Revisiting SME default predictors: The Omega Score

Figures & data

Table 1. Prediction performance metrics.

	Benchmark model	Financial indicators	Financial indicators, management- and employee-related variables	Financial indicators and payment behavior variables	Financial indicators, payment behavior variables, management- and employee-related variables
	(1)	(2)	(3)	(4)	(5)
AUC	70.4	79.6	82.6	86.0	88.0
Δ AUC over benchmark model	–	9.2	12.2	15.6	17.6
Accuracy	65.6	71.7	75.5	78.0	79.3
Δ Accuracy over benchmark model	–	6.1	9.8	12.4	13.7
Specificity	66.4	67.7	74.0	69.2	73.1
Δ Specificity over benchmark model	–	1.3	7.6	2.8	6.7

Note: all values are in percentages. Detailed prediction performance metrics are provided in the Supplementary Material (Table SM4).

Table 2. LASSO selected variables and SME default prediction: logit model.

	Dependent variable:
	Default 60 days (1)	Default 30 days (2)
Surplus dummy	0.346*** (0.140)	0.447*** (0.142)
Quick ratio	0.204*** 0.225)	0.183*** (0.204)
Days of debtors’ change	1.004*** (0.001)	1.003*** (0.000)
Days of clients’ change	1.258*** (0.062)
Retained earnings/Total assets	0.776** (0.108)
Personnel costs/Value added		1.309** (0.112)
Equity/Total investments		0.653*** (0.141)
Previous payment default (1)	3.713*** (0.200)	3.857*** (0.203)
Previous payment default (2)	5.278*** (0.309)	5.747*** (0.312)
Previous payment default (3)	6.450*** (0.573)	5.919*** (0.566)
Previous payment default (4)	12.713*** (0.770)	17.336*** (1.106)
Change in management	1.899*** (0.121)
Employee tenure	0.952***(0.013)	0.951*** (0.012)
Firing ratio	2.766*** (0.172)	2.682*** (0.157)
Constant	0.689 (0.227)	1.012 (0.225)
Observations	1,768	2,023
Log Likelihood	−857.540	−1,032.100
Akaike Inf. Crit.	1,741.100	2,088.200

Note: *p < 0.1, **p < 0.05, ***p < 0.01. Coefficients in the table represent the relative risk ratios, calculated as the exponentiated value of the logit coefficients. Previous payment default relates to the year prior to the default prediction. By definition, an SME cannot fulfil the SME default definition in prior years. Having no previous payment default is the reference category to having more blocks (reported in the brackets). Coefficients below 1 point to negative relationship between the predictor and the SME default, while coefficients above 1 point to positive relationship between the predictor and the SME default.

Table 3. Omega Score Groups and two SME default definitions: the test sample.

Omega Score Group	Defaulted SME	Non-defaulted SME	Total	Cumulative incidence (%)
SME default 60 days definition
Alpha	60	324	384	15.63
Beta	245	126	371	66.04
Gamma	153	13	166	92.17
SME default 30 days definition
Alpha	76	344	420	18.10
Beta	283	185	468	60.47
Gamma	182	15	197	92.39

Table 4. Prediction performance metrics: Omega vs Z’’-Score.

	Regular SME default (60 days)			Early warning SME default (30 days)
	Benchmark model	Omega groups	Omega Score	Benchmark model	Omega groups	Omega Score
	(1)	(2)	(3)	(4)	(5)	(6)
AUC	70.4	82.2	87.2	72.0	79.6	84.4
Δ AUC over benchmark model	–	11.8	16.8	–	7.6	12.4
Accuracy	65.6	78.4	78.4	67.0	74.6	75.8
Δ Accuracy over benchmark model	–	12.8	12.8	–	7.6	8.8
Specificity	66.4	74.1	82.0	71.5	69.9	79.1
Δ Specificity over benchmark model	–	7.7	15.6	–	−1.5	7.6

Note: All values are in percentages. Detailed prediction performance metrics are provided in the Supplementary Material (Table SM5).

Figure 1. ”Important variables” from XGBoost.

Table 5. Prediction performance metrics: Z’’, Omega Score and machine learning models.

	Benchmark model	Omega groups	Omega Score	Random forest	XG Boost
	(1)	(2)	(3)	(4)	(5)
AUC	70.4	82.2	87.2	89.0	90.3
Δ AUC over benchmark model	–	11.8	16.8	18.6	19.9
Accuracy	65.6	78.4	78.4	81.4	82.6
Δ Accuracy over benchmark model	–	12.8	12.8	15.8	17.0
Specificity	66.4	71.4	82.0	79.7	78.6
Δ Specificity over benchmark model	–	5.0	15.6	13.3	12.2

Note: All values are in percentages. Detailed prediction performance metrics are provided in the Supplementary Material (Table SM6).

Table 6. Quantifying the improved SME default prediction; monetary values (in million euros).

Test sample	SMEs defaulted	Bank defaulted debt	Supplier defaulted debt	Government defaulted debt	Total defaulted debt
SMEs defaulted	458 SMEs (100%)	135.3	113.9	24.8	274.0
Benchmark Type II error	172 SMEs (37.6%)	41.8	33.7	7.0	82.5
Omega Score Type II error	126 SMEs (28%)	32.2	28.0	6.7	66.9
Improved prediction	Benchmark (€82.5) – Omega Score (€66.9) = € 15.6

Note: Quantification is based on the Type II errors in the out-of-sample and out-of-time test sample. Assuming these SMEs end up in bankruptcy, we can quantify not just the sum of defaulted debts in correctly classified defaulted SMEs, but also the value of lost defaulted debt in the bankruptcy procedure (assuming World Bank average recovery rate for Croatia = 36%). Unrecovered debts in bankruptcy procedure are 64% (100%–36%) which can get to as much as 10 million euros (15.6 million euros *0.64). Data on recovery rates in Croatia’s bankruptcy procedure stems from the World Bank Doing Business. Recovery rates differ among countries. Those SMEs with probability of default above 0.5 are predicted to default, while those below 0.5 are predicted not to default.

Table

	Variable code name	Variable description
	Dependent variables
SME default	Default 1	Firm collects at least 30 days payment default in period t + 1.
	Default 2	Firm collects at least 60 days payment default in period t + 1.
	Independent variables
Altman Z-Score variables	X1	(Current assets – current liabilities)/total assets
	X2	Retained earnings/total assets
	X3	Earnings before interest and taxes/total assets
	X4	Book value of equity/total liabilities
	X5	Sales/total assets
	Z’’	Altman Z’’-Score, calculated as follows:
		3.25 + 6.56*X1 + 3.26*X2 + 6.72*X3 + 1.05*X4
	Safe Z zone	Z’’ > 2.99
	Grey Z zone	1.81 < Z’’ <2.9
	Distress Z zone	Z’’ < 1.81
Business development	b1	Turnover change: (turnover t-1-turnover t-2)/turnover t-2
	b2	Fixed assets variation: (fixed assets t-1- fixed assets t-2)/fixed assets t-2
	b3	(Depreciation fund/fixed assets) change
	b4	Equity change
Profitability	p1	Ebit variation
	p2	(Ebit + financial profit)/(total assets – nonfinancial debt)
	p3	Ebit/turnover
	p4	(Ebit/turnover) change
	p5	Personnel costs/gross profit
	p6	Inventories change/turnover change
	p7	Cost of goods sold/turnover
	p8	Added value/fixed asset
	p9	Ebit/total investments
	p10	Depreciation rate change
Interest rate risk exposure	ir1	Interest costs/financial debt
	ir2	(Ebit + Financial profit)/(Total assets – nonfinancial debt) – (interest costs/financial debt)
Liquidity	l1	Current ratio = current assets (non financial)/current liabilities (nonfinancial)
	l2	Liquid assets/current assets
	l3	Quick ratio = cash/current liabilities (nonfinancial)
	l4	Ebitda/turnover
	l5	(Working capital/turnover)
	l6	Days of clients’ change; days of clients =ending receivables/(Sales/360)
	l7	Days of inventories change
	l8	Days of debtors change
	l9	(Ebitda – tax)/short term financial debt
	l10	(Ebitda – tax)/financial debt
	l11	Ebitda/interest costs
	l12	Net profit + amortization/short-term financial debt
Financial leverage	le1	(Financial debt – cash)/turnover
	le2	(Financial debt – cash)/equity
	le3	(Financial debt – cash)/(equity – intangible assets)
	le4	Short term financial debt/financial debt
	le5	Equity/fixed assets
	le6	Interest cost/turnover
	le7	Equity/Total investments
Change in balance sheet and profit and loss statement values	Δ noncurrent assets	Change in noncurrent assets from t-1 to t. Noncurrent assets are calculated as log of 1+ the monetary value of noncurrent assets.
	Δ intangible assets	Change in intangible assets from t-1 to t. Intangible assets are calculated as log of 1+ the monetary value of intangible assets.
	Δ research and development costs	Change in research and development (R&D) costs from t-1 to t. R&D costs are calculated as log of 1+ the monetary value of R&D costs.
	Δ value of intellectual property	Change in concessions, patents, licensees and trademarks value from t-1 to t. Concessions, patents, licensees and trademarks value are calculated as log of 1+ the monetary value of concessions, patents, licensees and trademarks value.
	Δ current assets	Change in current assets from t-1 to t. Current assets are calculated as log of 1+ the monetary value of current assets.
	Δ inventories	Change in inventories from t-1 to t. Inventories are calculated as log of 1+ the monetary value of inventories.
	Δ receivables	Change in receivables from t-1 to t. Receivables are calculated as log of 1+ the monetary value of receivables.
	Δ current financial assets	Change in current financial assets from t-1 to t. Current financial assets are calculated as log of 1+ the monetary value of current financial assets.
	Δ cash	Change in cash from t-1 to t. Cash is calculated as log of 1+ the monetary value of cash in bank and cashier.
	Δ assets	Change in assets from t-1 to t. Assets are calculated as log of 1+ the monetary value of assets.
	Δ capital and reserves	Change in capital and reserves from t-1 to t. Capital and reserves are calculated as log of 1+ the monetary value of capital and reserves.
	Δ retained earnings (or losses)	Change in retained earnings (or losses) from t-1 to t. Retained earnings (or losses) are calculated as inverse hyperbolic sine of 1+ monetary value of retained earnings (or losses).
	Δ noncurrent liabilities	Change in noncurrent liabilities from t-1 to t. Noncurrent liabilities are calculated as log of 1+ the monetary value of noncurrent liabilities.
	Δ noncurrent liabilities to affiliates	Change in noncurrent liabilities to affiliates from t-1 to t. Noncurrent liabilities to affiliates are calculated as log of 1+ the monetary value of noncurrent liabilities to affiliates.
	Δ noncurrent liabilities for loans, deposits and similar	Change in noncurrent liabilities for loans, deposits and similar from t-1 to t. Noncurrent liabilities for loans, deposits and similar are calculated as log of 1+ the monetary value of noncurrent liabilities for loans, deposits and similar.
	Δ noncurrent liabilities to banks and other financial institutions	Change in noncurrent liabilities to banks and other financial institutions from t-1 to t. Noncurrent liabilities to banks and other financial institutions are calculated as log of 1+ the monetary value of noncurrent liabilities to banks and other financial institutions.
	Δ noncurrent liabilities to suppliers	Change in noncurrent liabilities to suppliers from t-1 to t. Noncurrent liabilities to suppliers are calculated as log of 1+ the monetary value of noncurrent liabilities to suppliers.
	Δ noncurrent liabilities for securities	Change in noncurrent liabilities for securities from t-1 to t. Noncurrent liabilities for securities are calculated as log of 1+ the monetary value of noncurrent liabilities for securities.
	Δ current liabilities	Change in current liabilities from t-1 to t. Current liabilities are calculated as log of 1+ the monetary value of current liabilities.
	Δ current liabilities to affiliates	Change in current liabilities to affiliates from t-1 to t. Current liabilities to affiliates are calculated as log of 1+ the monetary value of current liabilities to affiliates.
	Δ current liabilities for loans, deposits and similar	Change in current liabilities for loans, deposits and similar from t-1 to t. Current liabilities for loans, deposits and similar are calculated as log of 1+ the monetary value of current liabilities for loans, deposits and similar.
	Δ current liabilities to banks and other financial institutions	Change in current liabilities to banks and other financial institutions from t-1 to t. Current liabilities to banks and other financial institutions are calculated as log of 1+ the monetary value of current liabilities to banks and other financial institutions.
	Δ current liabilities to suppliers	Change in current liabilities to suppliers from t-1 to t. Current liabilities to suppliers are calculated as log of 1+ the monetary value of current liabilities to suppliers.
	Δ current liabilities for securities	Change in current liabilities for securities from t-1 to t. Current liabilities for securities are calculated as log of 1+ the monetary value of current liabilities for securities.
	Δ current liabilities on the basis of share in the result	Change in current liabilities on the basis of share in the result from t-1 to t. Current liabilities on the basis of share in the result are calculated as log of 1+ the monetary value of current liabilities on the basis of share in the result.
	Δ other current liabilities	Change in other current liabilities from t-1 to t. Other current liabilities are calculated as log of 1+ the monetary value of other current liabilities.
	Δ deferred payment	Change in deferred payment from t-1 to t. Deferred payment are calculated as log of 1+ the monetary value of deferred payment of expenses and income for the future period.
	Δ revenue	Change in revenue from t-1 to t. Revenue is calculated as log of 1+ monetary value of revenue.
	Δ sales	Change in sales from t-1 to t. Sales is calculated as log of 1+ monetary value of sales.
	Δ material costs	Change in material costs from t-1 to t. Material costs is calculated as log of 1+ monetary value of material costs.
	Δ costs of goods sold	Change in costs of goods sold from t-1 to t. Costs of goods sold are calculated as log of 1+ monetary value of costs of goods sold.
	Δ other external costs	Change in other external costs from t-1 to t. Other external costs are calculated as log of 1+ monetary value of other external costs.
	Δ employee costs	Change in employee costs from t-1 to t. Employee costs are calculated as log of 1+ monetary value of employee costs.
	Δ depreciation	Change in depreciation from t-1 to t. Depreciation is calculated as log of 1+ monetary value of depreciation.
	Δ other costs	Change in other costs from t-1 to t. Other costs are calculated as log of 1+ monetary value of other costs.
	Δ financial revenue	Change in financial revenue from t-1 to t. Financial revenue is calculated as log of 1+ monetary value of financial revenue.
	Δ other financial revenue	Change in other financial revenue from t-1 to t. Other financial revenue is calculated as log of 1+ monetary value of other financial revenue.
	Δ profits (or loss) before taxation	Change in profits (or loss) before taxation from t-1 to t. Profits (or loss) before taxation are calculated as inverse hyperbolic sine of 1+ monetary value of profits (or loss) before taxation.
	Δ profit tax	Change in profit tax from t-1 to t. Profit tax are calculated as log of 1+ monetary value of profit tax.
	Δ profits (or loss)	Change in profits (or loss) from t-1 to t. Profits (or loss) are calculated as inverse hyperbolic sine of 1+ monetary value of profits (or loss).
	Δ exports	Change in exports from t-1 to t. Exports are calculated as log of 1+ monetary value of exports.
	Δ imports	Change in imports from t-1 to t. Imports are calculated as log of 1+ monetary value of imports.
	Δ employees	Change in employees from t-1 to t. Employees are calculated as log of 1+ the number of employees.
Size	Firm size	1 – the firm has less than 10 employees, 2 – the firm has 10–49 employees, 3 – the firm has 50–249 employees, and 4 – firm has 250 and more employees.
Age	Firm age	Number of years the firm is active in the market.
	Firm age squared
Industry	NACE 2-digit	Categorical variable of NACE 2-digit sectors.
Region	County	Categorical variable for 21 counties in Croatia.
Calendar year	Year	Year dummies.
Internationalization	Exporter	Dummy equal to 1 if a firm exports, and 0 otherwise.
	Export intensity	Export/total sales.
	Import intensity	Import/total sales.
Innovation	Intellectual property dummy	Dummy of 1 if the firm has nonzero value of intellectual property (patents, trademarks).
	Intellectual property ratio	Intellectual property value/total assets.
	R&D active	Dummy of 1 if the firm has nonzero value of research and development expenditures.
Relational capital/public contract and political connections	Public contract	Dummy of 1 if the firm received a government contract.
	Number of public contracts	A count variable of number of government contracts received.
	Public revenue	Value of public money received through government contracts.
	Political connection	A dummy of 1 if the firm has owner or top management that is connected to local, regional, or national politicians. This variable was developed by Srhoj and Dragojević (2021).
	Donation	A dummy of 1 if the firm has donated funds to the political party.
Payment behavior variables	Blockage duration	Duration (in days) of the firms’ payment default.
	Category duration	0 – no default payment, 1 – default payment up to 7 days, 2–7 to 30 days, and 3–30 to 59 days default payment duration.
	Category blocks	Categorical variable of number of times a firm has experienced default payment in a year.
	Blockage duration (t-1)	In year t-1, duration (in days) of the firms’ payment default.
	Category duration (t-1)	In year t-1, 0 – no default payment, 1 – default payment up to 7 days, 2–7 to 30 days, and 3–30 to 59 days default payment duration.
	Category blocks (t-1)	Categorical variable of number of times a firm has experienced default payment in a year.
Employee-related variables	Share of HE	Share of employees with tertiary-level education in the total number of employees.
	Share of LE	Share of employees with primary or secondary-level education in the total number of employees.
	Share of males	Share of male employees in the total number of employees.
	Share of NFC	Share of nonfixed contracts in total number of contracts.
	Firing ratio	Total number of employees with which a firm terminated work contract in period t divided by the total number of employees at t-1.
	Hires ratio	Total number of employees with which a firm signed the work contract in period t divided by the total number of employees at t-1.
	Change ratio	(Total number of employees with which a firm signed the work contract in period t – Total number of employees with which a firm terminated work contract in period t) divided by the total number of employees at t-1.
	Turnover ratio	(Total number of employees with which a firm signed the work contract in period t + Total number of employees with which a firm terminated work contract in period t) divided by the total number of employees at t-1.
	Tenure	Employees mean number of years in the firm.
	Employee age	Mean employee age in the firm.
Firms age and employee-related variables	Age * turnover ratio	Firm age multiplied with turnover ratio.
	Age * firing ratio	Firm age multiplied with firing ratio.
	Age * hires ratio	Firm age multiplied with hires ratio.
	Age * change ratio	Firm age multiplied with change ratio.
	Age * tenure	Firm age multiplied with mean employee tenure.
	Age * employee age	Firm age multiplied with mean employee age.
	Age^2 * turnover ratio	Firm age squared multiplied with turnover ratio.
	Age^2 * firing ratio	Firm age squared multiplied with firing ratio.
	Age^2 * hires ratio	Firm age squared multiplied with hires ratio.
	Age^2 * tenure	Firm age squared multiplied with mean employee tenure.
	Age^2 * employee age	Firm age squared multiplied with mean employee age.
Management-related variables	CEO with prior experience	A dummy of 1 if managers have prior managerial experience, and 0 otherwise.
	CEO with prior experience in the same industry	A dummy of 1 if managers have prior managerial experience in the same industry as the current firm, and 0 otherwise.
	CEO with prior experience in SMEs	A dummy of 1 if managers have prior managerial experience with SMEs, and 0 otherwise.
	CEO with prior experience in large firms	A dummy of 1 if managers do not have prior managerial experience with large firms, and 0 otherwise.
	CEO managed defaulted firm	A dummy of 1 if managers have managed defaulted firm, and 0 otherwise.
	CEO previous experience: low	A dummy of 1 if managers prior managed firm was in the fourth quartile of same NACE 4-digit sectors distribution of return on assets when manager left the firm, and 0 otherwise.
	CEO previous experience: low medium	A dummy of 1 if managers prior managed firm was in the third quartile of same NACE 4-digit sectors distribution of return on assets when manager left the firm, and 0 otherwise.
	CEO previous experience: medium high	A dummy of 1 if managers prior managed firm was in the second quartile of same NACE 4-digit sectors distribution of return on assets when manager left the firm, and 0 otherwise.
	CEO previous experience: high	A dummy of 1 if managers prior managed firm was in the first quartile of same NACE 4-digit sectors distribution of return on assets when manager left the firm, and 0 otherwise.
	CEO with other current experience	A dummy of 1 if managers manage another firm simultaneously, 0 otherwise.
	CEO with other current experience in the same industry	A dummy of 1 if managers manage another firm in the same industry simultaneously, 0 otherwise.
	CEO with other current experience in SME	A dummy of 1 if managers manage another SME simultaneously, 0 otherwise.
	CEO with other current experience in large firm	A dummy of 1 if managers manage another large firm simultaneously, 0 otherwise.
	CEO managed current defaulted firm	A dummy of 1 if managers manage defaulted firm simultaneously in the last two years, 0 otherwise.
	CEO current experience: low	A dummy of 1 if managers other currently managed firm is in the fourth quartile of same NACE four-digit sectors distribution of return on assets, and 0 otherwise.
	CEO current experience: low medium	A dummy of 1 if managers other currently managed firm is in the third quartile of same NACE four-digit sectors distribution of return on assets, and 0 otherwise.
	CEO current experience: medium high	A dummy of 1 if managers other currently managed firm is in the second quartile of same NACE four-digit sectors distribution of return on assets, and 0 otherwise.
	CEO current experience: high	A dummy of 1 if managers other currently managed firm is in the first quartile of same NACE four-digit sectors distribution of return on assets, and 0 otherwise.
	Change in management	A dummy of 1 if there was a change in management during the last two years, 0 otherwise.
	CEO mean years’ experience	Mean age of all managers.
	First change in management	A dummy of 1 for the firm’s first significant change in management, 0 otherwise. This variable is year specific. For example, if the firm has changes in management board, for example, added and dropped management over a course of three years, this variable is equal to 1 only in the first year.
	CEO swap	A dummy of 1 if the top managers of a firm differ from the ones of the previous year.
	Any change in management	A dummy of 1 if there was any change in management during the last two years, and 0 otherwise.
	Number of board managers and owners	Number of board managers and owners in the SME.
	Number of managers	Number of managers in the SME.
	Number of board chairs	Number of board chairs in the SME.
	Number of deputy chairs	Number of deputy chairs in the SME.
	Number of board members	Number of board members in the SME.
	Number of bankruptcy officials	Number of bankruptcy officials in the SME.
	Number of founders	Number of founders in the SME.
	All male managers	A dummy of 1 if all managers are male, and 0 otherwise.
	All female board members	A dummy of 1 if all managers are female, and 0 otherwise.
	Mixed gender board members	A dummy of 1 if at least one manager is male and at least one manager is female, and 0 otherwise.

Srhoj, S., & Dragojević, M. (2022). Public procurement and supplier job creation: Insights from auctions. The Journal of Law, Economics, and Organization.

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