A LASSO-based model for financial distress of the Vietnamese listed firms: Does the covid-19 pandemic matter?

Figures & data

Table 1. Frequency counts of the dependent variable

Dependent variables	Classification	Frequency	Per cent
	0	4,013	82
DISTRESSi,t	1	907	18
	Total	4,920	100

Notes: This table counts the frequency of the classification dependent variable. DISTRESS is the dependent variable classifying the corporate financial distress, taking the value of 1 for distressed firms and 0 otherwise. A firm is classified as distressed if its interest coverage ratio is less than one.

Table 2. Descriptive statistics

Variables	Obs	Mean	Std. Dev.	Min	Max	p1	p99	Skew.	Kurt.
WCTA	4,898	0.2	0.2	−0.6	1	−0.3	0.8	0.4	3.1
CACL	4,919	2.6	6.2	0	242.6	0.4	18.4	24.1	835.1
CATL	4,919	2.1	5.8	0	242.6	0.1	16	28.1	1068.6
CLTA	4,920	0.4	0.2	0	1.2	0	0.9	0.2	2.3
RETA	4,900	0.1	0.1	−1.7	0.6	−0.4	0.4	−3.9	39.4
EBITTA	4,881	0.1	0.1	−1.4	0.8	−0.1	0.3	−0.1	29.3
SALESTA	4,918	1.2	1.1	0	12.7	0	5.3	2.8	16.7
NITA	4,899	0.1	0.1	−1.6	0.8	−0.2	0.3	−1.2	47.2
TLTA	4,920	0.5	0.2	0	1.2	0	0.9	−0.2	2.2
MVETL	4,851	3.5	58	0	3983.2	0	33.1	66.7	4565.5
TETL	4,920	2.6	11.6	−0.2	503.9	0.1	24.2	27.4	991.5
TLTE	4,920	1.7	3.1	−19.4	122.1	0	11.2	15.9	493.4

Notes: WCTA (Working Capital/Total Assets); CACL (Current assets/Current Liabilities); CATL (Current assets/Total Liabilities); CLTA (Current Liabilities/Total Assets); RETA (Retained Earnings/Total Assets); EBITTA (Earnings Before Interest and Taxes/Total Assets); SALESTA (Sales/Total Assets); NITA (Net Income/Total Assets); TLTA (Total Liabilities/Total Assets); MVETL (Market Value of Equity/Total Liabilities); TETL (Book Value of Equity/Total Liabilities); TLTE (Total Liabilities/Book Value of Equity).

Table 3. The selection of variables

Explanatory Variables			Adaptive LASSO Selection	Backward Stepwise Selection	Forward Stepwise Selection
X1	Liquidity	WCTA	x	x	x
X2		CACL
X3		CATL
X4		CLTA
X5	Profitability	RETA	x	x	x
X6		EBITTA	x	x	x
X7		SALESTA
X8		NITA	x	x	x
X9	Leverage	TLTA
X10		MVETL
X11		TETL
X12		TLTE

Notes: This table presents the results of the LASSO and STEPWISE selection. Symbol “x” denotes the variables selected by the variable selection techniques.

WCTA (Working Capital/Total Assets); CACL (Current assets/Current Liabilities); CATL (Current assets/Total Liabilities); CLTA (Current Liabilities/Total Assets); RETA (Retained Earnings/Total Assets); EBITTA (Earnings Before Interest and Taxes/Total Assets); SALESTA (Sales/Total Assets); NITA (Net Income/Total Assets); TLTA (Total Liabilities/Total Assets); MVETL (Market Value of Equity/Total Liabilities); TETL (Book Value of Equity/Total Liabilities); TLTE (Total Liabilities/Book Value of Equity).

Table 4. Logistic regression results for the LASSO-based model

	(1)	(2)	(3)	(4)
	DISTRESS	DISTRESS	DISTRESS	DISTRESS
WCTA	−1.414***	−1.431***	−1.440***	−1.459***
	(0.000)	(0.000)	(0.000)	(0.000)
RETA	−1.048*	−1.090*	−1.172**	−1.257**
	(0.058)	(0.054)	(0.041)	(0.032)
EBITTA	−75.226***	−76.336***	−76.426***	−77.556***
	(0.000)	(0.000)	(0.000)	(0.000)
NITA	−7.293***	−7.037***	−6.259***	−5.940***
	(0.001)	(0.002)	(0.004)	(0.007)
Industry Dummies	NO	YES	NO	YES
Year Dummies	NO	NO	YES	YES
Observations	4860	4860	4860	4860
Pseudo R^2	0.558	0.562	0.566	0.570
AUC	0.9484	0.9497	0.9505	0.9517

Notes: We estimate the model with predictors selected from the variable selection results through logistic regression. We also consider the industry and year-fixed effects to control for the potential endogeneity, but the coefficient estimates are omitted for brevity. AUC denotes the area under the receiving operating characteristic curve measuring the model’s predictive performance.

Symbols ***, **, * represent significance at 1, 5, and 10 per cent levels. WCTA (Working Capital/Total Assets; RETA (Retained Earnings/Total Assets); EBITTA (Earnings Before Interest and Taxes/Total Assets); NITA (Net Income/Total Assets).

Table 5. The comparison between our model and Altman Z”-score model – Logistic regression

	LASSO-based Model	Z”-score Model
	DISTRESS	DISTRESS
WCTA	−1.459***	−1.647***
	(0.000)	(0.000)
RETA	−1.257**	−1.647***
	(0.032)	(0.004)
EBITTA	−77.556***	−79.745***
	(0.000)	(0.000)
NITA	−5.940***
	(0.007)
TETL		−0.001
		(0.519)
Constant	2.858***	2.882***
	(0.000)	(0.000)
Industry Dummies	YES	YES
Year Dummies	YES	YES
Observations	4860	4860
Pseudo R^2	0.570	0.568
AUC	0.9517	0.9510

Notes: We estimate our model with the Altman Z”-score model through logistic regression. We also consider the industry and year-fixed effects to control for the potential endogeneity, but the coefficient estimates are omitted for brevity. AUC denotes the area under the receiving operating characteristic curve measuring the model’s predictive performance.

Symbols ***, **, * represent significance at 1, 5, and 10 per cent levels. WCTA (Working Capital/Total Assets; RETA (Retained Earnings/Total Assets); EBITTA (Earnings Before Interest and Taxes/Total Assets); NITA (Net Income/Total Assets); TETL (Book Value of Equity/Total Liabilities).

Figure 1. Normalized confusion matrix (%).

Notes: We compare the classification accuracy between our model with the Altman Z”-score model. The vertical axis represents the actual classification value, while the horizontal axis represents the predicted value through logistic regression. The upper left of the graph indicates the proportion of distressed firms correctly classified as distressed. In contrast, the lower right of the graph indicates the proportion of non-distressed firms correctly classified as non-distressed.

Figure 2. The area under the receiver operating characteristic curve (AUC).

Notes: We compare the predictive performance between our model with the Altman Z”-score model. AUC denotes the area under the receiving operating characteristic curve measuring the model’s predictive performance.

Table 6. Industry-level analysis during the Covid-19 pandemic

	2020	2021
Communication Services	23%	15%
Consumer Discretionary	40%	35%
Consumer Staples	30%	26%
Energy	67%	59%
Health Care	24%	18%
Industrials	55%	48%
Information Technology	53%	47%
Materials	47%	33%
Real Estate	51%	32%
Utilities	32%	20%

Notes: The table presents the proportion of distressed firms in each industry for 2020 and 2021. The Altman Z”-score model is utilized to classify distressed firms into each industry, then the number of distressed is computed. Industry classification is adopted based on the Global Industry Classification Standard (GICS).

Table

Variable and abbreviation			Definition
Dependent variables
Financial distress	Y	DISTRESS	A dummy variable of “1” when a firm is financially distressed and “0” otherwise.
Explanatory variables
Liquidity	X1	WC/TA	Working capital to total assets
	X2	CA/CL	Current assets to current liabilities
	X3	CA/TL	Current assets to total liabilities
	X4	CL/TA	Current liabilities to total assets
Profitability	X5	RE/TA	Retained earnings to total assets
	X6	EBIT/TA	Earnings before interest and taxes to total assets
	X7	SALES/TA	Total sales to total assets
	X8	NI/TA	Net income to total assets
Leverage	X9	TL/TA	Total liabilities to total assets
	X10	MVE/TL	The market value of equity to total liabilities
	X11	TE/TL	Book value of equity to total liabilities
	X12	TL/TE	Total liabilities to total equity

Notes: The table presents abbreviations and definitions of the variables used in our study. There are 12 candidate predictors in total, and they are classified into three categories, namely liquidity, profitability, and leverage.

Table

ID	Lambda	No. of nonzero coef.	CV mean deviance	Variables
63	18.027	1	0.919	A	EBITTA
117	0.119	2	0.442	A	WCTA
122	0.074	3	0.436	A	NITA
139	0.015	4	0.429	A	RETA
160*	0.002	4	0.429	U	—
158	0.002	4	0.429	U	—

Notes: The table presents detailed results of LASSO selection. Symbol * denotes lambda selected by cross-validation in the final adaptive step to choose the right-fitted model. (A) the denoted model with the added variable(s), and (U) denotes the model left unchanged.

Table

Backwards stepwise	Forward stepwise
Wald test, begin with full model: p = 0.5397 ≥ 0.1, removing CACL p = 0.5284 ≥ 0.1, removing SALESTA p = 0.2005 ≥ 0.1, removing TLTA p = 0.5283 ≥ 0.1, removing CLTA p = 0.2070 ≥ 0.1, removing CATL p = 0.1591 ≥ 0.1, removing MVETL p = 0.7544 ≥ 0.1, removing TETL p = 0.3938 ≥ 0.1, removing TLTE	Wald test, begin with empty model: p = 0.0000 < 0.1, adding EBITTA p = 0.0000 < 0.1, adding WCTA p = 0.0000 < 0.1, adding NITA p = 0.0675 < 0.1, adding RETA

Notes: The table presents detailed results of STEPWISE selection. Variables are removed or added based on p-value = 0.1

Table

Model	Training set		Testing set
Classified	Distress (Actual)	Non-distress (Actual)	Distress (Actual)	Non-distress (Actual)
Distress (Predicted)	436	79	201	36
Non-distress (Predicted)	191	2699	71	1147
Total	627	2778	272	1183
Correctly classified	92.07%		92.65%
Pseudo R2	0.5523		0.6315
AUC	0.9473		0.9650

Notes: The table provides split-sample metrics measuring our model’s predictive performance. The results indicate that our model—the Lasso-based model performs well across the training and testing set with high classification accuracy rates and AUC values.

Table

Model	Lasso-based model		Z”-score model
Classified	Distress (Actual)	Non-distress (Actual)	Distress (Actual)	Non-distress (Actual)
Distress (Predicted)	639	115	632	115
Non-distress (Predicted)	260	3846	267	3846
Total	899	3961	899	3961
Correctly classified	92.28%		92.14%
Pseudo R2	0.570		0.568
AUC	0.9517		0.9510

Notes: The table provides metrics measuring the predictive performance of our model and the Altman Z”-score model.

Table

	Pre Covid-19	During Covid-19
Lasso-based model	0.9468	0.9495
Z”-score model	0.9454	0.9505

Notes: The table provides AUC values for comparing the predictive performance of our model and the Altman Z-score model for two periods, namely pre-Covid-19 (2012–2019) and during COVID-19 (2020–2021).