name EcInquiry 'Generalized Leontief demand system'; ?***************************************************************** ?* * ?* Replication file for the Generalized Leontief factor demand * ?* system of: Stewart & Jones (April 1998) * ?* "Hedonics and demand analysis: the implicit demand for * ?* player attributes," Economic Inquiry 36(2) 192-202. * ?* * ?***************************************************************** SMPL 1 156; ? 26 teams x 6 seasons (1986-91) ? read in team characteristics; documented in Team.doc read(file='Team.dat') season team league attend attlag ticprice pmarkup gameswon gameslst wins salaries nplayers strkouts walks slugavg nhitters npitchrs experhit experpit nstars roadatt aleast alcentrl alwest nleast nlcentrl nlwest; ? delete variables not used in this analysis delete season team league attlag ticprice pmarkup gameswon gameslst salaries nplayers roadatt aleast alcentrl alwest nleast nlcentrl nlwest; ? read in hedonic prices read(file='HedPrice1.dat') p1 p2 p3 p4 nobs; ? define team output as either WINS or ATTEND GENR QY=wins; MSD QY; COPY @MEAN MEANQY; ? define team factor inputs: experience, hitting, pitching, stars GENR q1=experhit+experpit; GENR q2=nhitters*slugavg; GENR q3=npitchrs*strkouts/walks; GENR q4=nstars; ? DEFLATE HEDONIC PRICES TO 1991 DOLLARS SMPL 1 26; GENR p1=p1*135.0/109.6; GENR p2=p2*135.0/109.6; GENR p3=p3*135.0/109.6; GENR p4=p4*135.0/109.6; SMPL 27 52; GENR p1=p1*135.0/113.6; GENR p2=p2*135.0/113.6; GENR p3=p3*135.0/113.6; GENR p4=p4*135.0/113.6; SMPL 53 78; GENR p1=p1*135.0/118.3; GENR p2=p2*135.0/118.3; GENR p3=p3*135.0/118.3; GENR p4=p4*135.0/118.3; SMPL 79 104; GENR p1=p1*135.0/124.0; GENR p2=p2*135.0/124.0; GENR p3=p3*135.0/124.0; GENR p4=p4*135.0/124.0; SMPL 105 130; GENR p1=p1*135.0/130.7; GENR p2=p2*135.0/130.7; GENR p3=p3*135.0/130.7; GENR p4=p4*135.0/130.7; SMPL 1 156; GENR A1=P1*Q1/QY; ? some hedonic prices take on zero values; GENR A2=P2*Q2/QY; ? therefore GL system must be estimated in GENR A3=P3*Q3/QY; ? this form rather than in Berndt's GENR A4=P4*Q4/QY; ? parameterization GENR TC=P1*Q1+P2*Q2+P3*Q3+P4*Q4; ? hedonic costs GENR S1=P1*Q1/TC; ? cost shares GENR S2=P2*Q2/TC; GENR S3=P3*Q3/TC; GENR S4=P4*Q4/TC; MSD S1 S2 S3 S4; ? mean hedonic cost shares GENR P12=SQRT(P1*P2); GENR P13=SQRT(P1*P3); GENR P14=SQRT(P1*P4); GENR P21=P12 ; GENR P23=SQRT(P2*P3); GENR P24=SQRT(P2*P4); GENR P31=P13 ; GENR P32=P23 ; GENR P34=SQRT(P3*P4); GENR P41=P14 ; GENR P42=P24 ; GENR P43=P34 ; PARAM B11 B12 B13 B14 B1; PARAM B21 B22 B23 B24 B2; PARAM B31 B32 B33 B34 B3; PARAM B41 B42 B43 B44 B4; ? ** SYMMETRY NOT IMPOSED ** FRML EQ1 A1=B11*P1 +B12*P12+B13*P13+B14*P14+B1*P1*QY; FRML EQ2 A2=B21*P21+B22*P2 +B23*P23+B24*P24+B2*P2*QY; FRML EQ3 A3=B31*P31+B32*P32+B33*P3 +B34*P34+B3*P3*QY; FRML EQ4 A4=B41*P41+B42*P42+B43*P43+B44*P4 +B4*P4*QY; LSQ(het,MAXIT=100,tol=0.00001) EQ1 EQ2 EQ3 EQ4; FRML R1 B1; FRML R2 B2; FRML R3 B3; FRML R4 B4; ANALYZ R1 R2 R3 R4; ? test homotheticity FRML R12 B12-B21; FRML R13 B13-B31; FRML R14 B14-B41; FRML R23 B23-B32; FRML R24 B24-B42; FRML R34 B34-B43; ANALYZ R12 R13 R14 R23 R24 R34; ? test symmetry ? ** SYMMETRY IMPOSED ** FRML EQ1 A1=B11*P1 +B12*P12+B13*P13+B14*P14+B1*P1*QY; FRML EQ2 A2=B12*P21+B22*P2 +B23*P23+B24*P24+B2*P2*QY; FRML EQ3 A3=B13*P31+B23*P32+B33*P3 +B34*P34+B3*P3*QY; FRML EQ4 A4=B14*P41+B24*P42+B34*P43+B44*P4 +B4*P4*QY; LSQ(MAXIT=200,tol=0.000001) EQ1 EQ2 EQ3 EQ4; UNMAKE @FIT F1 F2 F3 F4; GENR CYFIT=F1+F2+F3+F4; ? obtaining fitted factor cost MSD F1 F2 F3 F4; COPY @MEAN UCVEC; MSD P1 P2 P3 P4; COPY @MEAN PVEC; MEDIV UCVEC PVEC AVEC; GENR CFIT=CYFIT*MEANQY; MSD CFIT; MSD CYFIT; COPY @MEAN CY; MDIV UCVEC CY SVEC; COPY PVEC PSQVEC; ? initialize SET PSQVEC(1)=SQRT(PVEC(1)); SET PSQVEC(2)=SQRT(PVEC(2)); SET PSQVEC(3)=SQRT(PVEC(3)); SET PSQVEC(4)=SQRT(PVEC(4)); MMAKE B B11 B12 B13 B14 B12 B22 B23 B24 B13 B23 B33 B34 B14 B24 B34 B44; MFORM(TYPE=GENERAL,NROW=4,NCOL=4) B; PRINT B; SET ALPHA=0.5; MFORM(NROW=4,TYPE=DIAG) P=PVEC; MFORM(NROW=4,TYPE=DIAG) S=SVEC; MFORM(NROW=4,TYPE=DIAG) PSQ=PSQVEC; MFORM(NROW=4,TYPE=DIAG) A=AVEC; LOAD(TYPE=GENERAL,NROW=4,NCOL=4) E; 0 -1 -1 -1 -1 0 -1 -1 -1 -1 0 -1 -1 -1 -1 0; INV P PINV; INV S SINV; INV PSQ PSQINV; INV A AINV; MMULT B PSQ BP; MMULT PSQINV BP PBP; MMULT AINV PBP APBP; MMULT ALPHA APBP AAPBP; PRINT AAPBP; ? OFF-DIAG ELEMENTS ARE CROSS-PRICE ELASTICITIES MMULT AAPBP E AAPBPE; PRINT AAPBPE; ? DIAG ELEMENTS ARE OWN-PRICE ELASTICITIES MMULT AAPBP SINV AAPBPS; PRINT AAPBPS; ? OFF-DIAG ELEMENTS ARE H-A CROSS ELASTICITIES OF SUBST MMULT AAPBPE SINV AAPBPES; PRINT AAPBPES; ? DIAG ELEMENTS ARE Hicks-Allen OWN-ELASTICITIES STOP;