*------------------------------------------------------------------------ * MUMIAS SCHEME METHOD OF MOMENT *------------------------------------------------------------------ OPTION LP=MINOS; OPTION NLP=MINOS; *------------------------------------------------------------------ *SET DEFINITION *----------------------------------------------------------------- SETS J OUTPUT AND INPUTS /CANE,SEED,FERT,FLAB,HLAB, LPREP/ OUT(J) SUGARCANE OUTPUT /CANE/ INP(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) COST OF LAND PREPARATION IN KSH N NUMBER OF DMUS ; VARIABLES A(H) INTERCEPT E(H) ERROR TERM SS SUM OF SQUARE OF ERRORS LIKE LOG LIKELIHOOD SIGMA TOTAL SIGMA VARIABLE LAMBDA LAMBDA VARIABLE EPSILON(H) EPSILON SIGMAU SIGMA FOR INEFFICIENCY SIGMAV SIGMA FOR NOISE ; 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/ OPTION solvelink = 0; OPTION limrow = 0; OPTION limcol = 0; OPTION SOLPRINT = OFF; OPTION optcr = 0.0; OPTION iterlim = 10000000; OPTION reslim = 10000000; OPTION decimals=7; SOLVE MUMIASTONED USING NLP MINIMIZING SS; *================================================= * FORMATTING FOR THE DISPLAY COMMAND *================================================= OPTION E:3:0:1; OPTION SS:3:0:1; DISPLAY E.L, SS.L; *============================================================ * DECOMPOSE INEFFICIENCY AND NOISE USING METHOD OF MOMENTS *========================================================== EQUATIONS QLIKE LOG LIKELIHOOD EQUATION QEPS(H) EPSILON EQUATION QSIGMA SIGMA EQUATION; QLIKE .. LIKE =E= -N*LOG(SIGMA)+SUM(H,LOG(ERRORF(-EPSILON(H)/SIGMA*LAMBDA))+0.000001) -0.5*SUM(H,EPSILON(H)**2)/(SIGMA**2); QEPS(H).. EPSILON(H)=E= E.L(H); *-SQRT(2)*SIGMA*LAMBDA/SQRT(PI*(1+LAMBDA**2)); QSIGMA .. SIGMA=E= (1/N)*(SUM(H,E.L(H))**2)/(1-(2*LAMBDA**2/SQRT(PI*(1+LAMBDA**2)))); *============================================================== * FORMATTING FOR THE DISPLAY COMMAND *============================================================== MODEL LIKELIHOOD /QLIKE,QEPS,QSIGMA/; LAMBDA.LO = 0.001; SIGMA.LO = 0.001; OPTION domlim = 5; SOLVE LIKELIHOOD USING NLP MAXIMIZING LIKE; SIGMAU.L = SIGMA.L*LAMBDA.L/(1+LAMBDA.L); SIGMAV.L = SIGMA.L/(1+LAMBDA.L); OPTION E:3:0:1; OPTION LIKE:3:0:1; OPTION EPSILON:3:0:1; OPTION SIGMA:3:0:1; OPTION LAMBDA:3:0:1; OPTION SIGMAU:3:0:1; OPTION SIGMAV:3:0:1; DISPLAY E.L, SIGMA.L, LAMBDA.L, LIKE.L, EPSILON.L, SIGMAU.L, SIGMAV.L;