1. 90 2 1 1 2 Friedman[1983] Friedman ( ) Dockner[1992] closed-loop Theorem 2 Theorem 4 Dockner ( ) 31
40 2010 Kinoshita, Suzuki and Kaiser [2002] () 1) 2) () VAR 32
() Mueller[1986], Mueller ed. [1990] Mueller[1986] OLS AR(1) AR(1) Geroski[1990] Gerosky Mueller ed.[1990] AR(1) Odagiri and Yamawaki[1990] Maruyama and Odagiri[2002] 60 90 2 [1999] AR(1) Geroski [1991] AR(1) 1 ( ) VAR VARMA 2 3 1 VAR 4 2. VAR 2.1 Sargent[1987](Chapter XI) VAR (a) 2 1 2 p 1t = A 01t A 11 q 1t A 12 q 2t + u 1t, p 2t = A 02t A 22 q 2t A 21 q 1t + u 2t, p it t i q it t i u it t 33
40 2010 u it MA(1) u it MA(1) A 01t A 02t (b) i ( ) C it = c 1it q it + (c 2i /2)(q it q it 1 ) 2 + s it q it. s it MA(1) 3) (c) (u it, s it ) (d) i b i (e) i t t κ ji q jt / q it q jt+ j / q it = 0 t closed-loop t open-loop i (1) V it = Σ j=0 b j i {p t+ j q it+ j C it+ j } V it / q it+ j = 0 (2) 1 b 1 c 21 q 1t+ j+1 q 1t+ j (2A 11 + A 12κ21 + c 21 + b 1 c 21 ) + c 21 q 1t+ j 1 = A 01t+ j + c 11t+ j + A 12 q 2t+ j + u 1t+ j + s 1t+ j, 2 b 2 c 22 q 2t+ j+1 q 2t+1 (2A 22 + A 21κ12 + c 22 + b 1 c 22 ) + c 22 q 2t+ j 1 = A 02t+ j + c 12t+ j + A 21 q 2t+ j + u 2t+ j + s 2t+ j. MA(1) 2.2 VAR (2) VARMA (2) t π it (i = 1, 2) (q 1t, q 2t ) 1 i (3) π it = π it + π 1 it (q 1t q 1t ) + π it 2 (q 2t q 2t ), i = 1, 2 π j it π it / q jt qit=qit, i=1,2. q 1t q 2t t i 1 G i t j q it+ j+1 = (2 G i ) q it+ j1. q it+ j+1 (2) π it (3) q 1t q 2t (4) q 1t q 1t = (π 2 2t π + 1t π 2 1t π + 2t )/Ω q 2t q 2t = (π 1 1t π + 2t π 1 2t π + 1t )/Ω π + it π it π it Ω π 1 1t π 2 2t π 2 1 1t π 2t (4) (2) 2 SVARMA structural VARMA SVARMA 34
(5) π 1t+ j+1 = const + α 1 π 2t+ j+1 + β 11 π 1t+ j + β 12 π 1t+ j 1 + γ 11 π 2t+ j + γ 12 π 2t+ j 1 + MA(1) π 2t+ j+1 = const + α 2 π 1t+ j+1 + β 21 π 2t+ j + β 22 π 2t+ j 1 + γ 21 π 1t+ j + γ 22 π 1t+ j 1 + MA(1) SVARMA (5) MA(1) (u it ) (s it ) MA(1) SVARMA π 1t+ j+1 π 2t+ j+1 VARMA (6) π 1t+ j+1 = v 10 + v 11 π 1t+ j+ v 12 π 1t+ j 1 + v 13 π 2t+ j + v 14 π 2t+ j 1 + ε 1t+ j+1 + θ 1 ε 1t+ j, π 2t+ j+1 = v 20 + v 21 π 2t+ j + v 22 π 2t+ j 1 + v 23 π 1t+ j + v 24 π 1t+ j 1 + ε 2t+ j+1 + θ 2 ε 2t+ j, ε it+ j+1 + θ i ε it+ j MA(1) 10 v in i=1,2. n=0,1,,4 1 1 b 1 b 2 b b 1 = b 2 v i2 = 1/b, v i4 = 0 (i = 1, 2) (7) Π 1t+ j+1 = v 10 + v 11 π 1t+ j + v 13 π 2t+ j + ε 1t+ j+1, Π 2t+ j+1 = v 20 + v 21 π 2t+ j + v 23 π 1t+ j + ε 2t+ j+1, Π it+ j+1 π it+ j+1 v i2 π it+ j 1 θ 1 ε it+ j, ε it i, i, d, Gaussian 1 v 10 H 20 /H 21 (A 02 c 12 )/(b 2 c 22 H 21 ) H 20 /(b 2 H 21 ) + A 21 H 10 /(b 2 c 22 H 21 ) + (2A 22 + c 22 + b 2 c22 + A 21 κ 12 )H 20 /(b 2 c 22 H 21 ) (1/(H 21 H))[H 22 {H 21 (H 10 + (A 01 c 11 )/(b 1 c 21 ) + H 10 /b 1 (2A 11 + c 21 + b 1 c 21 + A 12 κ 21 )H 10 /(b 1 c 21 ) A 12 H 20 /(b 1 c 21 )) H 11 (H 20 +(A 02 c 12 )/(b 2 c 22 )+ H 20 /b 2 A 21 H 10 /(b 1 c 21 )) H 11 (H 20 + (A 02 c 12 )/(b 2 c 22 ) + H 20 /b 2 A 21 H 10 /(b 2 c 22 ) (2A 22 + c 22 + b 2 c 22 + A 21 κ 12 )H 20 /(b 2 c 22 ))}], v 11 A 21 H 11 /(b 2 c 22 H 21 ) + (2A 22 + c 22 + b 2 c 22 + A 21 κ 12 )H 21 /(b 2 c 22 H 21 ) (1/H 21 H)[H 22 {H 21 ( (2A 11 + c 21 + b 1 c 21 + A 12 κ 21 )H11/(b 1 c 21 ) A 12 H 21 /(b 1 c 21 )) H 11 ( A 21 H 11 /(b 2 c 22 ) (2A 22 + c 22 + b 2 c22 + A 21 κ 12 )H 21 /(b 2 c 22 ))}], v 12 1/b 2 H 22 H 11 (1/b 1 1/b 2 )/H, v 13 A 21 H 12 /(b 2 c 22 H 21 )+(2A 22 +c 22 +b 2 c22+ A 21 κ 12 )H 22 /(b 2 c 22 H 21 ) (1/H 21 H)[H 22 {H 21 ( (2A 11 +c 21 +b 1 c 21 + A 12 κ 21 )H 12 /(b 1 c 21 ) A 12 H 22 /(b 1 c 21 )) H 11 ( A 21 H 12 /(b 2 c 22 ) (2A 22 + c 22 + b 2 c22 + A 21 κ 12 )H22/(b 2 c 22 ))}], v 14 H 22 /(b 2 H 21 ) H 22 (H 12 H 21 /b 1 H 11 H 22 /b 2 )/(H 21 H), v 20 (1/H)[H 21 {H 10 + (A 01 c 11 )/(b 1 c 21 ) + H 10 /b 1 (2A 11 + c 21 + b 1 c 21 + A 12 κ 21 )H 10 /(b 1 c 21 ) A 12 H 20 /(b 1 c 21 )} H 11 {H 20 + (A 02 c 12 )/(b 2 c 22 ) + H 20 /b 2 A 21 H 10 /(b 2 c 22 ) (2A 22 + c 22 + b 2 c22 + A 21 κ 12 )H 20 /(b 2 c 22 )}], v 21 (1/H)[H 21 { (2A 11 + c 21 + b 1 c 21 + A 12 κ 21 )H 12 /(b 1 c 21 ) A 12 H 22 /(b 1 c 21 )} H 11 { A 21 H 12 /(b 2 c 22 ) (2A 22 + c 22 + b 2 c22 + A 21 κ 12 )H 22 /(b 2 c 22 )}], v 22 (H 21 H 12 /b 1 H 11 H 22 /b 2 )/H, 35
40 2010 v 23 [H 21 { (2A 11 + c 21 + b 1 c 21 + A 12 κ 21 )H 11 /(b 1 c 21 ) A 12 H 21 /(b 1 c 21 )} H 11 { A 21 H 11 /(b 2 c 22 ) (2A 22 + c 22 + b 2 c 22 + A 21 κ 12 )H 21 /(b 2 c 22 )}], v 24 H 21 H 11 (1/b 1 1/b 2 )/H, H H 11 H 22 H 12 H 21, H 10 [e π2 {e π2 q 1 ( c 12 /(q 2 p 2 ) + A 21 ( c 12 q 1 0.5c 22 (1 G 2 )q 22 )/(q 2 p 2 2 )) + e π2 q 2 (A 22 ( c 12 0.5c 22 (1 G 2 )q 2 )/p 2 2 0.5c 22 (1 G 2 )/p 2 ) π 2 }]/{ c 12 /(q 2 p 2 )+A 21 ( c 12 q 1 0.5c 22 (1 G 2 )q 2 2 )/(q 2 p 2 2 )}+D/E D { 0.5c 22 (1 G 2 )/p 2 + A 22 ( c 12 0.5c 22 (1 G 2 )q 2 )/p 2 2 }[ e π2 { c 12 /(q 2 p 2 ) + A 21 ( c 12 q 1 0.5c 22 (1 G 2 )q 2 2 )/(q 2 p 2 2 )}{e π1 q 2 A 12 ( c 11 0.5c 21 (1 G 1 )q 1 )/p 2 1 +e π1 q 1 (A 11 ( c 11 o.5c 21 (1 G 1 )q 1 )/p 2 1 0.5c 21 (1 G 1 )/p 1 ) π 1 }+e π1 {A 11 ( c 11 0.5c 21 (1 G 1 )q 1 )/p 2 1 0.5c 21 (1 G 1 )/p 1 }{e π2 q 1 ( c 12 /(q 2 p 2 )+ A 21 ( c 12 q 1 0.5c 22 (1 G 2 )q 22 )/(q 2 p 2 2 )) + e π2 q 2 (A 22 ( c 12 0.5c 22 (1 G 2 )q 2 /p 2 2 0.5c 22 (1 G 2 )/p 2 ) π 2 )}] E { c 12 /(p 2 q 2 ) + A 21 ( c 12 q 1 0.5c 22 (1 G 2 )q 2 2 )/q 2 p 2 2 }[ e π1 π2 A 12 { c 11 0.5c 21 (1 G 1 )q 1 }(1/p 2 1 ){ c 12 /(q 2 p 2 ) + A 21 ( c 12 q 1 0.5c 22 (1 G 2 )q 2 2 )/q 2 p 2 2 } e π1 π2 {A 11 ( c 11 0.5c 21 (1 G 1 )q 1 )/p 2 1 0.5c 21 (1 G 1 )/p 1 }{A 22 ( c 12 0.5c 22 (1 G 2 )q 2 )/p 2 2 0.5c 22 (1 G 2 )/p2}], H 11 [ 0.5c 22 (1 G 2 )/p 2 + A 22 { c 12 0.5c 22 (1 G 2 )q 2 }]( e π2 )[ c 12 /(q 2 p 2 ) + A 21 { c 12 0.5c 22 (1 G 2 )q 2 2 }/(q 2 p 2 2 )]/F F [ c 12 /(q 2 p 2 )+A 21 { c 12 q 1 0.5c 22 (1 G 2 )q 2 2 }/q2p2 2 ](e π1 π2 )[A 12 { c 11 0.5c 21 (1 G 1 )q 1 }/p 2 1 ][ c 12 /(q 2 p 2 )+ A 21 { c 12 q 1 0.5c 22 (1 G 2 )q 2 2 }/q 2 p 2 2 ] (e π1 π2 )[A 11 { c 11 q 1 0.5c 22 (1 G 1 )q 2 2 }/p 2 1 0.5c 21 (1 G 1 )/p 1 ][A 22 { c 12 0.5c 22 (1 G 2 )q 2 }/p 2 2 0.5c 22 (1 G 2 /p 2 ], H 12 e π2 /[ c 12 /(q 2 p 2 ) + A 21 { c 12 q 1 0.5c 22 (1 G 2 )q 2 2 }/(q 2 p 2 2 )}] + [ 0.5c 22 (1 G 2 )/p 2 + A 22 { c 12 0.5c 22 (1 G 2 )q 2 }/p 2 2 ]( e π1 )[A 11 { c 11 0.5c 21 (1 G 1 )q 1 }/p 2 1 0.5c 21 (1 G 1 )/p 1 ]/L, L [ c 12 /(q 2 p 2 ) + A 21 { c 12 q 1 0.5c 22 (1 G 2 )q 2 2 }/(q 2 p2 2 )](e π1 π2 )[A 12 { c 11 q 1 0.5c 21 (1 G 1 )p 2 1 }/p 2 1 { c 12 /(q 2 p 2 ) + A 21 ( c 12 q 1 0.5c 22 (1 G 2 )q 2 2 )} {A 11 ( c 11 0.5c 21 (1 G 1 )q 1 )/p 2 1 0.5c 21 (1 G 1 )/p 1 }{A 22 ( c 12 0.5c 22 (1 G 2 )q 2 )/p 2 2 0.5c 22 (1 G 2 )/p 2 }], H 20 [ e π2 { c 12 /(q 2 p 2 ) + A 21 ( c 12 q 1 0.5c 22 (1 G 2 )q 2 2 )/(q 2 p 2 2 )}{e π1 q 2 (A 12 ( c 11 0.5c 21 (1 G 1 )q 1 )/p 2 1 ) + e π1 q 1 (A 11 ( c 11 0.5c 21 (1 G 1 )q 1 )/p 2 1 0.5c 21 (1 G 1 )/p 1 ) π 1 }+e π1 {A 11 ( c 11 0.5c 21 (1 G 1 )q 1 )/p 1 2 0.5c 21 (1 G 1 )/p 1 }{e π2 q 1 ( c 12 /(q 2 p 2 ) + A21( c 12 q 1 0.5c 22 (1 G 2 )q 2 2 )/(q 2 p 2 2 )) + e π2 q 2 (A 22 ( c 12 0.5c 22 (1 G 2 )q 2 )/p 22 0.5c 22 (1 G 2 )/p 2 ) π 2 }]/M, M (e π1 π2 )A 12 { c 11 0.5c 21 (1 G 1 )q 1 }/p 2 1 { c 12 /(q 2 p 2 ) + A 21 ( c 12 q 1 0.5c 22 (1 G 2 )q 2 2 )/q 2 p 2 2 } (e π1 π2 ){A 11 ( c 11 0.5c 21 (1 G 1 )q 1 )/p 2 1 0.5c 21 (1 G 1 )/p 1 }{A 22 ( c 12 0.5c 22 (1 G 2 )q 2 )/p 2 2 0.5c 22 (1 G 2 )/p 2 }, H 21 e π2 { c 12 /(q 2 p 2 ) + A 21 ( c 12 q 1 0.5c 22 (1 G 2 )q 2 2 )/q 2 p 2 2 }/N, N (e π1 π2 ){A 12 ( c 11 0.5c 21 (1 G 1 )q 1 )/p 1 2 }{ c 12 /(q 2 p 2 ) + A 21 ( c 21 q 1 0.5c 22 (1 G 2 )q 2 2 )/(q 2 p 2 2 }} (e π1 π2 ) {A 11 ( c 11 0.5c 21 (1 G 1 )q 1 )/p 1 2 0.5c 21 (1 G 1 )/p 1 }{A 22 ( c 12 0.5c 22 (1 G 2 )q 2 )/p 2 2 0.5c 22 (1 G 2 )/p 2 }, 36
H 22 e π1 {A 11 ( c 11 0.5(1 G 1 )q 1 )/p 2 1 0.5c 21 (1 G 1 )/p 1 }/R, R (e π1 π2 )A 12 { c 11 0.5c 21 (1 G 1 )q 1 }(1/p 2 1 ){ c 12 /(q 2 p 2 )+A 21 ( c 12 q 1 0.5c 22 (1 G 2 )q 2 2 )/(q 2 p 2 2 )} (e π1 π2 ) {A 11 ( c 11 0.5c 21 (1 G 1 )q 1 )/p 2 1 0.5c 21 (1 G 1 )/p 1 }{A 22 ( c 12 0.5c 22 (1 G 2 )q 2 )/p 2 2 0.5c 22 (1 G 2 )/p 2 }, 3. 2 ( ) 7 2 1967 1987 1964 2) 1960 2004 CAPM 1971 = (60 ) + β 60 β 1970 71 β 1977 = 10 +β 10 1976 1977 ( ) β 1 ( ) () 1 4. 1 (5) v i j (6) v 10 v 20 37
40 2010 4 1 1 Chen 3 ADF F ADF F 4 (6) VAR F VAR F VAR, VAMA 1 3 univariate AR, univariate ARMA VAR VAMA univariate AR, univariate ARMA (5) (5) (5) VARπ =MA VAR 2 L( ) 2 2 MA MA(1) 1 2 π 1 2 1 2 (5) (5) π =(VAR) 1 MA, (VAR) 1 VAR L 4 VAR (5) univariate ARMA(4,3) 4.1 3) 1 40 2 Lumsdaine and Papell [1997] 1 Zivot and Andrews[1992] 2 25 4) ADF T(ρ µ 1) T ρ µ ADF ADF 1 2 (k) t 1.6 5) 4 i T(ρ µ 1) T(ρ µ 1)/(1 Σ k π ik ) 2 38
2 T(ρ µ 1) (1) 1 (2) 2 1% 2.5% 5% 10% 1% 2.5% 5% 10% 20.0 17.3 15.1 12.9 33.7 30.7 27.7 22.5 1 2 ADF 4 4 2 2 3 3 2 2 7 2 1964 2004 ADF T(ρ µ 1) = 12.68 (k = 0) 25 4.9%1 2001 15.16 (k = 0) 4.7% 2 37.35(k = 1) 0.05% 2 1973 1999 ADF 8.40 (k = 0) 25 50 10% 22.08 (k = 1) 0.4% 2 33.57 (k = 1) 0.07% 2 1973 1998 4.2 Chen Chen Chen and Tiao[1990] ARMA ARIMA ARMA ARIMA Chen 2 1 Chen 3 2.8 1961 2004 1973 1975 1979 1995 39
40 2010 1964 1973 1974 1975 1978 2000 1973 2000 1961 1972 1973 2000 2001 2004 4.3 ADF F ADF ADF π it = +ρπ it 1 + α 1 π it 1 + α 2 π it 2 + α 3 π it 3 + ε it ε it i.i.d.gaussian π ip p = 3 ADF α i F F F OLS F 1970 1990 1996 1966 α 3 4.4 VAR F (7) VAR b = 0.9 Π 1t+ j+1 (6) MA(1) MA univaliate ARMA(4, 3) Π 1t+ j+1 = v 11 π 1t+ j + v 13 π 2t+ j + ε 1t+ j+1, Π 2t+ j+1 = v 21 π 2t+ j + v 23 π 1t+ j + ε 2t+ j+1, 1 2 3.3. VAR F 1968 v 11 1973 1989 v 13 1994 v 23 1997 v 21 v 23 = 0 F 1994 v 23 F 4.5 1 Chen AR(2) 0.089 1967 1972 0.262 0.013 ( ) 40
6) 5. (6) (7) ARMA(4,3) MA(3) i.i.d. ARMA(4,3) (6) univariate ARMA(4,3) b 1 = b 2 = 0.9 π it+ j+1 v i2 π it+ j 1 v i2 = 1/0.9, 1 (6) (6) (7) 1 2 VAR OLS SUR (7) (7) t t 1 3 3 1964 2001 (61,62,63 64 ) 1 2 3 π it ARMA(4,3) i.i.d. MA(3) (-1/0.9)π it 2 π it Π it v 10 0.0417 (5.8549) 90 1 0.0289 ( 4.7208) 98 1 0.01627 (1.7512) v 11 0.7977 (2.5751) v 13 1.1250 (2.8921) 73 v 11 0.6229 (1.9858) 73 v 13 2.0978 ( 4.2587) 90 v 13 1.5914 (4.4542) SBIC 120.639 135.683 R 2 0.9576 v 20 0.1285 (9.4862) v 21 0.2585 (1.3804) 73 1 0.0671 ( 6.5859) 90 1 0.1736 ( 2.2356) 98 1 0.0399 ( 1.4638) 90 v 21 1.6404 (2.8879) 98 v 21 6.5822 ( 3.3989) 66 v 23 0.2476 ( 2.3226) 70 v 23 0.4368 ( 3.4387) 95 v 23 0.6332 ( 1.8651) 98 v 23 5.8955 (3.2457) SBIC 113.665 134.351 R 2 0.9474 v i0 v i1 v i3 v i0 v i1 v i3 3 v i0, v i1, v i3 v i0, v i1, v i3 1 (8) v i j = v i j, i = 1, 2, j = 0, 1, 3, 3 (6) (7) v i2 = 1/0.9 v i4 = 0 v i j ( j = 0, 1, 3) 41
40 2010 3 t π i = π it π i 3 1 π i 4 4 1961 1965 0.0955 0.0718 66 69 0.0853 0.0602 70 72 0.0717 0.0448 73 89 0.0291 0.0228 90 94 0.0381 0.0212 95 97 0.0224 0.0040 98 0.0604 0.0185 p t q t (9) t i = {pit q it c 1it q it c 2it (1 G i ) 2 q 2 it /2}/(p it q it ), i = 1, 2, 1 q i+t t j q it+ j+1 = (2 G i )q it+ j (2) q 1t = (A 02 c 12 )/(A 21 G 1 ) [b 2 c 22 {1 + G 2 2 /b 2 G 2 (2A 22 + c 22 + b 2 c 22 + A 21 κ 12 )/(b 2 c 22 )}][ A 21 (A 01 c 11 )G 1 /(b 1 b 2 c 21 c 22 ) (A 02 c 12 ){1 + G 2 1 /b 1 G 1 (2A 11 + c 21 + b 1 c 21 + A 12 κ 21 )}/(b 2 c 22 )]/S, q 2t = A 21 G 1 [ A 21 (A 01 c 11 )G 1 /(b 1 b 2 c 21 c 22 ) (A 02 c 12 ){1 + G 2 1 /b 1 G 1 (2A 11 + c 21 + b 1 c 21 + A 12 κ 21 )/(b 1 c 21 )}/(b 2 c 22 )]/S, S A 21 G 1 [A 12 A 21 G 1 G 2 /(b 1 b 2 c 21 c 22 ) {1+G 2 2 /b 2 G 2 (2A 22 +c 22 +b 2 c 22 + A 21 κ 12 )/(b 2 c 22 )}{1+G 2 1 /b 1 G 1 (2A 11 + c 21 + b 1 c 21 + A 12 κ 12 )/(b 1 c 21 )}], i q it = (x it )/p it (10) (x it ) = p it q it, i = 1, 2, 3.5. 14 A 01, A 02, A 11, A 12, A 21, A 22, c 11, c 12, c 21, c 22, p 1t, p 2t, κ 21, κ 12 ) 10 (8),(9),(10) (a) 12 c 11 = c 12 = 1 12 (8),(9),(10) 2 A 11 = 1, A 12 = 1, A 21 = 1, A 22 = 1, c 21 = 1, c 22 = 1, p 1t = 100, p 2t = 100, κ 21 = 0, κ 12 = 0 Gauss=Newton A(A 11, A 12, A 21, A 22 ) = {0 10 }, c 2 (c 21, c 22 ) = {0 10 }, κ(κ 21, κ 12 ) = {0 10 }, p (p 1t, p 2t ) = {1, 100, 1000} (11) A i1 A i2, c 2i 0, c 2i 0, p it 0, A 11 A 12 A 21 A 22 () 0 1 0 A 11 A 21 /H 1989 1994 2004 5 1994 2 2004 A 11 < A 12 42
5 1989 1994 2004 A 11 8.994 7.628 7.895 6.847 11.191 A 12 8.308 6.399 4.889 7.392 4.216 A 21 10.804 10.935 10.480 9.394 6.237 A 22 12.463 12.152 13.544 10.683 11.287 c 21 10.193 8.598 6.238 2.719 5.676 c 22 11.586 11.742 13.919 11.068 12.019 p 1t 716.953 609.877 450.450 183.769 411.781 p 2t 878.896 900.285 1003.784 861.820 907.323 κ 21 6.605 5.712 3.536 0.946 3.755 κ 12 1.097 1.535 1.551 2.685 4.452 6. 5 1994 2004 1990 1 closed-loop b i 2 b i 0.9 b i Federal Reserve Board s Quarterly Model b i 3 2 3 3 2 3 12 3 4 c 11 = c 12 = 1 A 0i 1 1 2 MA 3 Worthington[1990] 2 () 4 1967 1964 1987 5 43
40 2010 6 225 (et) 1 y t y t = y t 1 + e t, 225 y t y t (y 0 ) 225 y t 200 25 2 ADF T(ρ µ 1) 4 4 2 2 3 10000 T(ρ µ 1) 7 t t = 1.6 8 x t t Sales t t D () T T () 1 ln(sales t x t ) = 0.946890 (ln(sales t 1 ) x t 1 ) 0.499144 (ln(sales t 2 ) x t 2 ), x t = 18.470369 + 0.116852D (73 1) 0.252039D(98 1)+0.213549T(62 = 1) 0.100547T (73 = 1) 0.111052T (90 = 1) + 0.046602T (98 = 1), ln(sales t x t ) = 1.243472 (ln(sales t 1 ) x t 1 ) 0.548219 ln(sales t 2 ) x t 2 ), x t = 18.393672 0.170114D (66 1) 0.07398D (95 1) + 0.129574T(62 = 1) + 0.138771T(66 = 1) 0.197986T (73 = 1)) 0.121494T(90 = 1) + 0.070929T(95 = 1) (1999) ( 10 ) NTT. Bresnahan, T. F. (1982) The Oligopoly Solution Concept is Identified, Economic Letters 10, pp. 87-92. Chen, C. and G. C. Tiao (1990) Random Level-Shift Time Series Models, ARIMA Approximation, and Level- Shift Detection, Journal of Business and Economic Statistics, vol.8, no.1, 83-97. Engelbert, J. D. (1992) A Dynamic Theory of Conjectural Variations, The Journal of Industrial Economics, Vol.XL, No.4, December 1992. 377-395. Friedman, J. W. (1983) Oligopoly and the Theory of Games, North-Holland, Amsterdam. Geroski, P. A. (1990) Modeling Persistent Profitability, in Muller, D. C., ed. The Dynamic of Company Profits: An International Comparison. (1991), Market Dynamics And Entry, Brackwell: Cambridge, MA. Kinoshita, J., N. Suzuki and H. M. Kaiser (2002) Explaining Pricing Conduct in a Product-Differentiated Oligopolistic Market: An Empirical Application of a price Conjectural Variations Model, Agribusiness, vol.18, No.4. Lumsdaine, R. L. and D. H. Papell (1997) Multiple Trend Breaks and the Unit-Root Hypothesis, The Review of Economics and Statistics, vol.79, 212-218. Maruyama, N. and H. Odagiri (2002) Does the Persistence of Profits Persists?: A Study of Company Profits in Japan. 1964-1997, International Journal of Industrial Organization, vol.20, 1513-1533. Muller, D. C., ed. (1986) Profits in the Long Run, Cambridge University Press: Cambriege, MA. (1990) The Dynamic of Company Profits: An International Comparison, WZB-Publication: Wissenschaftszentrum, Berlin. Odagiri, H. and H. Yamawaki (1990) The Persistence of Profits in Japan, in Mueller, D. C.,ed. The Dynamic of 44
Company Profits: An International Comparison. Roberts, M. L. and Samuelson (1988) An Empirical Analysis of Dynamic, Nonprice Competition in an Oligopolistic Industry, Rand journal of Economics, Vol.19, No.2. Seldon, B. J., S. Banerjee and R. G. Boyd (1993) Advertizing Conjectures and the Nature of Advertizing Competition in an Oligopoly, Managerial and Decision Economics, Vol.14, 489-498. Sergeant, T. J. (1987) Macroeconomic Theory, Academic Press, San Diego:CA. Worthington, P. R. (1990) Strategic Investment and Conjectural Variations, International Journal of Industrial Organization, Vol.8, 315-328. Zivot, E. and D. W. K. Andrews (1992) Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit- Root Hypothesis, Journal of Business and Economic Statistics, vol.10, no.3. 45