAKE MMAT M1-M100; | 10 MAT MMM = TR(MMAT'MMAT)/NS; | 11 MFORM (NROW = NS, NCOL = NS, TYPE = DIAG) IMAT = 1; | 12 MFORM (NROW = T, NCOL = T, TYPE = DIAG) TMAT = 1; | 13 MFORM (NROW = T, NCOL = T, TYPE = GENERAL) JMAT = 1; | 14 DO I = 1 TO T; | 15 DO J = 1 TO T; | 16 SET JMAT (I,J) = 1/T; | 17 ENDDO; | 18 ENDDO; | 19 MAT MMAT1 = TMAT#MMAT; | 20 MAT Q0 = (TMAT-JMAT)#IMAT; | 21 MAT Q1 = JMAT#IMAT; | 22 | 22 MAT MW=MMAT'MMAT; | 23 MAT MWT=TR(MW)/NS; | 24 MAT MWTT1=MW*(MMAT+MMAT'); | 25 MAT MWTT=TR(MWTT1)/NS; | 26 MAT MWW=MMAT*MMAT; | 27 MAT MWWW=MW*MW; | 28 MAT MWWWW=MW+MWW; | 29 MAT MQ0=TR(MWWW)/NS; | 30 MAT MQ1=TR(MWWWW)/NS; | 31 | 31 | 31 ?************************************************************* | 31 ?IN THE FIRST STEP ESTIMATE THE MODEL BY OLS * | 31 ?AND GET THE ESTIMATED DISTURBANCES * | 31 ?************************************************************* | 31 SMPL 1 NT; | 32 OLSQ (SILENT) Y X1 X2 ; | 33 SET AHOLS = @COEF(1); | 34 SET BHOLS = @COEF(2); | 35 SET SHOLS = (@SSR)/(NS-1); | 36 TITLE 'STEP 1: OLS ESTIMATORS AND ESTIMATED DISTURBANCES'; | 37 PRINT AHOLS BHOLS SHOLS; | 38 GENR UH = Y - AHOLS*X1 - BHOLS*X2 ; | 39 | 39 | 39 ?************************************************************* | 39 ?IN THE SECOND STEP USE THE ESTIMATES OF DISTURBANCES * | 39 ?FOR THE GENERAL MOMENTS(GM) ESTIMATOR * | 39 ?************************************************************* | 39 | 39 ?SET FLAG L FOR CHOICE OF PROCEDURE TO ESTIMATE RHO AND SIGMA | 39 ?************************************************************ | 39 ?L = 1.. SELECT INITIAL GM ESTIMATORS | 39 ? = 2.. SELECT PARTIALLY WEIGHTED GM ESTIMATORS | 39 ? = 3.. SELECT WEIGHTED GM ESTIMATORS | 39 | 39 SET L = 3; | 40 INPUT C:\TEMP\GMPROC3; | 40 SMPL 1 NT; | 41 MMAKE UVEC UH; | 42 SMPL 1 NT; | 43 MAT VVEC = MMAT1*UVEC;UNMAKE VVEC V; | 45 MAT WVEC = MMAT1*VVEC;UNMAKE WVEC W; | 47 MAT UQVEC = Q0*UVEC;UNMAKE UQVEC UQ; | 49 MAT VQVEC = Q0*VVEC;UNMAKE VQVEC VQ; | 51 MAT WQVEC = Q0*WVEC;UNMAKE WQVEC WQ; | 53 MAT UQ1TDE1EC = Q1*UVEC;UNMAKE UQ1TDE1EC UQ1; | 55 MAT VQ1TDE1EC = Q1*VVEC;UNMAKE VQ1TDE1EC VQ1; | 57 MAT WQ1TDE1EC = Q1*WVEC;UNMAKE WQ1TDE1EC WQ1; | 59 SMPL 1 NT; | 60 GENR UQ2 = UQ*UQ; | 61 GENR VQ2 = VQ*VQ; | 62 GENR WQ2 = WQ*WQ; | 63 GENR UQVQ = UQ*VQ; | 64 GENR UQWQ = UQ*WQ; | 65 GENR VQWQ = VQ*WQ; | 66 GENR UQ12 = UQ1*UQ1; | 67 GENR VQ12 = VQ1*VQ1; | 68 GENR WQ12 = WQ1*WQ1; | 69 GENR UQ1VQ1 = UQ1*VQ1; | 70 GENR UQ1WQ1 = UQ1*WQ1; | 71 GENR VQ1WQ1 = VQ1*WQ1; | 72 | 72 SET T1=T/(T-1); | 73 SET T2=T; | 74 | 74 MSD (SILENT) UQ2 VQ2 WQ2 UQVQ UQWQ VQWQ | 74 UQ12 VQ12 WQ12 UQ1VQ1 UQ1WQ1 VQ1WQ1 ; | 75 | 75 SET UQ2M=@MEAN(1)*T1;SET VQ2M=@MEAN(2)*T1; | 77 SET WQ2M=@MEAN(3)*T1;SET UQVQM=@MEAN(4)*T1; | 79 SET UQWQM=@MEAN(5)*T1;SET VQWQM=@MEAN(6)*T1; | 81 SET UQ12M=@MEAN(7)*T2;SET VQ12M=@MEAN(8)*T2; | 83 SET WQ12M=@MEAN(9)*T2;SET UQ1VQ1M=@MEAN(10)*T2; | 85 SET UQ1WQ1M=@MEAN(11)*T2;SET VQ1WQ1M=@MEAN(12)*T2; | 87 | 87 ?GM THREE EQUATION ESTIMATE FOR RHO AND SIGV | 87 ?------------------------------------------------- | 87 FRML EQUSU HMY = HM1*RHOH + HM2*RHOH**2 + HM3*SIGV; | 88 SMPL 1 3; | 89 GENR HM1 = 0; | 90 GENR HM2 = 0; | 91 GENR HM3 = 0; | 92 GENR HMY = 0; | 93 | 93 SMPL 1 1; | 94 HM1 = 2*UQVQM; | 95 HM2 = -VQ2M; | 96 HM3 = 1; | 97 HMY = UQ2M; | 98 | 98 SMPL 2 2; | 99 HM1 = 2*VQWQM; | 100 HM2 = -WQ2M; | 101 HM3 = MMM; | 102 HMY = VQ2M; | 103 | 103 SMPL 3 3; | 104 HM1 = VQ2M+UQWQM; | 105 HM2 = -VQWQM; | 106 HM3 = 0; | 107 HMY = UQVQM; | 108 | 108 | 108 ?ESTIMATE RHO AND SIGV FROM THREE EQUATIONS BY NLS | 108 ?INITIAL GM ESTIMATORS (L=1) | 108 ?------------------------------------------------- | 108 SMPL 1 3; | 109 PARAM RHOH SIGV ; | 110 LSQ (SILENT,MAXIT=500,MAXSQZ=20,TOL=0.001) EQUSU; | 111 SET SIGV = SIGV; | 112 SET RHOH = RHOH; | 113 SET SIG1 = UQ12M - (2*UQ1VQ1M*RHOH) - (-1*VQ12M*(RHOH**2)); | 114 SET VAR1= ((SIGV**2)/(T-1))**0.5; | 115 SET VAR2 = (SIG1**2)**0.5; | 116 | 116 IF L=1; THEN;TITLE 'INITIAL GM ESTIMATORS'; | 119 IF L=1; THEN;SET RHOGMP=RHOH; | 122 IF L=1; THEN;SET SIGVV=SIGV; | 125 IF L=1; THEN;SET SIG11=SIG1; | 128 IF L=2; THEN;TITLE 'PARTIALLY WEIGHTED ESTIMATORS'; | 131 IF L=3; THEN;TITLE 'WEIGHTED ESTIMATORS'; | 134 | 134 TITLE 'STEP 2, 1st. Part: '; | 135 TITLE 'INITIAL GM ESTIMATES FOR RHO AND THE VARIANCE COMPONENTS'; | 136 PRINT RHOH SIGV SIG1; | 137 | 137 ?ESTIMATE OF THE VARIANCE COVARIANCE MATRIX | 137 ?WEIGHTING MATRICES (L=2 AND L=3) | 137 ?------------------------------------------------- | 137 | 137 IF L=2; THEN;SET VAR11=NS*((1*(SIGV**2)/(NS*(T-1)))); | 140 IF L=2; THEN;SET VAR22=NS*((1*(SIGV**2)/(NS*(T-1)))); | 143 IF L=2; THEN;SET VAR33=NS*((1*(SIGV**2)/(NS*(T-1)))); | 146 IF L=2; THEN;SET VAR44=NS*((1*(SIG1**2)/NS)); | 149 IF L=2; THEN;SET VAR55=NS*((1*(SIG1**2)/NS)); | 152 IF L=2; THEN;SET VAR66=NS*((1*(SIG1**2)/NS)); | 155 IF L=2; THEN;SET VAR12 = 0; | 158 IF L=2; THEN;SET VAR23 = 0; | 161 IF L=2; THEN;SET VAR45 = 0; | 164 IF L=2; THEN;SET VAR56 = 0; | 167 | 167 IF L=3; THEN;SET VAR11 = NS*((2*(SIGV**2)/(NS*(T-1)))); | 170 IF L=3; THEN;SET VAR22 = NS*((2*(SIGV**2)/(NS*(T-1)))*MQ0); | 173 IF L=3; THEN;SET VAR33 = NS*((1*(SIGV**2)/(NS*(T-1)))*MQ1); | 176 IF L=3; THEN;SET VAR44 = NS*((2*(SIG1**2)/NS)); | 179 IF L=3; THEN;SET VAR55 = NS*((2*(SIG1**2)/NS)*MQ0); | 182 IF L=3; THEN;SET VAR66 = NS*((1*(SIG1**2)/NS)*MQ1); | 185 IF L=3; THEN;SET VAR12 = NS*(2*(SIGV**2)/(NS*(T-1)))*MWT; | 188 IF L=3; THEN;SET VAR23 = NS*(1*(SIGV**2)/(NS*(T-1)))*MWTT; | 191 IF L=3; THEN;SET VAR45 = NS*(2*(SIG1**2)/NS)*MWT; | 194 IF L=3; THEN;SET VAR56 = NS*(1*(SIG1**2)/NS)*MWTT; | 197 | 197 | 197 IF L>1;THEN;DO; | 200 MFORM (NROW=6,NCOL=6,TYPE=SYM) VCOV=0; | 201 | 201 SET VCOV(1,1)=VAR11; | 202 SET VCOV(1,2)=VAR12; | 203 SET VCOV(2,2)=VAR22; | 204 SET VCOV(2,3)=VAR23; | 205 SET VCOV(3,3)=VAR33; | 206 SET VCOV(4,4)=VAR44; | 207 SET VCOV(4,5)=VAR45; | 208 SET VCOV(5,5)=VAR55; | 209 SET VCOV(5,6)=VAR56; | 210 SET VCOV(6,6)=VAR66; | 211 MAT VCOV=VCOV"; | 212 MAT P = CHOL(VCOV); | 213 | 213 ?ESTIMATE RHO, SIGV AND SIG1 FROM SIX EQUATIONS BY NLS | 213 ?PARTIALLY WEIGHTED (L=2) AND WEIGHTED (L=3) GM ESTIMATORS | 213 ?--------------------------------------------------------- | 213 FRML EQUSS HMY = HM1*RHOGMP + HM2*RHOGMP**2 + HM3*SIGVV + HM4*SIG11; | 214 | 214 SMPL 1 6; | 215 GENR HM1 = 0; | 216 GENR HM2 = 0; | 217 GENR HM3 = 0; | 218 GENR HM4 = 0; | 219 GENR HMY = 0; | 220 | 220 SMPL 1 1; | 221 HM1 = 2*UQVQM*P(1,1)+2*VQWQM*P(1,2); | 222 HM2 = -VQ2M*P(1,1)-WQ2M*P(1,2); | 223 HM3 = 1*P(1,1)+MMM*P(1,2); | 224 HM4 = 0; | 225 HMY = UQ2M*P(1,1)+VQ2M*P(1,2); | 226 | 226 SMPL 2 2; | 227 HM1 = 2*UQVQM*P(2,1)+2*VQWQM*P(2,2)+(VQ2M+UQWQM)*P(2,3); | 228 HM2 = -VQ2M*P(2,1)-WQ2M*P(2,2)-VQWQM*P(2,3); | 229 HM3 = 1*P(2,1)+MMM*P(2,2); | 230 HM4 = 0; | 231 HMY = UQ2M*P(2,1)+VQ2M*P(2,2)+UQVQM*P(2,3); | 232 | 232 SMPL 3 3; | 233 HM1 = 2*VQWQM*P(3,2)+(VQ2M+UQWQM)*P(3,3); | 234 HM2 = -WQ2M*P(3,2)-VQWQM*P(3,3); | 235 HM3 = MMM*P(3,2); | 236 HM4 = 0; | 237 HMY = VQ2M*P(3,2)+UQVQM*P(3,3); | 238 | 238 SMPL 4 4; | 239 HM1 = 2*UQ1VQ1M*P(4,4)+2*VQ1WQ1M*P(4,5); | 240 HM2 = -VQ12M*P(4,4)-WQ12M*P(4,5); | 241 HM3 = 0; | 242 HM4 = 1*P(4,4)+MMM*P(4,5); | 243 HMY = UQ12M*P(4,4)+VQ12M*P(4,5); | 244 | 244 SMPL 5 5; | 245 HM1 = 2*UQ1VQ1M*P(5,4)+2*VQ1WQ1M*P(5,5)+(VQ12M+UQ1WQ1M)*P(5,6); | 246 HM2 = -VQ12M*P(5,4)-WQ12M*P(5,5)-VQ1WQ1M*P(5,6); | 247 HM3 = 0; | 248 HM4 = 1*P(5,4)+MMM*P(5,5); | 249 HMY = UQ12M*P(5,4)+VQ12M*P(5,5)+UQ1VQ1M*P(5,6); | 250 | 250 SMPL 6 6; | 251 HM1 = 2*VQ1WQ1M*P(6,5)+(VQ12M+UQ1WQ1M)*P(6,6); | 252 HM2 = -WQ12M*P(6,5)-VQ1WQ1M*P(6,6); | 253 HM3 = 0; | 254 HM4 = MMM*P(6,5); | 255 HMY = VQ12M*P(6,5)+UQ1VQ1M*P(6,6); | 256 | 256 ?------------------------------------------ | 256 SMPL 1 6; | 257 PARAM RHOGMP SIGVV SIG11; | 258 LSQ (SILENT,MAXIT=500,MAXSQZ=20,TOL=0.001) EQUSS; | 259 ENDDO; | 260 TITLE 'STEP 2, 2nd. Part: '; | 261 TITLE 'WEIGHTED NLS ESTIMATORS FOR RHO AND THE VARIANCE COMPONENTS'; | 262 TITLE '(FOR L=1 this part is ommited and the output should be'; | 263 TITLE 'equal to the one obtained in the 1st. part of step 2)'; | 264 PRINT RHOGMP SIGVV SIG11; | 265 | 265 | 265 ?************************************************************** | 265 ?IN THE THIRD STEP USE THE GM ESTIMATES FOR SPATIAL * | 265 ?AUTOREGRESSIVE PARAMETER, CORRECT FOR SPATIAL CORRELATION * | 265 ?IN DISTURBANCES AND ESTIMATE THE CORRECTED MODEL BY OLS * | 265 ?************************************************************** | 265 | 265 INPUT C:\TEMP\GLSPROC3; | 265 SMPL 1 NT; | 266 MMAKE YMAT Y; | 267 MMAKE X1MAT X1; | 268 MMAKE X2MAT X2; | 269 MAT GMAT = TMAT#(IMAT - RHOGMP*MMAT); | 270 MAT YSMAT = GMAT*YMAT; | 271 MAT X1SMAT = GMAT*X1MAT; | 272 MAT X2SMAT = GMAT*X2MAT; | 273 MAT OMGINV = (1/(SIGVV**0.5))*Q0 + (1/(SIG11**0.5))*Q1; | 274 MAT YTSMAT = OMGINV*YSMAT; | 275 MAT X1TSMAT = OMGINV*X1SMAT; | 276 MAT X2TSMAT = OMGINV*X2SMAT; | 277 UNMAKE YTSMAT YTS; | 278 UNMAKE X1TSMAT X1TS; | 279 UNMAKE X2TSMAT X2TS; | 280 OLSQ (SILENT) YTS X1TS X2TS; | 281 SET AHFGLS = @COEF(1); | 282 SET BHFGLS = @COEF(2); | 283 SET SHFGLS = (@SSR)/(NS-1); | 284 TITLE 'STEP 3: FEASIBLE GLS ESTIMATORS'; | 285 PRINT AHFGLS BHFGLS SHFGLS; | 286 | 286 | 286 DATE;STOP;END; EXECUTION ******************************************************************************* Current sample: 1 to 400 Current sample: 1 to 100 Current sample: 1 to 400 STEP 1: OLS ESTIMATORS AND ESTIMATED DISTURBANCES ================================================== AHOLS BHOLS SHOLS Value 1.09107 1.00003 22.21592 Current sample: 1 to 400 Current sample: 1 to 400 Current sample: 1 to 400 Current sample: 1 to 3 Current sample: 1 to 1 Current sample: 2 to 2 Current sample: 3 to 3 Current sample: 1 to 3 WEIGHTED ESTIMATORS =================== STEP 2, 1st. Part: ================== INITIAL GM ESTIMATES FOR RHO AND THE VARIANCE COMPONENTS ======================================================== RHOH SIGV SIG1 Value 0.63181 1.00192 6.55130 Current sample: 1 to 6 Current sample: 1 to 1 Current sample: 2 to 2 Current sample: 3 to 3 Current sample: 4 to 4 Current sample: 5 to 5 Current sample: 6 to 6 Current sample: 1 to 6 STEP 2, 2nd. Part: ================== WEIGHTED NLS ESTIMATORS FOR RHO AND THE VARIANCE COMPONENTS =========================================================== (FOR L=1 this part is ommited and the output should be ====================================================== equal to the one obtained in the 1st. part of step 2) ===================================================== RHOGMP SIGVV SIG11 Value 0.63731 0.99867 6.51341 Current sample: 1 to 400 STEP 3: FEASIBLE GLS ESTIMATORS =============================== AHFGLS BHFGLS SHFGLS Value 1.23529 0.99723 4.03824 03/31/04 1:51 PM ******************************************************************************* END OF OUTPUT. MEMORY USAGE: ITEM: DATA ARRAY TOTAL MEMORY UNITS: (4-BYTE WORDS) (MEGABYTES) MEMORY ALLOCATED : 31500000 128.0 MEMORY ACTUALLY REQUIRED : 2713979 13.0 CURRENT VARIABLE STORAGE : 1757408