Multiproduct Pricing in Major League Baseball (Figures)

Figure 1. Simple Structural Model and Principal Components Breakdown. M P2 G c m G m c M P1 Note: The ellipse circumscribes the scatterplot of realized (P1,P2) points in the (hypothetical) data. Line GG reflects the effect of changes in general demand on P1 and P2, as discussed in the text, and has a slope of β2/β1. Line cc reflects the effect of changes in cost, and has a slope of -γ2/γ1. Line MM, the major axis of the ellipse, reflects the first principal component. Line mm, the minor axis, reflects the second component. Table 1a: Descriptive Statistics Variable Description M ean Std. Dev. M in M ax RPTIX RPARK RPBEER RPSODA RPDOG RPPROGRAM RPHAT ATTEND LAGINC Average per-game season ticket price Price of parking Price of 20oz Beer Price of 20oz Soda Price of hotdog Price of program Price of ball cap Total season home attendance (100Ks) Previous year’s MSA per-capita income ($1000s) MSA population (millions) Previous season’s wins (fraction) Age of team’s stadium in years Real wage of amusement workers (arbitrary units) Team’s stadium is single purpose (0/1) Time trend (1=1991) 13.95 7.30 5.18 2.58 2.27 3.56 11.79 22.16 4.51 2.85 0.92 0.53 0.55 1.06 2.15 7.22 8.29 2.93 3.19 1.41 0.78 0.69 4.73 9.05 39.83 19.19 10.57 4.70 4.23 7.35 20.00 44.83 30.49 4.49 22.47 47.14 6.27 0.50 30.11 5.49 0.06 24.37 1.60 0.32 0.00 21.31 0.70 89.00 1.20 0.38 0.58 2.34 0.61 6.16 0.48 3.16 0.00 1.00 1.00 11.00 POP LAGWIN STAGE RWAM USE SPURP TIME Price data (reported in upper panel) describe all Major League Baseball teams from 1991 through 2003 and were obtained from various issues of Team Marketing Report (TMR). All prices, incomes, and wages converted to 2000 dollars using the Consumer Price Index from the Bureau of Labor Statistics. Attendance and team win percentage obtained from Major League Baseball. Population and income obtained from Census Bureau. Stadium characteristics ob tained from Munsey and S upp es at www.ballparks.co m. Wage data obtained from the Regional Economic Information System of the Bureau of Eco nomic Analysis, as described in the text. The price data comprise a sample of 372 observations used in the principal component analysis. Stadium, income, wage, and population data are 342 observations for U.S. baseball teams (two Canadian teams not included). Table 1b: Correlation Matrix of Real Ticket, Parking and Concession Prices RPTIX RPARK RPBEER RPSODA RPDOG RPPROGRAM RPHAT RPTIX RPARK 1.00 0.59 0.45 0.53 0.45 0.14 0.05 1.00 0.33 0.27 0.17 0.12 -0.02 RPBEER RPSODA 1.00 0.50 0.48 0.02 0.06 1.00 0.52 0.10 0.13 RPDOG 1.00 0.18 0.14 RPPROGRAM 1.00 0.15 RPHAT 1.00 Price data describe all Major League Baseball teams from 1991 through 2003, were obta ined from various issues of Team Marketing Report (TMR), and were converted to 2000 dollars using the Consumer Price Index from the Bureau of Labor Statistics. Table 2a: Principal Components of All MLB Prices: Eigenvalues and Eigenvectors Variable RPTIX RPARK RPBEER RPSODA RPDOG RPPROGRAM RPHAT Eigenvalue Proportion of Variance Explained Eigenvector One Eigenvector Two Eigenvector Three Eigenvector Four Eigenvector Five Eigenvector Six Eigenvector Seven 0.49 0.36 0.44 0.46 0.43 0.15 0.10 2.79 -0.18 -0.33 -0.12 0.04 0.20 0.54 0.72 1.14 0.21 0.53 -0.29 -0.26 -0.30 0.64 -0.14 0.98 0.15 0.41 -0.04 -0.11 -0.36 -0.46 0.67 0.80 -0.33 0.10 0.80 -0.46 -0.10 0.15 0.04 0.52 -0.12 -0.14 0.21 0.63 -0.70 0.17 -0.03 0.46 -0.73 0.53 -0.15 0.31 0.24 -0.04 -0.02 0.31 0.40 0.16 0.14 0.11 0.07 0.07 0.04 Table 2b: Principal Components of Five MLB Prices: Eigenvalues and Eigenvectors Variable RPTIX RPARK RPBEER RPSODA RPDOG Eigenvalue Proportion of Variance Explained Eigenvector One Eigenvector Two Eigenvector Three Eigenvector Four Eigenvector Five 0.50 0.37 0.45 0.47 0.43 -0.30 -0.74 0.19 0.28 0.49 -0.32 0.07 0.86 -0.32 -0.25 0.03 0.15 -0.07 -0.71 0.68 -0.74 0.53 -0.14 0.31 0.22 2.73 0.95 0.54 0.47 0.31 0.55 0.19 0.11 0.09 0.06 Table 3: Principal Components of NFL Prices Variable RPTIX RPARK RPBEER RPSODA RPDOG Eigenvalue Proportion of Variance Explained Eigenvector One Eigenvector Two Eigenvector Three Eigenvector Four Eigenvector Five 0.47 0.44 0.38 0.41 0.52 -0.43 -0.55 0.63 0.27 0.18 -0.18 -0.02 -0.47 0.85 -0.15 0.68 -0.39 0.21 0.15 -0.56 -0.31 0.59 0.43 0.08 -0.60 2.50 0.98 0.67 0.44 0.41 0.50 0.20 0.13 0.09 0.08 Table 4: Principal Components of Real Price Indices Variable RC PIT IX RCPIPARK RCPIBEER RCPISODA RCPIDOG Eigenvalue Proportion of Variance Explained Eigenvector One Eigenvector Two Eigenvector Three Eigenvector Four Eigenvector Five 0.50 0.50 0.49 -0.49 0.14 -0.09 -0.13 0.10 0.16 0.97 0.03 0.22 0.56 0.79 -0.15 0.72 0.16 -0.57 0.35 0.09 -0.48 0.81 -0.33 0.04 0.09 3.65 0.98 0.16 0.13 0.08 0.73 0.20 0.03 0.03 0.02 Note: Variables are real price indices, constructed as described in the text. Table 5: Auxiliary Regressions(coefficient estimates, with standard errors in parentheses) Dependent Variable ⇒ Independent Variable ⇓ ATTEND POP LAGINC LAGWIN STAGE STAGE²/100 SPURP RWAM USE TIME R² Wald (Χ 2 9 ) Component One Model I 0.99* (0.18) ----------0.43 (0.22) 0.01 (0.26) 0.25* (0.02) 0.48 655.9* Component Two Program Price Cap Price Model II Model I Model II Model I Model II Model I Model II --- -0.25 (0.13) --- --- 0.30 (0.16) --- --- -0.39 (0.36) --- --- 0.04 (0.03) 0.09* (0.02) 2.64* (0.82) -0.04* (0.02) 0.05* (0.01) 0.34 (0.24) 0.23 (0.24) 0.20* (0.02) 0.68 775.93* ---------0.65* (0.15) -0.08 (0.17) 0.03* (0.01) 0.06 39.65* 0.06* (0.02) -0.03 (0.02) -0.47 (0.53) 0.03* (0.01) -0.04* (0.02) -0.46* (0.17) -0.33 (0.18) 0.05* (0.02) 0.26 63.8* ---------0.37 (0.19) -0.03 (0.22) 0.12* (0.01) 0.19 120.1* 0.03 (0.02) -0.02 (0.02) 0.75 (0.53) -0.01 (0.01) 0.00 (0.01) -0.47 (0.25) -0.17 (0.25) 0.11* (0.02) 0.22 128.1* --------0.20 (0.38) 0.02 (0.44) 0.08* (0.03) 0.01 8.3 0.05 (0.05) -0.04 (0.05) 0.23 (1.64) 0.03 (0.02) -0.03 (0.03) -0.25 (0.44) -0.38 (0.50) 0.12* (0.05) 0.02 12.2 Note: N = 342: Canadian teams and fir st-year expansion teams are excluded because the lagged winning percentage or real wage cannot be measured. A random effects estimator was applied after Hausman specification tests. The first two principal components from Table 2b are the dependent variables, along with the real prices of programs and hats. * indicates significance at the 5% level in a two-tailed test.