The informational value contained in the different types of auditor’s opinions: Evidence from Portugal

Figures & data

Table 1. Distribution of firm-years that filed their accounts and have been assigned a failure score

Year	Cases that filed accounts			Cases required to have certification of accounts
	Total	Failed		Total	Failed
		(#)	(% of total)		(#)	(% of total)
2011	312,409	2,269	0.73%	26,674	222	0.83%
2012	308,509	1,302	0.42%	27,040	126	0.47%
2013	307,748	1,447	0.47%	26,622	128	0.48%
2014	272,425	1,009	0.37%	21,635	83	0.38%
2015	313,495	1,015	0.32%	25,872	96	0.37%
2016	294,229	904	0.31%	22,262	82	0.37%
Total	1,808,815	7,946	0.44%	150,105	737	0.49%

Table 2. Distribution of failed and non-failed cases required to have a CA per CA compliance and SA appointment

	Failed		Non-failed		Total
Firms required to have a CA	737	100%	149,368	100%	150,105
did not comply with the CA	235	31.9%	10,160	6.8%	10,395
did not appoint an SA	85	11.5%	3,275	2.2%	3,360

Table 3. Comparison of alternative bankruptcy prediction models

Variables	Altman and Sabato (2007)	Altman et al. (2010) incomplete	Altman et al. (2010) adapted	Informa D&B’s model
Cash_TA	-2.0107***	-2.2078***	-1.2560***
	(-2.99)	(-3.02)	(-3.91)
EBITDA_TA	-0.0001***	0.0001*
	(-3.72)	(1.63)
EBITDA_Int	0.0001*	0.0000***
	(1.81)	(-4.32)
Retain_TA	-0.0001	-0.0001***	-0.0001**
	(-0.65)	(-2.83)	(-2.56)
STD_E	0.0000***	-0.0001	-0.0001
	(-4.34)	(-0.32)	(-0.77)
Log of age		0.4823	0.5338***
		(8.97)	(11.35)
Age 3–9 years		-0.0126	-0.0835
		(-0.1)	(-0.68)
Size		-0.1129***	0.0079
		(-4.54)	(0.36)
Neg_EBITDA			2.3423***
			(24.23)
Failure score				-0.0428
				(-25.06)***
Intercept	-5.1784***	-5.6188***	-8.0153***	-3.5328
	(-97.85)	(-23.71)	-32.45	(-63.67)***
Pseudo-R^2	0.0068	0.0194	0.1085	0.1177
AUC	0.6425	0.6537	0.7989	0.8290
Likelihood ratio χ^2	42.61	152.76	710.72	1,095.43
Observations	144,141	144,141	144,141	150,105

This table reports coefficients and z-values (in parentheses) from logistic regressions with robust standard errors. The dependent variable is a binary variable denoting failure events observed within 1 year. Altman et al. (2010) is not complete because not all variables are available for our sample. Significance at the 1%, 5%, and 10% levels are marked with ***, **, and *, respectively.

Figure 1. Estimated contribution of explanatory variables to the global accuracy of the failure score.

(Weight of the Individual ARs Relative to the Model’s Total AR)

Table 4. Distribution of the different certification of accounts with alternative disclosures (CA-Type), by auditor size and by failed and non-failed cases

		Non-Big 4			Big 4
	CA-Type	Non-failed	Failed	Sub-total	Non-failed	Failed	Sub-total
1	Without reservations and	84,283	144	84,427	12,028	6	12,034
	without emphasis	67.19%	23.23%	66.98%	58.23%	18.75%	58.17%
2	With emphasis	16,917	106	17,023	4,523	9	4,532
		13.49%	17.10%	13.50%	21.90%	28.13%	21.91%
3	With reservations	10,631	83	10,714	1,716	3	1,719
		8.48%	13.39%	8.50%	8.31%	9.38%	8.31%
4	With reservations and	6,854	125	6,979	1,823	10	1,833
	with emphasis	5.46%	20.16%	5.54%	8.83%	31.25%	8.86%
5	With adverse opinion	89	2	91	9	0	9
		0.07%	0.32%	0.07%	0.04%	0%	0.04%
6	With disclaimer of opinion	277	14	291	58	0	58
		0.22%	2.26%	0.23%	0.28%	0%	0.28%
7	CA not issued	6,385	146	6,531	500	4	504
		5.09%	23.55%	5.18%	2.42%	12.50%	2.44%
	Total	125,436	620	126,056	20,657	32	20,689
		100%	100%	100%	100%	100%	100%

Table 5. Descriptive statistics. The statistics are from the full sample of 150,105 firm-years

	Total		Non-failed		Failed
Variables	Mean	Std. Dev.	Mean	Std. Dev.	Mean	Std. Dev.
Without reservations and emphasis	0.642	0.479	0.645	0.479	0.204	0.403
With emphasis	0.144	0.351	0.144	0.351	0.156	0.363
With reservations	0.083	0.276	0.083	0.275	0.117	0.321
With reservations and with emphasis	0.059	0.235	0.058	0.234	0.183	0.387
With adverse opinion	0.001	0.026	0.001	0.026	0.003	0.052
With disclaimer of opinion	0.002	0.048	0.002	0.047	0.019	0.137
CA not issued	0.069	0.254	0.068	0.252	0.319	0.466
Failure score	62.249	30.828	62.467	30.715	24.075	24.928

Table 6. Variance inflation factors

Variable	VIF
With emphasis	1.06
With reservations	1.04
With reservations and with emphasis	1.06
With adverse opinion	1.00
With disclaimer of opinion	1.00
CA not issued	1.05
Failure score	1.06

Table 7. Pairwise correlations

		Failure s.	1	2	3	4	5	6	7
0	Failure score	1
1	Without reservations and emphasis	0.216***	1
2	With emphasis	−0.084***	−0.230***	1
3	With reservations	−0.049***	−0.170***	−0.068***	1
4	With reservations and with emphasis	−0.141***	−0.143***	−0.057***	−0.042***	1
5	With adverse opinion	−0.010***	−0.016***	−0.006***	−0.005**	−0.004**	1
6	With disclaimer of opinion	−0.024***	−0.030***	−0.012***	−0.009***	−0.007***	−0.001	1
7	CA not issued	−0.103***	−0.163***	−0.065***	−0.048***	−0.040***	−0.004**	−0.009***	1

Significance at the 1%, 5%, and 10% levels are marked with ***, **, and *, respectively.

Table 8. Estimates for Eq. (2)

Variables	Coefficient	Odds ratio
Failure score	-0.036***	0.965
	(-21.97)
With emphasis	0.852***	2.344
	(6.81)
With reservations	1.125***	3.081
	(8.23)
With reservations and with emphasis	1.577***	4.840
	(12.88)
With adverse opinion	1.967***	7.150
	(2.71)
With disclaimer of opinion	2.579***	13.178
	(8.93)
CA not issued	2.127***	8.388
	(20.11)
Intercept	-4.663***	0.009
	(-48.03)
Pseudo-R^2	0.1674
AUC	0.8595
Likelihood ratio χ^2	1,557.93
Observations	150,105

This table reports coefficients and z-values (in parentheses) from logistic regressions with robust standard errors. The dependent variable is a binary denoting failure events within 1 year after the failure score and the auditor’s assessment. Significance at the 1%, 5%, and 10% levels are marked with ***, **, and *, respectively. The coefficients are converted to the respective odds ratio.

Table 9. Estimates for Equation 2(2) $F_{it}=\frac{1}{1+exp\left[-\left(\alpha +\sum _{j=1}^J{\beta }_j\cdot X_{jit}+\delta \cdot F{S}_{it}+{\epsilon }_{it}\right)\right]}$(2)

Variables	Small auditor		Mid-tier auditor		Big 4
	Coef.	OR	Coef.	OR	Coef.	OR
Failure score	-0.038***	0.963	-0.030***	0.971	-0.019***	0.981
	(-21.12)		(-4.89)		(-3.09)
With emphasis	0.872***	2.392	1.090**	2.974	1.235**	3.438
	(6.48)		(2.16)		(2.39)
With reservations	1.075***	2.929	1.529***	4.614	1.152*	3.165
	(7.37)		(2.92)		(1.63)
With reservations and with emphasis	1.557***	4.747	1.904***	6.712	2.109***	8.243
	(11.87)		(3.87)		(4.06)
With adverse opinion ^(1)	1.927***	6.871	0.000	1.000	0.000	1.000
	(2.63)		(omitted)		(omitted)
With disclaimer of opinion ^(2)	2.771***	15.975	0.000	1.000	0.000	1.000
	(9.83)		(omitted)		(omitted)
CA not issued	1.987***	7.292	2.423***	11.280	2.670***	14.437
	(17.76)		(5.42)		(4.19)
Intercept	-4.460***	0.012	-5.166***	0.006	-6.550***	0.001
	(-43.30)		(-11.98)		(-14.51)
Pseudo-R^2	0.1751		0.1556		0.087
AUC	0.865		0.859		0.784
Likelihood ratio χ^2	981.01		75.95		33.49
Observations	118,087		11,304		20,622

Mid-tier auditors are the 4 biggest ones after the Big 4. This table reports coefficients and z-values (in parentheses) from logistic regressions with robust standard errors. The dependent variable is a binary denoting failure events within 1 year after the failure score and the auditor’s assessment. Significance at the 1%, 5%, and 10% levels are marked with ***, **, and *, respectively. The coefficients are converted to the respective odds ratio (denoted as OR).

Altman, E., & Sabato, G. (2007). Modelling credit risk from SMEs: Evidence from the US market. Abacus, 43(3), 332–357. https://doi.org/10.1111/j.1467-6281.2007.00234.x

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Altman, E., Sabato, G., & Wilson, N. (2010). The value of non-financial information in small and medium-sized enterprises risk management. The Journal of Credit Risk, 6(2), 1–33. https://doi.org/10.21314/JCR.2010.110

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