name EcInquiry 'Nonhomothetic translog demand system'; ?***************************************************************** ?* * ?* Replication file for the (nonhomothetic) translog 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.txt 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') h1 h2 h3 h4 nobs; ? define team output as either WINS or ATTEND GENR Y=log(WINS); ? 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 with US CPI SMPL 1 26; ? 1986 GENR H1=H1*135.0/109.6; GENR H2=H2*135.0/109.6; GENR H3=H3*135.0/109.6; GENR H4=H4*135.0/109.6; SMPL 27 52; ? 1987 GENR H1=H1*135.0/113.6; GENR H2=H2*135.0/113.6; GENR H3=H3*135.0/113.6; GENR H4=H4*135.0/113.6; SMPL 53 78; ? 1988 GENR H1=H1*135.0/118.3; GENR H2=H2*135.0/118.3; GENR H3=H3*135.0/118.3; GENR H4=H4*135.0/118.3; SMPL 79 104; ? 1989 GENR H1=H1*135.0/124.0; GENR H2=H2*135.0/124.0; GENR H3=H3*135.0/124.0; GENR H4=H4*135.0/124.0; SMPL 105 130; ? 1990 GENR H1=H1*135.0/130.7; GENR H2=H2*135.0/130.7; GENR H3=H3*135.0/130.7; GENR H4=H4*135.0/130.7; SMPL 1 156; GENR TCOST=H1*q1+H2*q2+H3*q3+H4*q4; ? total hedonic costs ? generate cost shares GENR S1=H1*q1/TCOST; GENR S2=H2*q2/TCOST; GENR S3=H3*q3/TCOST; GENR S4=H4*q4/TCOST; ? select the 87 hedonic price vectors that do not include a ? zero price SELECT (H1>0.00001)&(H2>0.00001)&(H3>0.00001)&(H4>0.00001); ? descriptive statistics for cost shares under this subsample msd s1 s2 s3 s4; GENR P1=LOG(H1); GENR P2=LOG(H2); GENR P3=LOG(H3); GENR P4=LOG(H4); PARAM A1 B11 B12 B13 B14 B1; PARAM A2 B21 B22 B23 B24 B2; PARAM A3 B31 B32 B33 B34 B3; ? ** COBB-DOUGLAS SPECIAL CASE ** FRML E1 S1=A1; FRML E2 S2=A2; FRML E3 S3=A3; ?LSQ E1 E2 E3; ? ** FULL TRANSLOG SYSTEM ** FRML E1 S1=A1+B11*P1+B12*P2+B13*P3+B14*P4+B1*Y; FRML E2 S2=A2+B21*P1+B22*P2+B23*P3+B24*P4+B2*Y; FRML E3 S3=A3+B31*P1+B32*P2+B33*P3+B34*P4+B3*Y; LSQ(HET,TOL=0.0001) E1 E2 E3; COPY @VCOV VCOV1; LIST NAMES1 @RNMS; FRML H1 B1; FRML H2 B2; FRML H3 B3; ? JOINT TEST OF HOMOTHETICITY ?ANALYZ(NAMES=NAMES1,VCOV=VCOV1) H1 H2 H3; FRML HOM1 B11+B12+B13+B14; FRML HOM2 B21+B22+B23+B24; FRML HOM3 B31+B32+B33+B34; ANALYZ(NAMES=NAMES1,VCOV=VCOV1) HOM1 HOM2 HOM3; ? JOINT TEST OF HOMOGENEITY ?ANALYZ(NAMES=NAMES1,VCOV=VCOV1) HOM1 HOM2 HOM3 H1 H2 H3; ? JOINT TEST OF HOMOGENEITY AND HOMOTHETICITY FRML SYM1 B12-B21; FRML SYM2 B13-B31; FRML SYM3 B23-B32; ANALYZ(NAMES=NAMES1,VCOV=VCOV1) HOM1 HOM2 HOM3 SYM1 SYM2 SYM3; ? JOINT TEST OF HOMOGENEITY AND SYMMETRY ? ANALYZ(NAMES=NAMES1,VCOV=VCOV1) HOM1 HOM2 HOM3 H1 H2 H3 ? SYM1 SYM2 SYM3; ? JOINT TEST OF HOMOGENEITY, SYMMETRY, AND HOMOTHETICITY ? ** TRANSLOG WITH HOMOGENEITY IMPOSED ** FRML E1 S1=A1+B11*(P1-P4)+B12*(P2-P4)+B13*(P3-P4)+B1*Y; FRML E2 S2=A2+B21*(P1-P4)+B22*(P2-P4)+B23*(P3-P4)+B2*Y; FRML E3 S3=A3+B31*(P1-P4)+B32*(P2-P4)+B33*(P3-P4)+B3*Y; LSQ(HET,TOL=0.0001) E1 E2 E3; ANALYZ SYM1 SYM2 SYM3; ? ** TRANSLOG WITH HOMOGENEITY AND SYMMETRY IMPOSED ** FRML E1 S1=A1+B11*(P1-P4)+B12*(P2-P4)+B13*(P3-P4)+B1*Y; FRML E2 S2=A2+B12*(P1-P4)+B22*(P2-P4)+B23*(P3-P4)+B2*Y; FRML E3 S3=A3+B13*(P1-P4)+B23*(P2-P4)+B33*(P3-P4)+B3*Y; LSQ(TOL=0.0001) E1 E2 E3; UNMAKE @FIT S1FIT S2FIT S3FIT; GENR S4FIT=1-S1FIT-S2FIT-S3FIT; SET B14=-B11-B12-B13; SET B24=-B12-B22-B23; SET B34=-B13-B23-B33; SET B44=-B14-B24-B34; 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; YLDFAC B D L; PRINT D; ? THESE ARE FUNCTIONS OF EIGENVALUES OF B ? AND ARE REPRODUCED BELOW IN ESTIMATION MSD S1FIT S2FIT S3FIT S4FIT; ? EVALUATE ELASTICITIES AT MFORM S=@MEAN; ? POINT OF VARIABLE MEANS PRINT S; MFORM(NROW=4,TYPE=DIAG) MS=S; LOAD(TYPE=GENERAL,NROW=4,NCOL=4) E; 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1; INV MS MSINV; MMULT B MSINV BS; MMULT MSINV BS SBS; MADD SBS E SBSE; MSUB SBSE MSINV SUBST; ? ELASTICITIES OF SUBSTITUTION PRINT SUBST; YLDFAC SUBST D L; PRINT D; ? EIGENVALUES OF SUBST ? SHOULD BE NEGATIVE FOR CONCAVITY TO HOLD MMULT SUBST MS DEMAND; ? PRICE ELASTICITIES OF DEMAND PRINT DEMAND; STOP;