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)
	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; ΔPT_i (i = SMT, 10BT, SBT, 10BT, TC): rates of growth of deflated prices for Metro and bus tickets; LBQ: Ljung-Box Q statistics; = residual standard error.