Table 4: Estimated Causal Models for the Metro and Bus Variables

Table 4: Estimated Causal Models for the Metro and Bus Variables

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  ∇∇12SMT ∇∇1210MT ∇∇12SBT ∇∇1210BT
Constant 0.0004 -0.0009 0.0009 0.0003
(0.0022) (0.0027) (0.0016) (0.0002)
DAYS 0.0096* 0.0151* 0.0073* 0.0164*
(0.0017) (0.0030) (0.0022) (0.0021)
EASTER -0.0479* -0.0987* -0.0310* -0.1064*
(0.0101) (0.0158) (0.0127) (0.0141)
MAR89 -0.0311 -0.1064*    
(0.0235) (0.0451)    
MAR90 0.0609* - 0.1265*B - 0.006*B2   -0.6667* - 0.1482*B -0.6491* - 0.2287*B
(0.0322) (0.0364) (0.0270)   (0.0759) (0.0631) (0.0457) (0.0387)
APR90   0.0494    
  (0.0520)    
JAN91 -0.0998*      
(0.0272)      
APR91 0.0436*      
(0.0245)      
FEB92 0.0942*   -1.6170* - 0.3406*B - 0.1301*B2 -2.0973* - 0.4516*B
(0.0216)   (0.0323) (0.0417) (0.0381) (0.0383) (0.0411)
JAN98 -0.1190* - 0.0951*B - 0.0721*B2   -0.1107* - 0.1010*B  
(0.0269) (0.0303) (0.0283)   (0.0360) (0.0349)  
ΔPSMT -1.2817* 0.7601*    
(0.1202) (0.1640)    
ΔP10MT -0.1878 -2.4665*    
(0.4350) (0.6658)    
ΔPSBT     -1.2776* 0.2205*
    (0.1600) (0.0679)
ΔP10BT     0.7461 -0.5178*
    (0.5128) (0.1838)
ΔPTC 0.6922 2.6274* -0.6958 0.9075*
(0.5463) (0.8564) (0.6393) (0.2516)
φ1 -0.5577   -0.2586*  
(0.3319)   (0.0961)  
φ2     -0.3086*  
    (0.0908)  
θ1 -0.5775     0.4047*
(0.3386)     (0.0767)
θ2       0.5842*
      (0.0774)
Φ12     -0.5154*  
    (0.0731)  
Θ12 0.3145* 0.5629*   0.7979*
(0.0830) (0.0651)   (0.0871)
Θ24       -0.2589*
      (0.0809)
lowercase sigma caret subscript {lowercase a} 0.035717 0.065537 0.040829 0.041271
R2 0.89 0.6 0.98 0.99
LBQ (12, 24, 36) 5.4, 16.0, 27.2 9.1, 11.5, 22.3 14.6, 23.1, 25.0 7.8, 19.7, 36.2
Jarque-Bera (p-value) 2.43 (0.297) 0.289 (0.865) 2.11 (0.348) 6.36 (0.042)
White's heterosk (p-value) 22.82 (0.83) 6.08 (0.81) 4.35 (0.99) 2.11 (0.999)

Notes: Standard errors are in parenthesis. * significant at 5%; ∇ = (1 - B) and ∇12 = (1 - B12): regular and seasonal differences; B: lag operator; ΔPTi (i = SMT, 10BT, SBT, 10BT, TC): rates of growth of deflated prices for Metro and bus tickets; LBQ: Ljung-Box Q statistics; lowercase sigma caret subscript {lowercase a} = residual standard error.