name REStat 'Homothetic translog demand system'; ?***************************************************************** ?* * ?* Replication file for the (homothetic) translog factor * ?* demand system of Ferguson, Stewart, and Jones (August 2000) * ?* "Competition within a cartel: League conduct and team * ?* conduct in the market for baseball player services," * ?* Review of Economics and Statistics 82(3) 422-430. * ?* * ?***************************************************************** 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 attend attlag ticprice pmarkup gameswon gameslst wins salaries nplayers roadattaleast alcentrl alwest nleast nlcentrl nlwest; ? read in city characteristics; documented in City.doc read(file='City.dat') season team pop income white black hispanic landarea hincome nprfsprt; ? read in hedonic prices read(file='HedPrice2.dat') h1 h2 h3 h4 nobs; ? 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; ? 6 seasons: 1986-91 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; ? define instruments for use in Hausman tests genr I1=log(pop/1000000); ? population of home city genr I2=log(income/10000); ? per capita income of the home city genr I3=black; ? percent black genr I4=hispanic; ? percent hispanic genr I5=log(landarea); ? urban land area genr I6=log(hincome/10000);? average household income genr I7=log(nprfsprt); ? number of professional sports teams ? in city ? select the 84 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); olsq P1 c I1 I2 I3 I4 I5 I6 I7; ? obtain residuals for use as genr T1=@RES; ? test variables in Hausman test olsq P2 c I1 I2 I3 I4 I5 I6 I7; genr T2=@RES; olsq P3 c I1 I2 I3 I4 I5 I6 I7; genr T3=@RES; olsq P4 c I1 I2 I3 I4 I5 I6 I7; genr T4=@RES; PARAM A1 B11 B12 B13 B14; PARAM A2 B21 B22 B23 B24; PARAM A3 B31 B32 B33 B34; PARAM C11 C12 C13 C14; PARAM C21 C22 C23 C24; PARAM C31 C32 C33 C34; ? ** COBB-DOUGLAS SPECIAL CASE ** FRML E1 S1=A1; FRML E2 S2=A2; FRML E3 S3=A3; ?LSQ E1 E2 E3; ? ** HOMOTHETIC TRANSLOG ** FRML E1 S1=A1+B11*P1+B12*P2+B13*P3+B14*P4; FRML E2 S2=A2+B21*P1+B22*P2+B23*P3+B24*P4; FRML E3 S3=A3+B31*P1+B32*P2+B33*P3+B34*P4; LSQ(TOL=0.0001) E1 E2 E3; FRML HOM1 B11+B12+B13+B14; FRML HOM2 B21+B22+B23+B24; FRML HOM3 B31+B32+B33+B34; ? JOINT TEST OF HOMOGENEITY ANALYZ HOM1 HOM2 HOM3; FRML SYM1 B12-B21; FRML SYM2 B13-B31; FRML SYM3 B23-B32; ? JOINT TEST OF HOMOGENEITY AND SYMMETRY ANALYZ HOM1 HOM2 HOM3 SYM1 SYM2 SYM3; ? ** HOMOTHETIC TRANSLOG WITH HAUSMAN TEST VARIABLES ** FRML E1 S1=A1+B11*P1+B12*P2+B13*P3+B14*P4 +C11*T1+C12*T2+C13*T3+C14*T4; FRML E2 S2=A2+B21*P1+B22*P2+B23*P3+B24*P4 +C21*T1+C22*T2+C23*T3+C24*T4; FRML E3 S3=A3+B31*P1+B32*P2+B33*P3+B34*P4 +C31*T1+C32*T2+C33*T3+C34*T4; LSQ(TOL=0.0001) E1 E2 E3; ? ** HOMOTHETIC TRANSLOG WITH HOMOGENEITY IMPOSED ** FRML E1 S1=A1+B11*(P1-P4)+B12*(P2-P4)+B13*(P3-P4); FRML E2 S2=A2+B21*(P1-P4)+B22*(P2-P4)+B23*(P3-P4); FRML E3 S3=A3+B31*(P1-P4)+B32*(P2-P4)+B33*(P3-P4); LSQ(HET,TOL=0.0001) E1 E2 E3; ANALYZ SYM1 SYM2 SYM3; ? test of symmetry ? ** HOMOTHETIC TRANSLOG WITH HOMOGENEITY AND SYMMETRY IMPOSED ** FRML E1 S1=A1+B11*(P1-P4)+B12*(P2-P4)+B13*(P3-P4); FRML E2 S2=A2+B12*(P1-P4)+B22*(P2-P4)+B23*(P3-P4); FRML E3 S3=A3+B13*(P1-P4)+B23*(P2-P4)+B33*(P3-P4); 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;