Application of Benford’s law to detect signs of under-invoicing in companies in the restaurant sector during the COVID-19 pandemic

Martins, Ana; Alves, Jorge; Vaz, Clara

Application of Benford’s law to detect signs of under-invoicing in companies in the restaurant sector during the COVID-19 pandemic

European Journal of Tourism, Hospitality and Recreation

Volume 14 (2024): Issue 2 (December 2024)

By:

Ana Martins

, Jorge Alves

and Clara Vaz

Open Access

|Dec 2024

Figures & Tables

First digit test_

First digit	All			Variation 25% to 35%			Variation 35% to 75%			Micro-enterprises
First digit	Po	Pe	Z	Po	Pe	Z	Po	Pe	Z	Po	Pe	Z
1	6079	5851	3.6	1097	1064	1.2	2400	2331	1.7	6003	5747	4.0
2	3313	3423	2.1	615	623	0.3	1288	1364	2.3	3179	3362	3.5
3	2311	2428	2.5	424	442	0.9	958	968	0.3	2256	2385	2.8
4	1749	1884	3.3	322	343	1.2	691	750	2.3	1718	1850	3.2
5	1525	1539	0.4	299	280	1.2	616	613	0.1	1511	1512	0.0
6	1285	1301	0.5	221	237	1.1	512	518	0.3	1274	1278	0.1
7	1160	1127	1.0	222	205	1.2	468	449	0.9	1152	1107	1.4
8	1028	994	1.1	168	181	1.0	430	396	1.7	1019	977	1.4
9	987	889	3.4	168	162	0.5	381	354	1.4	978	874	3.6
X²			5.13			7.9			16.8			53.9

Descriptive statistics_

Group	n	Statistics	VN	TA	SE
Total	19,437	Min	€42	€79	€2
		Max	€102,839,963	€190,580,920	€6,148,155
		x¯$\bar x$	€259,074	€269,928	€26,997
		s	€1,723,541	€84	€70,473
		Min	€900	€320	€44
Variation 25% to 35%	5,356	Max	€85,942,653	€146,861,014	€2,065,550
		x¯$\bar x$	€299,299	€267,355	€21,054
		s	€1,385,987	€6,220,523	€80,215
		Min	€128	€84	€13
Variation 35% to 75%	7,744	Max	€35,079,616	€46,613,670	€2,641,701
		x¯$\bar x$	€213,915	€283,069	€30,914
		s	€738,058	€4,964,952	€63,895
		Min	€42	€79	€2
Micro-enterprises	19,090	Max	€1,995,478	€1,999,423	€352,160
		x¯$\bar x$	€179,797	€168,190	€19,950
		s	€234,318	€3,038,999	€37,210

Limit for extraordinary support for progressive recovery_

Loss of turnover	≥25% to 40%	≥40% to 60%	≥60% to 75%	≥75%
Measure adopted by the State	NWP reduction of up to 33%	NWP reduction of up to 40%	NWP reduction of up to 60%	NWP reduction of up to 100%

Measures under the APOIAR Programme_

Measures	Recipient	Loss of turnover	Support to be received	Effective date
APOIAR.PT	Belong to the CAE in Annex A toMinisterial Order no. 69-A/2021, of 24March	25% or more	20% of the amount of the decrease in the company’s turnover	25 November2020
APOIAR RESTAURAÇÃO	Belong to the CAE in Annex B toMinisterial Order no. 69-A/2021, of 24March	20% or more (of the two weekends with the most intense restrictions)	20% of the amount of the decrease in the company’s turnover	25 November2020
APOIAR RENDAS	Belong to the CAE in Annex A toMinisterial Order no. 69-A/2021, of 24March	25% or more	Table 3	16 January2021

Funding rate to be allocated—APOIAR RENDAS_

Loss of turnover	Amount receivable
≥25% and ≤40%	30% of the monthly rent up to a maximum of €1200 per month and per establishment
>40%	50% of the monthly rent up to a maximum of €2000 per month and per establishment

The first two digits test (some results)_

First two digits	All			Variation 25% to 35%			Variation 35% to 75%			Micro-enterprises
First two digits	Po	Pe	Z	Po	Pe	Z	Po	Pe	Z	Po	Pe	Z
10	861	805	2.03	166	146	1.66	354	321	1.91	855	790	2.35
11	808	734	2.76	142	134	0.74	352	293	3.54	796	721	2.83
22	343	375	1.68	73	68	0.58	127	149	1.86	335	369	1.76
24	316	345	1.55	58	63	0.60	112	137	2.18	299	338	2.16
29	260	286	1.56	45	52	0.99	101	114	1.23	248	281	1.99
43	168	194	1.88	33	35	0.39	67	77	1.18	164	191	1.94
44	157	190	2.39	28	35	1.11	57	76	2.15	154	186	2.38
47	161	178	1.26	36	32	0.65	52	71	2.25	158	175	1.26
49	142	171	2.20	24	31	1.27	68	68	0.01	142	167	1.98
50	156	167	0.87	18	31	2.26	70	66	0.42	154	164	0.80
57	157	147	0.84	37	27	2.00	68	58	1.25	157	144	1.07
76	131	110	1.97	32	20	2.67	45	44	0.16	131	108	2.18
79	106	106	0.02	29	19	2.21	36	42	0.97	106	104	0.17
80	112	105	0.70	15	19	0.94	52	42	1.59	112	103	0.89
88	108	95	1.29	11	17	1.53	51	38	2.11	107	94	1.38
90	113	93	2.05	14	17	0.72	47	37	1.62	110	92	1.93
96	104	87	1.77	22	16	1.53	42	35	1.21	104	86	1.96
98	122	86	3.93	27	16	2.90	38	34	0.66	119	84	3.80
X²			120			98			106			131

Second digit test_

Second digit	All			Variation 25% to 35%			Variation 35% to 75%			Micro-enterprises
Second digit	Po	Pe	Z	Po	Pe	Z	Po	Pe	Z	Po	Pe	Z
0	2415	2326	2.0	432	423	0.5	974	927	1.7	2368	2285	1.9
1	2270	2214	1.3	421	403	1.0	926	882	1.6	2222	2174	1.1
2	2108	2115	0.2	387	385	0.1	826	843	0.6	2078	2077	0.0
3	1972	2028	1.3	343	369	1.4	782	808	1.0	1937	1992	1.3
4	1935	1950	0.4	353	355	0.1	746	777	1.2	1895	1915	0.5
5	1908	1879	0.7	342	342	0.0	776	749	1.1	1873	1846	0.7
6	1779	1815	0.9	359	330	1.7	698	723	1.0	1753	1783	0.7
7	1759	1756	0.1	305	319	0.8	705	700	0.2	1726	1725	0.0
8	1719	1702	0.4	321	310	0.7	681	678	0.1	1688	1672	0.4
9	1572	1652	2.1	273	301	1.7	630	658	1.1	1550	1623	1.9
			11.7			8.9			10.1			10.1

DOI: https://doi.org/10.2478/ejthr-2024-0020 | Journal eISSN: 2182-4924 | Journal ISSN: 2182-4916

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Language: English

Page range: 273 - 284

Submitted on: Jan 29, 2024

Accepted on: Oct 14, 2024

Published on: Dec 31, 2024

Published by: Polytechnic Institute of Leiria

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

support,

Related subjects:

Business and economics,

Business management,

Business management, other,

Industries,

Tourism, hospitality, travel,

Event industry, leisure industry,

Sports and recreation,

Sports and recreation, other

© 2024 Ana Martins, Jorge Alves, Clara Vaz, published by Polytechnic Institute of Leiria
This work is licensed under the Creative Commons Attribution 4.0 License.

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