The Demand for J-League with Fixed Effect Tobit Model: Effects toward Community Formation Tomonori Ito and Yoichiro Higuchi The J-League was established in 993 expecting to encourage the community to form its "comprehensive sport club." For verifying the J-League s effect, it is very meaningful to econometrically analyze the attendance demand for J-League matches. This study proposed the football attendance model, which considers the demand that exceeded a stadium capacity, with panel data analysis. We had three hypotheses. First, examining hypothesis() that the structure of demand for football attendance changed between 996 and 997, we found that it changed significantly. Secondly, hypothesis() that supporters decided their attendance on the basis of attributions of away clubs and games themselves after the structural change and we examined hypothesis(3) that supporters decided their attendance on the basis of attributions of home clubs before the structural change. As a result we proved that the J-League helped the development of the community through the hometown sports last eight s. KeywordsDemand for football, Panel analysis, Tobit - W J-LEAGUE 993 J-LEAGUE J-LEAGUE J-LEAGUE J-LEAGUE (Tokyo Institute of Technology) (Tokyo Institute of Technology)
J-LEAGUE 8000 V.Kawasaki 993 6000 Urawa.R 5000 J-LEAGUE 0 4000 000 8 0000 0 8000 8 7 6000 4000 000 0000 8000 6000 -- 993 994 995 996 997 998 999 000 00 99300 00 969 --V -- 993 5000 995 J-LEAGUE 000 Division- -3 - J-LEAGUE - 00 W W - W - -3-4 -5 60000 0000 3 3- Tobit-Model 3-3-3 4 J-LEAGUE 4-4- - 4-3 4-4 5 J-LEAGUE 993 000 attendance per match
3 - -- Simmons[996] -- Dobson & Goddard[998] Dobson & Goddard[998] - -- Walker[986] Dobson & Goddard[99] -- Cairns[987] -3
y Bird[98] -4 Cairns[987] x Dobson & Goddard[99] -5- ( ) Peel & Tobit-Model Thomas[988] Tobit-Model Tobit-Model ( ) (3--) 5 95 y = α + βx + ε ε ~ N ( 0, σ ) (3--) (50 ) -5 y y capacity -5- y = capacity y capacity (3--) -5- -5- y = y y < capacity (3--3) -5- µ σ y ~ N ( µ, σ ) (3--) Prob( y = capacity) = Prob( y capacity) J-LEAGUE capacity µ (3--4) = Φ σ (3--3) Prob( y = y ) = Prob( y < capacity) 3 capacity µ (3--5) 3- Tobit Model = Φ σ Φ( ) 4
(3--3) y µ f y y < capacity = φ σ σ = ( α βx) y + σ πσ e (3--6) yit yi. = yit (3--3) φ() T Fixed-Effect Model (3--4) (3--) L α ( α βx) capacity + L = Φ σ y capacity y < capacity ( α βx) σ y + e πσ y it = αi + β k xitk + ε it k= (3--7) i =,,, N t =,,, T (3--4) Random-Effect Model (3--5) Fixed-Effect capacity ( + x) Model α α β i log L = Φ = σ y capacity m ( ) ( ) y α + βx y it = αi + β k xitk + ε it + log π + logσ + k= σ i =,,, N t =,,, T (3--5) y< capacity Between Model (3--) OLS y it = α + β x + ε (3--8) (3--8) E( αi ) = 0 E( α i ) = σ α 3- E( αiα j ) = 0 ( i j) E( εit ) = 0 E( ε it ) = σ ε (3--6) 3-- E( ε itε js ) = 0 ( i j, t s) E( α iε it ) = 0 N ( T ) u it = α i + ε it ( ) E ( u it ) = 0 σα + σε ( i = j, t = s) E( uitu js ) = σ α ( i = j, t s) (3--7) 0 ( i j) 3-- E( α ) = 0 i x it (3--8) Total Model Variance-Components Model OLS (3--) 3--3 4 m F y it = α + β k xitk + ε it Hausman k= i =,,, N t =,,, T (3--) 3-- m k k= itk it i =,,, N t =,,, T (3--) m i 5
Yes No Total-Model y α + α α β β β +β Fixed Effect-Model Random Effect-Model α x 3-- 3-4- 3-3Fixed-Effect-Tobit Model α Fixed-Effect-Tobit Model α + α i t (3-3-) β β + β yit = α i + βxit + ε it it (3-3-) 4 J-LEAGUE 4-4-- 993 000 8 y it = capacity i yit capacityi (3-3-) J-LEAGUE 06 y it = y it y it < capacityi (3-3-3) 05 4-- J-LEAGUE Tobit Model J-LEAGUE Baltagi[00] (3-3-) α i β σ ε βˆ σˆε Fixed-Effect-Tobit Model (incidental parameters problem) Greene[00] Fixed-Effect-Tobit Model 3-4 90 4--3 (3-4-) 4-- y = α + βx + ε (3-4-) D ( 0 ) (3-4-) 3-4- y ε ~ N( 0, σ ) = α + α D + βx + β Dx + ε (3-4-) Dobson & Goddard[00] 6
4-- 993 000 ( V G ) 4-- 4-- 4 4-- J-LEAGUE 4--3 4 V 993 995 3 997 G 994 4 997 4- J-LEAGUE 6000 JEF.Ichihara 4000 V.Kawasaki G.Osaka 000 S.Hirosima 4--J-LEAGUE 0000 8000 4-- 993 000 J-LEAGUE 6000 J-LEAGUE 4000 3 993 7976 000 994 9598 0000 8000 4000 6000 ( )80 4000 995 993 994 995 996 997 998 999 000 69 996 3353 6000 4-- V G 997 03 998 000 6 0000 4 9000 8000 attendance per 7000 6000 5000 4000 3000 000 000 0000 993 994 995 996 997 998 999 000 attendance per match league position 0 8 6 4 JEF.Ichihara V.Kawasaki G,Osaka S.Hirosima 0 993 994 995 996 997 998 999 000 4--J-LEAGUE 4--3 V G J-LEAGUE 993 996 J-LEAGUE 4--4 ( 997 000 ) 4-- 7
J-LEAGUE J-LEAGUE 6000 Kasima.A Urawa.R 4000 J-League 0000 000 attendance per 9000 8000 7000 6000 5000 0000 993 994 995 996 997 998 999 000 4000 993 994 995 996 997 998 999 000 4--6 J-LEAGUE 4--4 4-3 4--5 J-LEAGUE 6000 4000 000 0000 8000 6000 3 4000 000 0000 J-LEAGUE J-LEAGUE 993 994 995 996 997 998 999 000 4--5 3 000 Division- 3 J-LEAGUE 3 J-LEAGUE 4--6 J-LEAGUE J-LEAGUE J-LEAGUE 993 994 4-4 J-LEAGUE (4-4-) Fixed-Effect-Tobit Model J-LEAGUE 996 yit J-LEAGUE - attendance per match 8 attendance per match 0000 8000 6000 4000 000
9 5 7 9 yit = α i + βkh( k) it + γ la( l) it + δom( o) it + ηrd( r) it + εit k = l= o= r= (4-4-) % 997 α i h( k )it 4-5- a ( l) it m ( o) it d ( r) it ε it 0 σ ε 4-5- y it = capacity i yit capacityi (4-4-) 4-5- 993 y it = y it y it < capacityi 996 6000 observation i t estimates 0 4000 number of full matches α i i 000 00 h( k )it 0000 80 8000 60 6000 40 4000 0 000 0 0000 a ( l) it 99 993 994 995 996 997 998 999 000 00 0 4-5- m ( o ) it 993 996 997 000 0 4-5- Fixed-Effect-Tobit Model 4-5- 993 996 0 4-5 4-5- 3 0 4-5- 996 997 50.37 % 9 attendance per match match
4-5- Fixed-Effect-Tobit Model 993 996 997 000 993 996 997 000 993 996 997 000 993 996 997 000 993 996 997 000 993 996 997 000 997 000 993 996 993 996 3 3 997 000 997 000 5 5- J-LEAGUE 996 997 ( ) 997 000 ( ) 3( ) J-LEAGUE 4-5-3 993 996 5- J-LEAGUE J-LEAGUE 0
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