*------------------------------------------------------------------------ * MUMIAS SCHEME METHOD OF MOMENTS *------------------------------------------------------------------ OPTION LP=MINOS; OPTION NLP=MINOS; *------------------------------------------------------------------ *DIMENSION DEFINITION *----------------------------------------------------------------- SETS J OUTPUT AND INPUTS /CANE,SEED,FERT,FLAB,HLAB, LPREP/ OUTPUT(J) CANE OUTPUT /CANE/ INPUTS(J) INPUTS /SEED,FERT,FLAB,HLAB, LPREP/ H DMUS /1*53/; ALIAS (H,I); *-------------------------------------------------------- *DATA ENTRY *-------------------------------------------------------- TABLE DATA (H,J) CANE SEED FERT FLAB HLAB LPREP 1 33.33 4.00 166.67 1.33 166.67 5600.00 2 36.67 5.33 200.00 13.33 168.67 4000.00 3 34.00 5.00 200.00 10.00 212.00 4800.00 4 35.00 3.50 200.00 10.00 183.00 3750.00 5 35.00 4.50 200.00 3.00 169.00 2600.00 6 37.71 5.71 200.00 2.29 185.14 4114.29 7 38.67 4.67 166.67 5.33 184.67 5600.00 8 40.22 4.00 180.00 3.20 200.80 4000.00 9 36.00 4.00 200.00 3.00 181.00 4000.00 10 37.33 4.67 200.00 13.33 180.00 4000.00 11 42.50 3.50 200.00 2.00 225.00 3597.23 12 35.00 4.00 175.00 3.00 150.00 5600.00 13 32.00 4.00 166.67 2.67 130.00 5600.00 14 30.00 6.00 175.00 3.00 143.50 7600.00 15 30.00 6.00 150.00 4.00 150.00 4000.00 16 37.50 5.00 200.00 2.00 154.00 6050.00 17 40.00 6.00 250.00 2.00 177.00 5000.00 18 40.00 6.00 233.33 5.33 169.33 3333.33 19 46.00 4.00 200.00 16.00 264.00 6000.00 20 38.00 4.00 200.00 8.00 208.00 6000.00 21 38.00 4.00 200.00 4.00 200.00 4800.00 22 46.67 5.33 200.00 1.33 213.67 3333.33 23 48.00 4.00 200.00 2.00 240.00 4000.00 24 40.00 3.00 200.00 1.00 206.00 4000.00 25 38.67 4.67 200.00 10.67 190.00 4063.87 26 40.00 3.00 200.00 3.00 178.50 4100.00 27 40.00 3.50 200.00 2.00 215.00 4000.00 28 46.00 4.00 200.00 3.00 228.00 4000.00 29 40.00 4.00 200.00 1.33 202.67 3933.33 30 38.67 3.33 200.00 1.33 190.00 4000.00 31 28.00 5.00 200.00 2.00 112.00 4000.00 32 32.00 4.00 200.00 2.67 173.33 3333.33 33 45.00 6.00 200.00 12.00 198.00 7000.00 34 38.00 4.00 200.00 10.00 188.00 2400.00 35 38.00 3.50 200.00 2.25 205.00 3450.00 36 45.60 4.00 200.00 0.10 287.90 4800.00 37 32.50 4.50 200.00 4.00 172.25 4050.00 38 43.33 4.00 200.00 2.67 203.33 4533.33 39 30.00 5.00 200.00 12.00 179.00 5200.00 40 35.00 4.00 225.00 4.00 229.50 4000.00 41 40.00 4.80 200.00 1.60 247.20 4800.00 42 34.67 4.67 200.00 2.67 198.67 5600.00 43 45.00 4.00 200.00 4.00 340.50 4000.00 44 34.29 5.14 142.86 2.29 205.14 4342.86 45 42.00 4.00 200.00 9.00 220.00 4200.00 46 40.00 4.00 200.00 3.00 199.00 4000.00 47 32.00 4.67 200.00 13.33 168.00 5333.33 48 42.00 5.00 200.00 9.00 190.00 4000.00 49 37.33 4.00 200.00 3.33 181.33 3466.67 50 27.52 4.00 200.00 1.33 143.33 3297.33 51 45.33 5.33 200.00 2.67 219.33 5866.67 52 44.00 4.00 200.00 16.00 200.00 5333.33 53 38.00 6.00 200.00 4.00 175.00 3597.25 ; *---------------------------------------------------------- *DEFINITING PARAMETERS AND VARIABLES *------------------------------------------------------------ PARAMETERS Y(H) SUGARCANE OUTPUT IN METRIC TONNES S(H) SEED CANE IN METRIC TONNES F(H) FAMILY LABOUR IN PERSONDAYS R(H) FERTILIZER IN KILOGRAMS L(H) HIRED LABOUR IN PERSONDAYS P(H) LAND PREPARATION IN MACHINE HOURS N NUMBER OF DMUS ; VARIABLES A(H) INTERCEPT E(H) ERROR TERM SS SUM OF SQUARE OF ERRORS MRESID MEAN OF THE RESIDUES M2(H) SECOND MOMENT AROUND THE MEAN M3(H) THIRD MOMENT AROUND THE MEAN MM2 AVERAGE OF THE SECOND MOMENT MM3 AVERAGE OF THE THIRD MOMENT SIGMAU SIGMAV SUMSIGMA2 LAMDA MYY EPSILON(H) TEMP2(H) EU(H) ETHETA(H) ; POSITIVE VARIABLES BS(H) MARGINAL PRODUCT OF SEED BF(H) MARGINAL PRODUCT OF FAMILY LABOUR BR(H) MARGINAL PRODUCT OF FETILIZER BL(H) MARGINAL PRODUCT OF HIRED LABOUR BP(H) MARGINAL PRODUCT OF LAND PREPARATION ; *================================================================= *SETTING UP THE EQUATIONS *================================================================= EQUATIONS QSSE OBJECTIVE=SUM OF SQUARES OF ERRORS QREGR(H) REGRESSION EQUATION QCONC(H,I) CONCAVITY CONSTRAINT ; QSSE .. SS =E= SUM(H, E(H)*E(H)); QREGR(H) .. Y(H)=E= A(H)+ BS(H)*S(H)+ BF(H)*F(H)+BR(H)*R(H)+BL(H)*L(H)+BP(H)*P(H)+ E(H); QCONC(H,I).. A(H)+ BS(H)*S(H)+ BF(H)*F(H)+BR(H)*R(H)+BL(H)*L(H)+BP(H)*P(H)=L=A(I) +BS(I)*S(I)+ BF(I)*F(I)+BR(I)*R(I)+BL(I)*L(I)+BP(I)*P(I); ALIAS (H,ITER); *================================================== * ASSIGNING THE DATA TO VARIABLES *================================================== Y(H)= DATA(H,'CANE'); S(H)= DATA(H,'SEED'); F(H)= DATA(H,'FLAB'); R(H)= DATA(H,'FERT'); L(H)= DATA(H,'HLAB'); P(H)= DATA(H,'LPREP'); N = CARD(H); *================================================= * SOLVE THE MODEL *================================================ MODEL MUMIASTONED /QSSE, QREGR, QCONC/ SOLVE MUMIASTONED USING NLP MINIMIZING SS; *================================================= * FORMATTING FOR THE DISPLAY COMMAND *================================================= OPTION SS:3:0:1; DISPLAY SS.L; *============================================================ * DECOMPOSE INEFFICIENCY AND NOISE USING METHOD OF MOMENTS *========================================================== MRESID.L = SUM(H,E.L(H))/N; M2.L(H) = (E.L(H) - MRESID.L)*(E.L(H) - MRESID.L); M3.L(H) = (E.L(H) - MRESID.L)*(E.L(H) - MRESID.L)*(E.L(H) - MRESID.L); MM2.L = SUM(H,M2.L(H))/N; MM3.L = SUM(H,M3.L(H))/N; IF (MM3.L > 0, MM3.L = 0); SIGMAU.L =(MM3.L/((2/PI)**(1/2)*(1-4/PI)))**(1/3); SIGMAV.L = (MM2.L-((PI-2)/PI)*SIGMAU.L**2)**(1/2); SUMSIGMA2.L = SIGMAU.L**2 + SIGMAV.L**2; LAMDA.L = SIGMAU.L / SIGMAV.L; MYY.L = (SIGMAU.L**2*2/PI)**(1/2); EPSILON.L(H) = (E.L(H) - MYY.L); TEMP2.L(H) = (1/(1*(2*PI)**(1/2)))*EXP((-((EPSILON.L(H)/(SIGMAV.L**2)) )* ((EPSILON.L(H)/(SIGMAV.L**2))))/(2*1**2)); EU.L(H) = (-EPSILON.L(H)*(SIGMAU.L**2)/SUMSIGMA2.L) + (TEMP2.L(H) / (1-ERRORF((EPSILON.L(H)/(SIGMAV.L**2)))))* (SIGMAU.L**2) * (SIGMAV.L**2) / SUMSIGMA2.L; ETHETA.L(H) = (A.L(H)+ BS.L(H)*S(H)+ BF.L(H)*F(H)+BR.L(H)*R(H) +BL.L(H)*L(H)+BP.L(H)*P(H)-EU.L(H))/(A.L(H)+ BS.L(H)*S(H)+ BF.L(H)*F(H) +BR.L(H)*R(H)+BL.L(H)*L(H)+BP.L(H)*P(H)); *======================================================== * FORMATTING FOR THE DISPLAY COMMAND *======================================================== OPTION ETHETA:3:0:1; OPTION E:3:0:1; OPTION MRESID:3:0:1; OPTION M2:3:0:1; OPTION M3:3:0:1; OPTION MM2:3:0:1; OPTION MM3:3:0:1; OPTION SIGMAU:3:0:1; OPTION SIGMAV:3:0:1; OPTION SUMSIGMA2:3:0:1; OPTION LAMDA:3:0:1; OPTION MYY:3:0:1; OPTION EPSILON:3:0:1; OPTION EU:3:0:1; DISPLAY E.L,MRESID.L,M2.L,M3.L,MM2.L,MM3.L,SIGMAU.L,SIGMAV.L,SUMSIGMA2.L,LAMDA.L,MYY.L,EPSILON.L,EU.L,ETHETA.L