Using Standardized Revenue and Cost Norm Analyses to Reveal Subsidy Fraud in Contracted Public Transport Services

Figures & data

Table 1. Descriptive statistics for all services in the data set for the years 1996–2005 (costs and revenues are reported in 2006 prices)

		Year
		1996	1997	1998	1999	2000	2003	2004	2005
No. of observations (N)		67	67	66	61	57	57	58	51
Revenue, Rip , 1000 NOK	Mean	3470	3426	3694	3623	3853	3765	3443	3612
	SD	3295	3383	3642	4308	4482	4371	3722	4076
Revenue, Riv , 1000 NOK	Mean	11 200	11 500	12 000	11 500	11 900	13 800	14 600	14 500
	SD	13 200	13 800	14 900	14 900	15 600	18 700	19 900	18 800
Costs, Ci , 1000 NOK	Mean	18 600	18 800	19 200	18 900	21 800	25 400	26 400	29 100
	SD	14 400	14 900	14 900	15 500	18 500	22 000	22 100	25 200
PCE transported, Xi 1 in 1000	Mean	213	226	236	216	221	273	296	325
	SD	210	223	236	218	227	298	317	346
Passengers transported, Pi in 1000	MeanSD	204201	209210	209202	194192	204203	219224	231233	243251
Distance of service, Xi 2 in km	MeanSD	7.77.9	7.87.9	7.88	7.98.1	8.18.3	7.37.4	7.27.3	7.17.6
OVDS services (Di 1 = 1) or not (Di 1 = 0)	MeanSD	0.090.29	0.090.29	0.090.29	0.100.30	0.110.31	0.110.31	0.100.31	0.120.33
Unsheltered stretches (Di 2 = 1) or not (Di 2 = 0)	MeanSD	0.220.42	0.220.42	0.230.42	0.230.42	0.230.42	0.190.40	0.190.40	0.180.39

Table 2. Estimation results of the passenger revenue model for every year (t‐values in parentheses)

Year	a 0p	a 1p	a 2p	a 3p	Adjusted R ^2	F‐value
1996	107 210 (0.76)	10.88 (16.30)	0.85 (15.98)	212 880 (0.71)	0.958	469
1997	38 807 (0.28)	11.48 (17.80)	0.80 (15.20)	20 964 (0.07)	0.960	491
1998	2366 (0.02)	13.11 (19.37)	0.75 (14.00)	−1500 (−0.00)	0.963	521
1999	−69 475 (−0.50)	12.06 (17.56)	0.98 (19.17)	−313 093 (−0.95)	0.979	732
2000	−89 365 (−0.47)	13.48 (15.47)	0.73 (12.05)	132 823 (0.31)	0.968	421
2003	−114 211 (1.08)	14.77 (31.47)	0.51 (15.86)	−282 262 (−1.29)	0.988	1355
2004	31 760 (0.29)	12.67 (26.42)	0.56 (18.29)	237 247 (1.10)	0.984	1006
2005	−21 025 (−0.17)	13.39 (26.12)	0.50 (15.90)	111 456 (0.48)	0.985	949

Table 3. Estimation results of the vehicle revenue model for every year (t‐values in parentheses)

Year	a 0v	a 1v	a 2v	a 3v	Adjusted R ^2	F‐value
1996	−29 914 (−0.08)	27.07 (17.58)	3.36 (26.56)	727 880 (0.91)	0.981	1107
1997	−32 350 (−0.10)	26.86 (19.34)	3.31 (28.87)	1 009 811 (1.30)	0.984	1308
1998	−187 773 (−0.51)	28.50 (19.47)	3.21 (26.75)	526 778 (0.62)	0.984	1235
1999	−500 581 (−1.36)	34.74 (20.67)	2.73 (22.03)	−199 206 (−0.25)	0.985	1227
2000	−284 525 (−0.64)	31.35 (15.97)	3.03 (20.68)	−309 639 (−0.33)	0.982	928
2003	−254 083 (−0.56)	31.92 (20.32)	2.60 (23.20)	50 640 (0.05)	0.986	1266
2004	−908 040 (−1.37)	33.73 (16.25)	2.57 (16.31)	722 562 (0.48)	0.972	651
2005	−153 678 (−0.25)	29.76 (15.95)	2.60 (20.33)	505 470 (0.40)	0.978	731

Table 4. Estimation results of the cost model for every year (t‐values in parentheses)^a

Year	b 0	b 1	b 2	b 4	b 5	b 6	Adjusted R ^2	F‐value
1996	16.389 (491.76)	0.154 (3.86)	0.354 (11.75)	0.052 (5.07)	0.177 (2.03)	0.107 (1.60)	0.893	111
1997	16.385 (484.63)	0.170 (4.17)	0.332 (10.54)	0.064 (6.18)	0.252 (2.83)	0.148 (2.15)	0.886	103
1998	16.428 (432.87)	0.192 (4.28)	0.309 (8.84)	0.060 (5.28)	0.131 (1.33)	0.153 (2.03)	0.863	83
1999	16.391 (438.04)	0.237 (5.40)	0.280 (7.83)	0.064 (5.84)	0.193 (2.14)	0.124 (1.74)	0.888	96
2000	16.485 (434.20)	0.210 (4.56)	0.320 (8.59)	0.060 (5.33)	0.186 (2.10)	0.167 (2.25)	0.904	107
2003	16.657 (399.31)	0.174 (3.39)	0.331 (8.30)	0.055 (5.05)	0.007 (0.06)	0.257 (2.90)	0.873	78
2004	16.695 (378.15)	0.167 (3.06)	0.330 (7.69)	0.057 (4.80)	0.057 (0.51)	0.253 (2.67)	0.854	67
2005	16.779 (343.62)	0.116 (1.88)	0.409 (8.20)	0.034 (2.60)	−0.008 (−0.07)	0.345 (3.43)	0.890	82
^aThe second order explanatory variable (ln X i1 − µ 1)^2, and thereby the estimation of b 3 in Equation (3), is omitted.

Table 5. Overstated costs from OVDS during the period 1996–2000 for the six services in our data set in 2006 prices (90% confidence interval)

	Percentage overstating of costs (100b 5)	Overstated costs (1000 NOK)
Year	Low	Expected	High	Low	Expected	High
1996	3.2	17.7	32.3	3799	18 650	30 252
1997	10.3	25.2	40.2	11 814	25 449	36 182
1998	−3.3	13.1	29.6	−4370	14 629	28 800
1999	4.2	19.3	34.4	5296	21 089	33 339
2000	3.8	18.6	33.3	5444	23 510	37 568
Average	3.6	18.8	33.9	4397	20 665	33 228
Total	–	–	–	21 983	103 327	166 141

Table 6. Model results compared with the verdict for the years 1996–2000 in 2006 prices

	Understated revenues, 1000 NOK	Overstated costs, 1000 NOK	Overstated subsidy needs, 1000 NOK
Year	Model results	The verdict	Model results, TOCt	The verdict	Model results	The verdict	Significant level of difference (%)^a
19961997	No indications of understated revenues	096	29 84040 669	86228312	29 84040 669	86228408	61
1998		663	23 384	7673	23 384	8336	19
1999		0	33 731	11 999	33 731	11 999	7
2000		0	37 696	12 476	37 696	12 476	7
1996–2000	–	759	165 320	49 082	165 320	49 841	–
^aSignificant level of difference between overstated subsidy needs from the model and the verdict; One‐tailed test.