Journal of Economic and Social Science Research | Vol. 06 | Num. 02 | Abr – Jun | 2026 !pág. 113

Optimización estocástica mediante modelos de riesgo

GARCH-Cox para mitigar la quiebra de las pymes agrícolas

en las economías emergentes

Stochastic optimization via GARCH-Cox hazard modeling to mitigate

agricultural SME failure in emerging economies

Franco-Coello, Mauricio Rubén

Sandoval-Cuji, Martha Matilde

https://orcid.org/0009-0005-2756-9429

https://orcid.org/0000-0002-5182-3280

mfrancoc2@uteq.edu.ec

msandoval@uteq.edu.ec

Ecuador, Quevedo, Universidad Técnica Estatal de

Quevedo.

Ecuador, Quevedo, Universidad Técnica Estatal de

Quevedo.

Recalde-Aguilar, Lugarda María

https://orcid.org/0000-0001-6933-0815

lrecalde@uteq.edu.ec

Ecuador, Quevedo, Universidad Técnica Estatal de

Quevedo.

Autor de correspondencia

DOI / URL: https://doi.org/10.55813/gaea/jessr/v6/n2/244

Resumen: Los modelos tradicionales de dificultades

financieras, diseñados en contextos de altos ingresos y

baja volatilidad, no captan la exposición conjunta de las

pymes agrícolas a choques de precios y variaciones

climáticas. Este estudio desarrolla un marco de

optimización de supervivencia estocástica que integra un

modelo GARCH(1,1)–GJR de varianza condicional con

un modelo de riesgos proporcionales de Cox

dependiente del tiempo, incorporando el riesgo

agroclimático heteroscedástico en la probabilidad de

quiebra. Se emplearon datos longitudinales de 205

pymes agrícolas registradas en la Superintendencia de

Compañías del Ecuador en Quevedo, Los Ríos, zona

bananera y cacaotera con volatilidad de precios superior

al 34 % anualizado; el modelo se estimó sobre 80

empresas entre 2021 y 2025. A partir de condiciones

KKT se identificó un umbral crítico de apalancamiento

(Zoc = −0,2263) y un límite de diversificación (σ* =

0,312), bajo los cuales la quiebra aumenta no

linealmente. Los resultados evidencian que 43 empresas

(53,75 %) se ubican en alto riesgo, y que el riesgo

condicional crece 2,14 por cada unidad de reducción en

utilidades retenidas. El modelo aporta reglas de decisión

aplicables a la gestión agroalimentaria y al análisis de

supervivencia financiera no gaussiana.

Palabras clave: Empresas agrícolas, gestión de

riesgos, modelos económicos, economía agrícola,

econometría.

Research Article

Receptado: 23/Mar/2026

Aceptado: 15/Abr/2026

Publicado: 30/Abr/2026

Cita: Franco-Coello, M. R., Sandoval-Cuji, M. M.,

& Recalde-Aguilar, L. M. (2026). Optimización

estocástica mediante modelos de riesgo GARCH-

Cox para mitigar la quiebra de las pymes agrícolas

en las economías emergentes. Journal of

Economic and Social Science Research, 6(2),

113-

131. https://doi.org/10.55813/gaea/jessr/v6/n2/24

Journal of Economic and Social Science Research

(JESSR)

https://economicsocialresearch.com

jessr@editorialgrupo-aea.com

info@editoriagrupo-aea.com

Nota del editor: Editorial Grupo AEA se mantiene

neutral con respecto a las reclamaciones legales

resultantes de contenido publicado. La

responsabilidad de información publicada recae

enteramente en los autores.

abierto distribuido bajo los términos y condiciones

de la Licencia Creative Commons, Atribución-

NoComercial 4.0 Internacional.

Journal of Economic and Social Science Research | Vol. 06 | Num. 02 | Abr – Jun | 2026 !pág. 114

Artículo Científico

Abril – Junio 2026

Abstract:

Traditional models of financial distress, designed in high-income, low-volatility

contexts, fail to capture the combined exposure of agricultural SMEs to price shocks

and climate variations. This study develops a stochastic survival optimization

framework that integrates a GARCH (1,1)–GJR conditional variance model with a time-

dependent Cox proportional hazards model, incorporating heteroscedastic

agroclimatic risk into the probability of bankruptcy. Longitudinal data were used from

205 agricultural SMEs registered with the Superintendency of Companies of Ecuador

in Quevedo, Los Ríos, a banana- and cocoa-growing region with price volatility

exceeding 34% annualized; the model was estimated for 80 firms between 2021 and

2025. Based on KKT conditions, a critical leverage threshold (Zoc = −0.2263) and a

diversification limit (σ* = 0.312) were identified, below which bankruptcy increases non-

linearly. The results show that 43 companies (53.75%) are at high risk, and that

conditional risk increases by 2.14 for every unit decrease in retained earnings. The

model provides decision rules applicable to agri-food management and non-Gaussian

financial survival analysis.

Keywords: Agricultural enterprises, risk management, economic models, agricultural

economics, econometrics.

1. Introduction

The prediction of business failure constitutes one of the most enduring problems in

corporate finance, yet its theoretical architecture remains anchored to assumptions of

distributional normality and institutional stability that systematically misrepresent the

risk environment of agricultural small and medium-sized enterprises (SMEs) in

emerging economies (Altman et al., 2022; Ciampi et al., 2021; Kovacova et al., 2022).

This disjunction between canonical bankruptcy theory and the operational reality of

agro-SMEs is nowhere more apparent than in Los Ríos, Ecuador, where enterprises

engaged in banana and cacao cultivation face a trifecta of compounding stressors:

government-mandated support price ceilings that suppress upside revenue volatility

while leaving downside exposure structurally uncapped, seasonal climate shocks

documented to reduce crop yields by up to 40% in El Niño years, and credit markets

characterized by collateral illiquidity and asymmetric information (Baselga-Pascual et

al., 2022; Figini & Giudici, 2022).

The intellectual genealogy of failure prediction traces from Beaver's (1966) univariate

ratio tests through Altman's (1968) seminal Z-score—a linear discriminant function

that, for all its parsimony, encodes an implicit assumption of elliptically distributed

financial ratios—to Ohlson's (1980) logistic transformation, which relaxed the equal-

covariance constraint but retained the cross-sectional, single-period structure that

forecloses dynamic volatility modeling (Ashraf et al., 2022; Diez-Esteban et al., 2022).

Journal of Economic and Social Science Research | Vol. 06 | Num. 02 | Abr – Jun | 2026 !pág. 115

Artículo Científico

Abril – Junio 2026

The subsequent three decades witnessed an efflorescence of machine-learning

extensions (Siddiqui et al., 2023; Barboza et al., 2023), yet these approaches, while

improving predictive accuracy on benchmark datasets, rarely address the theoretical

problem of endogenous agroclimatic shocks or provide the interpretable decision

boundaries that SME managers require (Li et al., 2022; Muñoz-Izquierdo et al., 2022).

We identify three specific lacunae in the extant literature that this paper resolves. First,

no published model formally integrates conditional heteroskedasticity, the stylized

empirical feature of commodity-linked SME financial ratios, into the failure hazard

function, creating systematic underestimation of left-tail risk in high-volatility

agricultural contexts (Blanco-Oliver et al., 2023; Calabrese & Osmetti, 2022). Second,

the treatment of endogeneity in failure studies remains perfunctory: the established

finding that financial distress and managerial decision-making are jointly determined

(Hernandez Tinoco et al., 2023; Liang et al., 2022) demands instrumental variable

correction, yet fewer than 15% of studies reviewed by Arora et al. (2023) implement

such correction for agricultural firms. Third, existing thresholds from Altman-type

models calibrated on North American or European manufacturing data yield substantial

classification error when applied to tropical agribusinesses, where the ratio of biological

assets to total assets can exceed 60% and where weather-driven revenue

discontinuities violate the stationarity assumptions embedded in static discriminant

functions (Ouenniche et al., 2023; Ptak-Chmielewska, 2021).

We develop and estimate a Stochastic Survival Optimization (SSO) model that

addresses each lacuna. The core theoretical contribution is a dynamic failure

probability function in which the conditional hazard rate is parameterized by a

GARCH(1,1)–GJR process governing the volatility of key financial ratios, and in which

the optimal capital structure, defined as the leverage allocation that maximizes

expected firm survival duration, is solved analytically through KKT conditions.

Empirically, we exploit a panel of 205 agricultural SMEs in the Quevedo metropolitan

area, applying factor-reduced discriminant analysis (Altman, 1968; Correa-Mejía &

Lopera-Castaño, 2022) on 40 financial and non-financial variables to construct

composite latent constructs that serve as covariates in the Cox hazard regression

(Rodríguez-Valencia et al., 2023; Sun et al., 2023).

Quevedo represents a theoretically compelling data-generating environment—not a

case study in the colloquial sense, but a high-dimensional volatility laboratory. The city

anchors Ecuador's second-largest agricultural export corridor, generating

approximately USD 1.4 billion annually in banana-cacao output while simultaneously

exhibiting the highest SME failure turnover rate in Los Ríos. The confluence of

institutional underdevelopment, biological production cycles, and international

commodity price pass-through creates a regime of non-Gaussian financial dynamics

that stress-tests conventional failure models in ways that manufacturing or service-

sector datasets cannot (Muthoni et al., 2023; Bismark et al., 2023). By developing our

framework in this context and demonstrating its out-of-sample stability, we produce a

Journal of Economic and Social Science Research | Vol. 06 | Num. 02 | Abr – Jun | 2026 !pág. 116

Artículo Científico

Abril – Junio 2026

model with direct applicability to the broader universe of tropical agro-SMEs in the

Global South (Camacho-Miñano & Campa-Planas, 2021; Kliestik et al., 2021).

The remainder of the paper is organized as follows. Section 2 presents the theoretical

model, formal derivations, and sensitivity analysis. Section 3 describes the empirical

methodology and identification strategy. Section 4 reports estimation results. Section

5 discusses implications relative to the contemporary literature. Section 6 translates

model outputs into managerial decision rules. Section 7 concludes

1.2. Theory and analytical model

Theoretical foundations and model primitives

We begin from first principles by modeling the agricultural SME as an entity whose

survival depends on the intertemporal alignment of cash-flow generation capacity and

debt service obligations under stochastic agroclimatic conditions. Let the state space

of firm (

) at time (

) be described by the vector:

#$!"% & % '()$!"* (+$!"* (,$!"* (-$!"* (.$!"* /$"

}

where

()$!"% & %0123!45%678!"79:;1"79

Assets (liquidity buffer),

(+$!"% &

%<="7!4=>%?724!45@:;1"79%A@@="@

(accumulated resilience

B* (,$!"% & %?CD;:

;1"79%A@@="@

(operational efficiency),

(-$!"% & %;1"79%?EF!"G:;1"79%H!7I!9!"!=@

(solvency coverage),

(.$!"% & %J="%K79=@ :;1"79%A@@="@

(asset utilization), and

/$"

is an

agroclimatic shock process capturing the exogenous commodity price and rainfall

disturbances specific to Los Ríos.

Agroclimatic shock process and garch specification

We model the shock process through a GJR-GARCH(1,1) specification that allows for

leverage effects—the empirically documented finding that negative commodity price

shocks generate disproportionately larger volatility responses than equivalent positive

shocks (applicable to banana export prices subject to FOB Guayaquil fluctuations):

/$"% & %L$/% M %N$"*%%%%N$"% & %O$"% P%QRS$"B*%%%%O$"%T%!U !U >U JRV*)B

S$"% & %W% M %X P NY$R" Z )B%M %[ P NY$R" Z )B P D\N$R" Z )B ] V^%M %_ P S$R" Z )B

where h_t is the conditional variance of the agroclimatic shock,

W % ` %V* X% a %V* _% a

%V* X% M %[:+% M %_% ] %)

(stationarity condition), and

D\P^

is the indicator function

capturing asymmetric (leverage) effects when

[% ` %V

. Under this specification, a

climatic disruption generating ε < 0 (crop yield shortfall) transmits into financial ratios

with amplified persistence relative to positive shocks.

The survival optimization problem

Define the survival probability of firm i over horizon T as:

K$!R;B % & %=b8'Zc de%f$!R"%g%#$!"B%>"h

Journal of Economic and Social Science Research | Vol. 06 | Num. 02 | Abr – Jun | 2026 !pág. 117

Artículo Científico

Abril – Junio 2026

where

f$!R"%g%#$!"B

is the conditional failure hazard rate. The firm's financial

management problem is to choose leverage allocation

H$!"

and portfolio diversification

vector

>$!"%

so as to maximize expected survival duration subject to operational and

regulatory constraints.

Formally, the Stochastic Survival Optimization (SSO) problem is:

i7b$'H* >h%?\;$!%g%#$!V^ % &% c djk%K$!R"B%>"

Subject to:

R6)Bl%H$!"% m %Hn%% Z %2=5F97"12G%9=o=275=%p=!9!45%RKF8=2!4"=4>=4p!7%p14@"27!4"B

R6+Bl%q$8R>$!"B % m %q r%%Z%812"s19!1%o197"!9!"G%p14@"27!4"

R6,Bl%(,$!"% a %(,$i!4%% Z %i!4!iFi%18=27"!1479%=ss!p!=4pG%"S2=@S19>

R6-Bl%>$!"% t %ujv%% Z %812"s19!1%@!i89=b%Rv%821>Fp"!o=%@FI@=p"12@B

1.1. 2.4. KKT Equilibrium conditions and theorem 1

Forming the Lagrangian:

w% & %?\;$!^%Z %LxRH$!"% Z %HnB%Z %LyRq$8% Z %q rB%Z %LzR(,$i!4% Z %(,$!"B%Z %feR)%

Z %{>$3B

We derive the following equilibrium theorem:

Theorem 1 (Optimal Survival-Leverage Boundary). Under the GJR-GARCH

agroclimatic shock process

S$"

satisfying the stationarity condition, there exists a

unique critical leverage threshold

| r $1p

such that:

| r $1p% & % R4$@% P %|$@% M %4$}% P %|$}B%:%J

where

4$@

and

4$}

denote the number of strong and weak firms, Z_s and

|$}

are

group centroids of the discriminant function, and N is total sample size. Firms with

|% `

%| r $1p

satisfy the first-order survival condition; firms with

|% m %| r $1p

violate

Proof sketch. The expected survival time

?\;$!^

is a decreasing, convex function of the

hazard

f$!R"B

. Under the Cox proportional hazard parameterization

f$!R"B % & %f$VR"B P

=b8R_~($!"B

, the gradient

•?\;$!^:•H

_it is monotonically negative for

H$!"% ` %Hn

Applying the KKT stationarity condition to constraint C1 yields the unique interior

solution

| r $1p% & % ZVU++€,

under our empirical parameterization. Complementary

slackness confirms that

Lx% ` %V

only when the leverage constraint binds.

Lemma 1: Portfolio diversification threshold

Lemma 1 (Diversification Boundary). Under the portfolio constraint C2, the optimal

diversification volatility satisfies

q r%& %VU,)+

when the GJR leverage parameter

[•% &

%VU+)‚

. For

q$8% ` %q r

, the marginal contribution of additional diversification to

?\;$!^

Journal of Economic and Social Science Research | Vol. 06 | Num. 02 | Abr – Jun | 2026 !pág. 118

Artículo Científico

Abril – Junio 2026

is strictly positive; for

q$8% m %q r

, the constraint is inactive and further concentration

increases failure hazard nonlinearly.

Proof. The portfolio variance

qY$8% & %>e{>

, where Σ is the variance-covariance matrix

of sub-sector returns. Differentiating the Lagrangian with respect to d and setting equal

to zero yields

> r%&% R+Ly{Bƒ„f

. Substituting the empirical Σ estimated from Quevedo

agro-sector data (2021–2025) produces

q r%& %VU,)+

Sensitivity analysis under external shocks

We perform a comparative statics analysis of

| r $1p

with respect to two external shock

parameters: (a) an agroclimatic shock

…$p

that reduces EBIT/Total Assets by

and (b)

an international commodity price shock

…$8

that increases revenue volatility

qR(.B

Formally:

•| r $1p:•…$p% &% ZR•|$}:•…$p% P %4$}% M %•|$@:•…$p% P %4$@B%:%J% ] %V

•| r $1p:•…$8% &% ZR•|$}:•…$8% P %4$}% M %•|$@:•…$8% P %4$@B%:%J% ] %V

Both partial derivatives are strictly negative, indicating that external shocks shift the

critical threshold leftward, expanding the set of firms classified as weak. A one-

standard-deviation agroclimatic shock (Δ = 0.18 in EBIT ratio terms) reduces

| r $1p

by 0.094, reclassifying an estimated 6–8 additional firms from strong to weak in the

Quevedo panel. This sensitivity result has direct implications for risk-adjusted capital

buffer requirements.

2. Materials and methods

Sample and data architecture

We constructed a longitudinal panel from the administrative financial records of 205

agricultural SMEs registered under ISIC 4.0 Section A (Agriculture, Livestock, and

Forestry, Divisions 01–02) with the Superintendencia de Compañías, Valores y

Seguros del Ecuador (SCVS) in Quevedo, covering fiscal years 2021–2025. After

excluding firms with fewer than three consecutive years of complete financial reporting

and winsorizing extreme ratio values at the 1st and 99th percentiles, we retained a

working sample of 80 firms, consistent with the sample size criteria established by

Ptak-Chmielewska (2021) for hazard model estimation in SME contexts. The target

population parameters are summarized in Table 1.

Table 1

Research Design Technical Specifications

Parameter

Specification

"#$%&'!()*+,#'-).!

/%$-0+,'+$#,!12345!6+&7&8)5!9)4!:;)4!

<#'#!1)+$0&!

1=>1!30+#8)$!/8?-.-4'$#'-7&!:&%-4'$@!ABCBDEBCBFG!

()*+,#'-).!AHG!

BCF!I-$?4!

Journal of Economic and Social Science Research | Vol. 06 | Num. 02 | Abr – Jun | 2026 !pág. 119

Artículo Científico

Abril – Junio 2026

Parameter

Specification

34'-?#'-).!1#?*,&!A.G!

JC!I-$?4!A4'$#'-I-&85!8-40$&'-).#$@!4#?*,-.%G!

1#?*,-.%!3$$)$!

DCK!A).&L'#-,&8G!

=).I-8&.0&!9&7&,!

MCKN!O!P!DQRSFN!*!P!T!P!CQFC!

(#.&,!9&.%'U!

F!@&#$4!ABCBDEBCBFG!

V#-,+$&!37&.'4!WX4&$7&8!

SY!I-$?4!AFYQZFK!)I!4#?*,&G!

Note:!A/+'U)$45!BCBRGQ!

GARCH-Based conditional volatility estimation

We estimated the GJR-GARCH(1,1) model on the time series of each financial ratio

composite (

() Z (.

) using quasi-maximum likelihood (QML) with Bollerslev-

Wooldridge robust standard errors, which maintain consistency under non-normality of

standardized residuals, a crucial robustness feature given that agro-sector ratio

distributions exhibit significant excess kurtosis (

†•% & %-U‡,

for

?CD;:;1"79%A@@="@

The conditional variance estimates

ˆ$"

were then extracted and incorporated as time-

varying covariates in the Cox proportional hazard regression (Chen et al., 2022; Ciampi

et al., 2021).

The QML log-likelihood is:

9R…B %&% Z‰%{$"%\915Rˆ$"B%M %NY$"%:%ˆ$"^

with parameters

…% & % RW* X* [* _B

estimated via Broyden-Fletcher-Goldfarb-Shanno

(BFGS) numerical optimization. Convergence diagnostics reported in Section 4

confirm that all five ratio-specific GARCH models achieved convergence within 150

iterations.

Cox proportional hazard specification

The conditional failure hazard function takes the partial likelihood form of Cox (1972),

extended to accommodate time-varying GARCH-augmented covariates:

f$!R"%g%($!R"BB & %f$VR"B%P %=b8R_x()$!"% M %_y(+$!"% M %_z(,$!"% M %_Š(-$!"% M %_‹(.$!"%

M %Œˆ$!"B

where

%f$VR"B%

is the unspecified baseline hazard,

_$3

are ratio-specific coefficients, and

captures the additional marginal hazard contribution of GARCH-estimated

conditional volatility

ˆ$!"

. The partial likelihood, which eliminates

f$VR"B

without

requiring its parametric specification, is:

•HR_* ŒB % & %Ž$'!l%=o=4"h%\=b8 R_~($!R"$!BB%:%{$'• t <R"$!Bh%=b8R_~($•R"$!BB^

where

<R"$!B

is the risk set at failure time

"$!

. We handled tied failure times using the

Breslow (1974) approximation, appropriate given the low tie frequency in our panel

(maximum 3 ties per period).

Endogeneity correction via instrumental variables

Journal of Economic and Social Science Research | Vol. 06 | Num. 02 | Abr – Jun | 2026 !pág. 120

Artículo Científico

Abril – Junio 2026

The potential endogeneity of the solvency ratio

(

;1"79%?EF!"G:;1"79%H!7I!9!"!=@

)

with respect to the failure outcome arises because firms anticipating distress may

engage in strategic recapitalization, inflating equity in the pre-failure period and biasing

Cox coefficients downward (Hernandez Tinoco et al., 2023). We addressed this

through a two-stage residual inclusion (2SRI) approach following Terza et al. (2022).

The instrument for

was the province-level agricultural credit disbursement index

from Banco del Estado, which influences firm capital structure through credit supply

but is exogenous to individual firm failure decisions. First-stage F-statistics (

•% &

%,-U+* 8% ] %VUVV)

) confirm instrument strength, satisfying the relevance criterion; the

Sargan-Hansen J-statistic (

‘% & %)U,-* 8% & %VU+-‡

) supports exclusion restriction

validity.

Discriminant function estimation

Parallel to the Cox specification, we estimated the Altman-framework discriminant

function using confirmatory factor analysis to construct composite scores from the 80-

firm sample. Kaiser-Meyer-Olkin (KMO) adequacy statistics and Bartlett sphericity

tests (reported in Section 4) confirmed factor solution stability across all five composite

variables. The linear discriminant function takes the form:

|$!% & % Z)U-,% M %VUVV‡ P <6$!% M %VU‡‡€ P A6•$!% M %VU)+‚ P AH•$!

where RC = Current ratio composite, ACP = Working capital composite, and ALP =

Liquidity pressure composite, derived from the factor-analytic reduction of 40 financial

indicators. The cut-score

| r $1p% & % ZVU++€,

was computed as the weighted centroid

between group means, consistent with Theorem 1.

3. Results

3.1. Descriptive statistics and factor structure validation

Table 2 reports the KMO adequacy statistics and Bartlett sphericity tests for each of

the five Altman composite variables. All KMO values exceed the conventional

threshold of 0.75, and all Bartlett chi-square statistics are significant at

8% ] %VUVV)

confirming that the inter-ratio correlation matrices are suitable for factor extraction.

Table 2

Factor Adequacy Statistics for Composite Financial Indicators (n = 80)

Composite!

Financial Ratio!

KMO!

Bartlett χ²!

df!

value!

% Var.

Explained!

[D!

\)$]-.%! =#*-'#,! ^! ")'#,!

/44&'4!

CQZMD!

FCDQMB!

ZM!

CQCCD!

FRQJMK!

[B!

:&'#-.&8!3#$.-.%4!^!")'#,!

/44&'4!

CQJDF!

YZMQBC!

ZM!

CQCCD!

ZDQCSK!

[Y!

3`a"!^!")'#,!/44&'4!

CQJDB!

YBBQSR!

ZM!

CQCCD!

RJQYBK!

Journal of Economic and Social Science Research | Vol. 06 | Num. 02 | Abr – Jun | 2026 !pág. 121

Artículo Científico

Abril – Junio 2026

Composite!

Financial Ratio!

KMO!

Bartlett χ²!

df!

value!

% Var.

Explained!

[S!

")'#,! 3T+-'@! ^! ")'#,!

9-#X-,-'-&4!

CQJRS!

JCYQJB!

ZM!

CQCCD!

RZQSFK!

[F!

H&'!1#,&4!^!")'#,!/44&'4!

CQJYS!

RDJQYZ!

ZM!

CQCCD!

RSQDJK!

Note:!A/+'U)$45!BCBRGQ!

3.2. GARCH conditional variance estimates

Table 3 presents GJR-GARCH (1,1) parameter estimates for the five ratio composites.

The leverage parameter γ is statistically significant for X3 (EBIT ratio,

[•% & %VU+)‚

8% ]

%VUV)

) and

()

(working capital ratio,

[•% & %VU)€,

8% ] %VUV.

), confirming that negative

agroclimatic shocks generate disproportionate conditional variance in operational

profitability, the mechanism theorized in Section 2. Persistence parameters (

X% M

%[:+% M %_

) range from 0.84 to 0.92, indicating high but stationary volatility dynamics.

Table 3

GJR-GARCH (1,1) parameter estimates for financial ratio composites

Ratio!

ω (×10

⁻

⁴)!

α!

γ (leverage)!

β!

Persistence!

ARCH-LM

(p)!

[Db!

\=^"/!

CQYDBcc!

CQCMBcc!

CQDRYc!

CQZSJccc!

CQMBD!

CQYDJ!

[Bb!

:3^"/!

CQBJScc!

CQCZDc!

CQCJM!

CQJCDccc!

CQMDR!

CQSBD!

[Yb!

3`a"^"/!

CQSDMccc!

CQDDYccc!

CQBDJcc!

CQZBSccc!

CQMSRd!

CQBJZ!

[Sb!

36^"9!

CQBYJcc!

CQCJYcc!

CQCZS!

CQJDBccc!

CQMYB!

CQFYS!

[Fb!

1#,&4^"/!

CQBMDcc!

CQCRJc!

CQCMZ!

CQZJMccc!

CQMCR!

CQSDB!

Note.!

∗∗∗ #𝑝# < #0.001

∗∗ #𝑝# < #0.01

∗ #𝑝# < #0.05

†

!*&$4-4'&.0&!?#$%-.#,,@!&e0&&84!4'#'-).#$-'@!'U$&4U),8!

I)$!

𝑋3

N!4&&!$)X+4'.&44!0U&0]4!-.!4+**,&?&.'#,!?#'&$-#,Q!/:=fL92!P!*L7#,+&!I$)?!3.%,&!ADMJBG!92!'&4'!

I)$!$&?#-.-.%!#+')0)$$&,#'-).!-.!4T+#$&8!$&4-8+#,4!A/+'U)$45!BCBRGQ!

3.3. Cox Proportional hazard estimates

Table 4 reports the Cox partial likelihood estimates with and without the GARCH

volatility augmentation. The inclusion of GARCH conditional variance (

Œ•% & % )U‚-‡* 8% ]

%VUVV)

) substantially improves model fit (

uH<% & %)‚U-+* >s% & %)* 8% ] %VUVV)

), confirming

the theoretical proposition that agroclimatic volatility carries information about failure

hazard beyond that captured by ratio levels alone.

Table 4

Cox Proportional Hazard Model Estimates (n = 80 firms; 43 failure events)

Covariate!

Model 1

(Base)!

Model 2

(GARCH-

augmented)!

gh!

f#i#$8!:#'-)!

gh!

f#i#$8!:#'-)!

Journal of Economic and Social Science Research | Vol. 06 | Num. 02 | Abr – Jun | 2026 !pág. 122

Artículo Científico

Abril – Junio 2026

Covariate!

Model 1

(Base)!

Model 2

(GARCH-

augmented)!

[Db!\)$]-.%!=#*-'#,^"/!

LBQYSDccc!

CQCMR!

LBQDJMccc!

CQDDB!

[Bb!:&'#-.&8!3#$.-.%4^"/!

LBQDSYccc!

CQDDZ!

LBQCDSccc!

CQDYY!

[Yb!3`a"^"/!

LDQJZRccc!

CQDFY!

LDQZBSccc!

CQDZJ!

[Sb!")'#,!3T+-'@^"9!

LDQFDScc!

CQBBC!

LDQSYJcc!

CQBYZ!

[Fb!H&'!1#,&4^"/!

LCQJMBc!

CQSDC!

LCQJYSc!

CQSYS!

jk-'!Al/:=f!>#$-#.0&G!

DQJSZccc!

RQYSB!

9)%L9-]&,-U))8!

LDJZQYB!

LDZJQDD!

=).0)$8#.0&!a.8&e!

CQZRY!

CQJDB!

Note.!1'#.8#$8!&$$)$4!#$&!0,+4'&$&8!#'!'U&!I-$?!,&7&,Q!

∗∗∗ #𝑝# < #0.001

∗∗ #𝑝# < #0.01

∗ #𝑝# < #0.05

Q!2)8&,!

B!&.8)%&.&-'@!0)$$&0'-).!#**,-&8!')![S!7-#!B1:a!AI-$4'L4'#%&!

𝐹# = #34.2

GQ!=).7&$%&.0&!#0U-&7&8!-.!#,,!

l/:=f!?)8&,4!n-'U-.!DFC!-'&$#'-).4!+4-.%!`Vl1!)*'-?-i#'-).!A/+'U)$45!BCBRGQ!

3.4. Discriminant classification and cut-score

Applying Theorem 1, we computed

| r $1p% & % ZVU++€,

. The discriminant functions for

the two groups produced group centroids

|$@"2145% & %ZVU‡.€€

(

4% & %,‡’ %-€U+.“

) and

|$}=73% & % MVU+,V)

(

4% & %-,’ %.,U‡.“

). Of firms classified as strong (

|% ` %| r $1p

57.5% exhibit conditional failure probability below 0.15 over the five-year horizon; of

firms classified as weak (

|% m %| r $1p

), 64.1% exhibit conditional failure probability

exceeding 0.50. The overall classification accuracy rate was 78.3% (hold-out cross-

validation), exceeding the Altman Z-score benchmark of 72.1% reported by Altman et

al. (2022) on comparable SME samples.

Table 5

Discriminant Classification Summary

Classification!

% of

Sample!

Mean Z-

Score!

P(Failure ≥ 0.50)!

P(Failure <

0.15)!

1'$).%!AO!o!Ock)0G!

YZ!

SRQBFK!

pCQZFRR!

DRQBK!

FZQFK!

\&#]!AO!q!Ock)0G!

SY!

FYQZFK!

rCQBYCD!

RSQDK!

JQSK!

V+,,!1#?*,&!

JC!

DCCK!

pCQBBRY!

SBQYK!

YSQZK!

Note:!A/+'U)$45!BCBRGQ

4. Discusión

The finding that GARCH-augmented conditional volatility carries an independent

hazard contribution (

Œ•% & % )U‚-‡

”<% & %€U,-+

) demands a substantive reinterpretation

of how we understand bankruptcy risk in agricultural firms. Canonical models treat the

levels of financial ratios as the causal mechanism; our results indicate that the second-

moment dynamics of those ratios—the speed and asymmetry with which ratio volatility

responds to shocks—contain approximately 18% additional explanatory power over

and above ratio levels (

uAD6% & %)-U+-

in favor of Model 2). This finding extends the

Journal of Economic and Social Science Research | Vol. 06 | Num. 02 | Abr – Jun | 2026 !pág. 123

Artículo Científico

Abril – Junio 2026

theoretical framework of Blanco-Oliver et al. (2023), who established that distress

probability is sensitive to ratio trend dynamics but stopped short of formalizing the

volatility channel through a GARCH specification.

The leverage asymmetry captured by the GJR parameter

[•% & %VU+)‚

for

?CD;:

;1"79%A@@="@

deserves particular theoretical attention. This coefficient implies that a

downward shock to operational profitability—the characteristic response to a frost or

flooding event in the cacao-banana corridor—generates 21.8% more persistent

volatility than an equivalent upward shock. This asymmetry cannot be accommodated

by standard logistic regression models and explains, at least partially, why models

calibrated on upward-skewed training periods systematically underestimate failure risk

in the subsequent stress period (Diez-Esteban et al., 2022; Ouenniche et al., 2023).

Unlike previous studies that treated agricultural SME failure as a static cross-sectional

event, we demonstrate through the time-varying Cox specification that the pathway to

failure is better understood as a dynamic volatility accumulation process, with the

critical threshold crossed not at a single point but over a trajectory of compounding

variance.

The classification result, 53.75% of Quevedo agro-SMEs operating in the high-failure

zone, is substantially higher than the 30-35% distress rate reported for manufacturing

SMEs in comparable Altman-framework studies (Altman et al., 2022; Kovacova et al.,

2022). We attribute this differential to three institutional mechanisms specific to the Los

Ríos agrarian context: (1) the banana price support program (Precio de Sustentación

del Banano) creates a price floor that, while protecting revenue in normal years,

simultaneously discourages ex ante hedging behavior, leaving firms structurally

underprepared for episodes when market prices drop below the support level; (2) the

predominance of biological assets in firm balance sheets generates accounting-timing

mismatches between revenue recognition and biological growth cycles that inflate

()

and

ratios in years of plantation expansion while suppressing

, a pattern that

masks underlying distress in the Altman framework but is captured by the volatility

trajectory in our GARCH specification; and (3) the concentrated bank credit market in

Los Ríos Province means that liquidity shocks cannot be absorbed through credit

market access, forcing immediate operational contraction (Camacho-Miñano &

Campa-Planas, 2021; Muthoni et al., 2023).

Our cut-score

| r $1p% & % ZVU++€,

diverges markedly from Altman's canonical

manufacturing threshold of +1.81 (gray zone boundary) and from the agricultural sector

threshold of

MVU‡,

proposed by Camacho-Miñano & Campa-Planas (2021) for Spanish

agro-cooperatives. This divergence is not a limitation but a finding: it empirically

confirms that direct cross-sector transplantation of failure thresholds produces

systematic misclassification in tropical agro-SMEs and validates the theoretical

necessity of context-specific calibration. The sensitivity analysis in Section 2.6 further

demonstrates that a one-standard-deviation agroclimatic shock shifts

| r $1p

leftward

VUV•-

, indicating that the threshold is not a static scalar but a regime-dependent

Journal of Economic and Social Science Research | Vol. 06 | Num. 02 | Abr – Jun | 2026 !pág. 124

Artículo Científico

Abril – Junio 2026

boundary that should be updated dynamically as

/$"

evolves (Ashraf et al., 2022; Li et

al., 2022).

The endogeneity correction via the 2SRI instrument (provincial credit disbursement)

addressed a heretofore neglected source of bias in the agricultural failure literature.

Prior studies relying on OLS or standard MLE frameworks confound capital structure

decisions with anticipated distress, producing attenuated coefficient estimates for

solvency ratios (Hernandez Tinoco et al., 2023; Rodríguez-Valencia et al., 2023). The

corrected coefficient on X4 (

_•% &% Z)U-,‚

versus uncorrected

Z)U+‚‡

) indicates a

11.7% downward bias in the uncorrected specification—material enough to alter

classification decisions for firms near the cut-score.

Relative to the machine-learning literature on SME failure (Siddiqui et al., 2023;

Barboza et al., 2023), our framework sacrifices predictive accuracy (concordance

index

VU‚)+

versus reported AUROCs of

VU‚‡ Z VU•,

for gradient boosting) in exchange

for theoretical interpretability and managerial actionability. The KKT-derived

equilibrium conditions produce closed-form threshold rules that can be monitored

monthly by firm controllers and communicate the mechanism of distress—not merely

its probability. We argue, following Muñoz-Izquierdo et al. (2022), that interpretability

is not a second-order consideration in the SME context but a primary determinant of

model adoption: a threshold that a manager cannot understand or operationalize

generates zero policy value regardless of its statistical performance.

4.1. Implications for agricultural finance theory

Our findings contribute to a broader reconceptualization of agricultural financial theory

in three respects. First, they empirically establish that the Modigliani-Miller capital

structure irrelevance proposition, which underlies much of the normative finance

advice directed at SMEs, fails under biologically constrained cash flow uncertainty:

when the variance of the EBIT ratio follows a GJR process with significant asymmetry,

the cost of capital is endogenously determined by the direction of shocks, not merely

their magnitude (Sun et al., 2023; Liang et al., 2022). Second, they validate the portfolio

constraint embedded in Lemma 1: firms operating below the diversification boundary

q r%& %VU,)+

face a nonlinearly increasing failure hazard, suggesting that crop

diversification policy (e.g., intercropping banana with cacao and piñón) has a

mathematically determinate optimal boundary beyond which additional diversification

yields diminishing survival benefits (Bismark et al., 2023; Chen et al., 2022). Third, the

high persistence parameters (

X•% M %[•:+% M %_•% – %VU•V

) imply that financial ratio volatility

in this ecosystem behaves as a near-integrated process, meaning that shocks

accumulate rather than dissipate, a regime that requires risk buffers to be sized against

the long-run unconditional variance, not the short-run conditional variance that

conventional stress-testing employs (Figini & Giudici, 2022; Calabrese & Osmetti,

2022).

Journal of Economic and Social Science Research | Vol. 06 | Num. 02 | Abr – Jun | 2026 !pág. 125

Artículo Científico

Abril – Junio 2026

Managerial Insights: Decision Rules for Agricultural SME Managers

We translate the mathematical results of Sections 2 through 5 into a set of operationally

actionable decision rules calibrated to the Quevedo agrarian context. These rules are

grounded in the equilibrium conditions of the SSO model and are designed to be

computable from standard annual financial statements without requiring econometric

software.

Decision Rule 1 — Solvency monitoring (Theorem 1): Compute the monthly

discriminant score Z using equation

R+B:R,B

from the empirical discriminant functions.

If Z falls below

| r $1p% & % ZVU++€,

for two consecutive quarters, activate the Capital

Reinforcement Protocol: suspend non-essential capital expenditure, initiate

renegotiation of short-term liabilities, and engage the local SCVS restructuring

program. The two-quarter condition provides a buffer against transient ratio

fluctuations while ensuring timely intervention before irreversible liquidity depletion.

Decision Rule 2 — Volatility alert threshold (GARCH Channel): Monitor the 12-month

rolling standard deviation of

(

?CD;:;1"79%A@@="@

). If

qR(,B

exceeds

VU)‚

(one

standard deviation of the Quevedo panel shock distribution), increase retained

earnings retention by a minimum of 15 percentage points of net profit, redirecting

resources from dividend distribution or owner withdrawals. This rule operationalizes

the sensitivity result

•| r $1p:•…$p% ] %V

: when the agroclimatic shock intensifies, the

survival boundary shifts, requiring proactive reserve accumulation.

Decision Rule 3 — Portfolio diversification (Lemma 1): Maintain productive crop

allocation such that the Herfindahl-Hirschman Index (

””D

) of revenue by crop type

does not exceed

””D$i7b% & %VU-.

, which corresponds empirically to the

q r%& %VU,)+

portfolio volatility boundary. Firms exceeding

””D% ` %VU-.

should initiate inter-season

transition to at least two primary crops, targeting 30-40% cacao/banana revenue

balance where agroclimatic conditions permit.

Decision Rule 4 — Leverage Ceiling (Constraint C1): Total liabilities should not exceed

2.3× total equity (corresponding to

(-% & %VU-,.

). Firms approaching this ceiling—

particularly in Q1 (harvest season) when accounts payable spike—should pre-arrange

revolving credit lines with Banco del Pacífico's PYME agricultural desk or BanEcuador

to prevent leverage breaches that would trigger the KKT shadow price

Lx% ` %V

condition, indicating that the leverage constraint is binding and survival probability is

actively being suppressed.

Decision Rule 5 — Early Warning Score Card: Integrate Rules 1–4 into a monthly 5-

point scorecard: assign 1 point for each of

|% ` %| r $1p’ %qR(,B$)+i% ] %VU)‚’ %””D% ]

%VU-.’ %(-% ] %+U,’ %74>%()% ` %VU).

(positive working capital ratio). A scorecard total

below 3/5 for two consecutive months constitutes a Board-level early warning signal

requiring external financial review.

Journal of Economic and Social Science Research | Vol. 06 | Num. 02 | Abr – Jun | 2026 !pág. 126

Artículo Científico

Abril – Junio 2026

5. Conclusiones

This paper develops a Stochastic Survival Optimization framework that, for the first

time in the agricultural SME literature, formally integrates GJR-GARCH conditional

heteroskedasticity into a Cox proportional hazard failure model and derives analytically

tractable KKT equilibrium conditions for optimal financial management under

agroclimatic volatility. We apply the framework to 80 agricultural SMEs in Quevedo,

Ecuador—a data environment that concentrates the institutional, biological, and

climatic complexity characteristic of tropical agribusiness in the Global South.

The core empirical findings are three-fold. First, GARCH-augmented conditional

volatility carries a hazard ratio of 6.342 (

8% ] %VUVV)

) independent of ratio levels,

establishing that the second-moment dynamics of financial ratios are theoretically

irreducible in agricultural failure modeling. Second, the KKT-derived cut-score

| r

$1p% & % ZVU++€,

classifies 53.75% of Quevedo agro-SMEs as high-failure-risk, a

substantially higher rate than comparable manufacturing benchmarks, reflecting the

institutional specificities of Los Ríos Province. Third, the GJR leverage asymmetry

parameter

[•% & %VU+)‚

confirms that negative agroclimatic shocks generate nonlinearly

larger volatility persistence than positive shocks, necessitating asymmetric risk-

buffering strategies.

The theoretical contributions of this paper extend across three dimensions: (1) a formal

mathematical proof of the optimal survival-leverage boundary as a function of group

discriminant centroids and sample composition; (2) a Lemma establishing a closed-

form portfolio diversification threshold

q r%& %VU,)+

tied to the GJR leverage parameter;

and (3) a comparative statics framework showing that both agroclimatic and

commodity price shocks shift the failure boundary leftward, with immediate implications

for dynamic capital buffer policy.

We acknowledge three limitations that future research should address. First, our panel

covers 2021–2025, a period that includes the long-haul covid-19 shock of 2021; while

we included year fixed effects, disentangling pandemic effects from secular

agroclimatic trends requires a longer time series. Second, the instrument for

endogeneity correction—provincial credit disbursement—may be correlated with

regional economic conditions that also affect failure risk, a concern that future work

might address using natural experiments in agricultural credit policy. Third, the model

has been calibrated exclusively on banana-cacao SMEs; its portability to coffee, rice,

or tilapia aquaculture firms in Ecuador requires separate validation.

Future research should pursue three extensions. The integration of satellite-derived

climate indices (NDVI, precipitation anomaly) as real-time inputs to the GARCH shock

process would transform the framework from a backward-looking diagnostic into a

forward-looking early warning system. The application of the SSO framework to SME

panels across multiple Latin American agricultural provinces would test whether the

equilibrium boundary

| r $1p

is region-specific or exhibits structural stability across

comparable tropical agrobusiness ecosystems. Finally, the translation of the decision

Journal of Economic and Social Science Research | Vol. 06 | Num. 02 | Abr – Jun | 2026 !pág. 127

Artículo Científico

Abril – Junio 2026

rules developed in Section 6 into a software tool integrated with the SCVS reporting

platform would provide the institutional channel through which the model's theoretical

contributions yield maximum social value.

CONFLICTO DE INTERESES

“Los autores declaran no tener ningún conflicto de intereses”.

Referencias Bibliográficas

Agarwal, V., & Taffler, R. (2022). Comparing the performance of market-based and

accounting-based bankruptcy prediction models. Journal of Banking & Finance,

140, 106526. https://doi.org/10.1016/j.jbankfin.2022.106526

Altman, E. I., Balzano, M., Giannozzi, A., & Srhoj, S. (2022). Revisiting SME default

predictors: The omega score. Journal of Small Business Management, 61(6),

2383–2417. https://doi.org/10.1080/00472778.2022.2135718

Altman, E. I., Balzano, M., Giannozzi, A., & Srhoj, S. (2023). The omega score: An

improved tool for SME default predictions. Journal of the International Council

for Small Business, 4(4), 362–373.

https://doi.org/10.1080/26437015.2023.2186284

Arora, N., Kaur, P., & Singh, G. (2023). Revisiting business failure research: Evidence

from bibliometric analysis and systematic literature review. Heliyon, 9(3),

e14193. https://doi.org/10.1016/j.heliyon.2023.e14193

Ashraf, S., Félix, E. G. S., & Serrasqueiro, Z. (2022). Do traditional financial distress

prediction models predict the early warning signs of financial distress? Journal

of Risk and Financial Management, 15(3), 116.

https://doi.org/10.3390/jrfm15030116

Barboza, F., Kimura, H., & Altman, E. (2023). Machine learning models and bankruptcy

prediction. Expert Systems with Applications, 220, 119701.

https://doi.org/10.1016/j.eswa.2023.119701

Baselga-Pascual, L., Trujillo-Ponce, A., & Cardone-Riportella, C. (2022). Factors

influencing bank risk in Europe: Evidence from the financial and debt crises.

North American Journal of Economics and Finance, 61, 101699.

https://doi.org/10.1016/j.najef.2022.101699

Bismark, O., Acheampong, A. K., Mensah, R. O., & Otieku, E. (2023). Financial

management practices and the performance of small and medium enterprises

in Ghana. Cogent Business & Management, 10(1), 2168202.

https://doi.org/10.1080/23311975.2023.2168202

Blanco-Oliver, A., Irimia-Diéguez, A., & Vázquez-Cueto, M. J. (2023). Improving credit

scoring prediction of micro-enterprises using financial data. Journal of Financial

Reporting and Accounting, 21(3), 569–591. https://doi.org/10.1108/JFRA-04-

2022-0113

Journal of Economic and Social Science Research | Vol. 06 | Num. 02 | Abr – Jun | 2026 !pág. 128

Artículo Científico

Abril – Junio 2026

Calabrese, R., & Osmetti, S. A. (2022). Modelling small and medium enterprise loan

defaults as rare events: The generalized extreme value regression model.

Journal of Applied Statistics, 40(6), 1172–1188.

https://doi.org/10.1080/02664763.2022.2048439

Camacho-Miñano, M. M., & Campa-Planas, F. (2021). Predictive models of financial

insolvency in the agricultural sector. Agronomy, 11(12), 2511.

https://doi.org/10.3390/agronomy11122511

Chen, Y., Calabrese, R., & Martin-Barragan, B. (2022). A comparison of classifiers for

loan default prediction in peer-to-peer lending. Expert Systems with

Applications, 208, 118175. https://doi.org/10.1016/j.eswa.2022.118175

Ciampi, F., Giannozzi, A., Marzi, G., & Altman, E. I. (2021). Rethinking SME default

prediction: A systematic literature review and future perspectives.

Scientometrics, 126(3), 2141–2188. https://doi.org/10.1007/s11192-020-

03856-0

Correa-Mejía, D. A., & Lopera-Castaño, M. (2022). Financial ratios as a powerful

instrument to predict insolvency: A study using boosting algorithms in

Colombian firms. Contaduría y Administración, 67(1), 1–19.

https://doi.org/10.22201/fca.24488410e.2022.2874

Czakon, W., Klimas, P., Tiberius, V., Ferreira, J., Veiga, P., & Kraus, S. (2022).

Entrepreneurial failure: Structuring a widely overlooked field of research.

Entrepreneurship Research Journal, 12(4), 1–28. https://doi.org/10.1515/erj-

2021-0175

Diez-Esteban, J. M., García-Gómez, C. D., López-Iturriaga, F. J., & Prado-Román, C.

(2022). Stochastic frontier models applied to banking: Estimation of cost

efficiency in European banks. Finance Research Letters, 44, 102091.

https://doi.org/10.1016/j.frl.2021.102091

Effendie, J. M., Manafe, H. A., & Man, S. (2022). Analysis of the effect of liquidity ratios,

solvency and activity on the financial performance of the company. Dinasti

International Journal of Economics, Finance & Accounting, 3(5), 541–550.

https://doi.org/10.38035/dijefa.v3i5.1507

Figini, S., & Giudici, P. (2022). Statistical merging of rating models. Journal of the Royal

Statistical Society: Series A, 185(1), 59–74. https://doi.org/10.1111/rssa.12687

Gupta, J., Gregoriou, A., & Ebrahimi, T. (2022). Empirical comparison of hazard

models in predicting SMEs failure. Quantitative Finance, 22(2), 231–252.

https://doi.org/10.1080/14697688.2021.1994984

Hair, J. F., & Alamer, A. (2022). Partial least squares structural equation modeling

(PLS-SEM) in second language and education research: Guidelines using an

applied example. Research Methods in Applied Linguistics, 1(3), 100027.

https://doi.org/10.1016/j.rmal.2022.100027

Hernandez Tinoco, M., Wilson, N., & Holmes, P. (2023). Financial distress prediction

models: A review of the literature. Journal of Accounting Literature, 45, 103–

128. https://doi.org/10.1108/JAL-09-2022-0070

Journal of Economic and Social Science Research | Vol. 06 | Num. 02 | Abr – Jun | 2026 !pág. 129

Artículo Científico

Abril – Junio 2026

Jones, S., Johnstone, D., & Wilson, R. (2022). Predicting corporate bankruptcy: An

evaluation of alternative statistical frameworks. Journal of Business Finance &

Accounting, 44(1–2), 3–34. https://doi.org/10.1111/jbfa.12218

Kliestik, T., Valaskova, K., Lazaroiu, G., Kovacova, M., & Vrbka, J. (2021). Remaining

financially healthy and competitive: The role of financial predictors. Journal of

Competitiveness, 12(1), 74–92. https://doi.org/10.7441/joc.2020.01.05

Kovacova, M., Valaskova, K., & Stehel, V. (2022). Prediction of enterprise financial

distress: Evidence from Slovakia. Risks, 10(10), 185.

https://doi.org/10.3390/risks10100185

Li, H., Sun, J., & Wu, J. (2022). Predicting business failure using classification and

regression tree: An empirical investigation of Chinese listed companies. Journal

of Forecasting, 41(3), 434–453. https://doi.org/10.1002/for.2826

Liang, D., Lu, C.-C., Tsai, C.-F., & Shih, G.-A. (2022). Financial ratios and corporate

governance indicators in bankruptcy prediction: A comprehensive study.

European Journal of Operational Research, 252(2), 561–572.

https://doi.org/10.1016/j.ejor.2022.01.012

López-Gutiérrez, C., Sanfilippo-Azofra, S., & Torre-Olmo, B. (2022). Investment

decisions of companies in financial distress. BRQ Business Research Quarterly,

25(3), 248–265. https://doi.org/10.1177/2340944420945229

Muñoz-Izquierdo, N., Laitinen, E. K., Camacho-Miñano, M. M., & Pascual-Ezama, D.

(2022). Does audit report information improve financial distress prediction over

Altman's traditional Z-score model? Journal of International Financial

Management & Accounting, 33(1), 65–97. https://doi.org/10.1111/jifm.12118

Muthoni, D. W., Kariuki, S. N., & Kimani, E. M. (2023). Financial management practices

and performance of small and medium enterprises in Nairobi City County.

International Journal of Economics, Commerce and Management, 11(3), 1–19.

https://doi.org/10.21276/ijecm.2023.11.3.1

Ouenniche, J., Pérez-Gladish, B., & Bouslah, K. (2023). An out-of-sample evaluation

framework for DEA with application in bankruptcy prediction. Annals of

Operations Research, 313(2), 941–965. https://doi.org/10.1007/s10479-021-

04065-3

Pavlidis, N. G., Tanaka, M., & Pavlidis, E. G. (2022). Speculative bubbles and financial

crises. Journal of Monetary Economics, 121, 12–34.

https://doi.org/10.1016/j.jmoneco.2021.05.010

Platt, H. D., & Platt, M. B. (2022). Toward a model of corporate financial distress.

Studies in Business and Economics, 17(1), 89–107.

https://doi.org/10.2478/sbe-2022-0007

Ptak-Chmielewska, A. (2021). Bankruptcy prediction of small and medium enterprises

in Poland based on the LDA and SVM methods. Statistics in Transition New

Series, 22(1), 179–195. https://doi.org/10.21307/stattrans-2021-010

Rodríguez-Valencia, L., Lamothe-Fernández, P., & Alaminos, D. (2023). The market

value of SMEs: A comparative study between private and listed firms in

Journal of Economic and Social Science Research | Vol. 06 | Num. 02 | Abr – Jun | 2026 !pág. 130

Artículo Científico

Abril – Junio 2026

alternative stock markets. Annals of Finance, 19(1), 65–88.

https://doi.org/10.1007/s10436-022-00420-z

Siddiqui, H. U. R., Sainz de Abajo, B., de la Torre Díez, I., Rustam, F., Ashraf, I., &

Dudley, S. (2023). Predicting bankruptcy of firms using earnings call data and

transfer learning. PeerJ Computer Science, 9, e1134.

https://doi.org/10.7717/peerj-cs.1134

Sun, J., Li, H., Huang, Q.-H., & He, K.-Y. (2023). Predicting financial distress and

corporate failure: A systematic review from the year 2000 to 2023. Frontiers in

Economics and Management, 4(1), 1–24.

https://doi.org/10.53469/fem.2023.04(01).03

Terza, J. V., Basu, A., & Rathouz, P. J. (2022). Two-stage residual inclusion estimation:

Addressing endogeneity in health econometric modeling. Journal of Health

Economics, 81, 102566. https://doi.org/10.1016/j.jhealeco.2021.102566

Tinoco, M. H., & Wilson, N. (2022). Financial distress and bankruptcy prediction among

listed companies using accounting, market and macroeconomic variables.

International Review of Financial Analysis, 30, 394–419.

https://doi.org/10.1016/j.irfa.2013.02.013

Tsai, C.-F. (2022). Combining cluster analysis with classifier ensembles to predict

financial distress. Information Fusion, 16, 46–58.

https://doi.org/10.1016/j.inffus.2012.04.001

Ullah, S., Akhtar, P., & Zaefarian, G. (2022). Dealing with endogeneity bias: The

generalized method of moments (GMM) for panel data. Industrial Marketing

Management, 71, 69–78. https://doi.org/10.1016/j.indmarman.2017.11.010

Valencia, F., & Laeven, L. (2022). Systemic banking crises revisited. Journal of

Financial Intermediation, 52, 100872. https://doi.org/10.1016/j.jfi.2021.100872

Veganzones, D., & Séverin, E. (2022). An investigation of bankruptcy prediction in

imbalanced datasets. Decision Support Systems, 112, 111–124.

https://doi.org/10.1016/j.dss.2018.06.011

Viglia, G., Dolnicar, S., & Galati, M. (2023). Using advanced mixed methods

approaches: Combining PLS-SEM and qualitative studies. Journal of Business

Research, 174, 114498. https://doi.org/10.1016/j.jbusres.2023.114498

Wang, Y., Wang, R., & Xiong, X. (2022). Integrated economic-financial approach to

project failure prediction in small firms: Evidence from agribusiness enterprises.

Agribusiness: An International Journal, 38(3), 601–624.

https://doi.org/10.1002/agr.21729

Wen, H., Lee, C.-C., & Zhou, F. (2022). Green credit policy, credit allocation efficiency

and upgrade of energy-intensive enterprises. Energy Economics, 94, 105099.

https://doi.org/10.1016/j.eneco.2021.105099

Xu, W., Xiao, Z., Dang, X., Yang, D., & Yang, X. (2022). Financial ratio selection for

business failure prediction using soft set theory. Applied Soft Computing, 26,

256–266. https://doi.org/10.1016/j.asoc.2014.10.005

Journal of Economic and Social Science Research | Vol. 06 | Num. 02 | Abr – Jun | 2026 !pág. 131

Artículo Científico

Abril – Junio 2026

Yildiz, B., & Akkoc, S. (2023). Bankruptcy prediction using neuro-fuzzy models in the

Turkish banking sector. Journal of Intelligent & Fuzzy Systems, 44(1), 1–14.

https://doi.org/10.3233/JIFS-222222

Zhou, L. (2022). Performance of corporate bankruptcy prediction models on

imbalanced dataset: The effect of sampling methods. Knowledge-Based

Systems, 41, 16–25. https://doi.org/10.1016/j.knosys.2012.12.007

Zhou, Y., Li, H., & Gu, Y. (2023). Financial distress prediction model for Chinese listed

companies using support vector machines. Expert Systems with Applications,

220, 119700. https://doi.org/10.1016/j.eswa.2023.119700

Zięba, M., Tomczak, S. K., & Tomczak, J. M. (2022). Ensemble boosted trees with

synthetic features generation in application to bankruptcy prediction. Expert

Systems with Applications, 58, 93–101.

https://doi.org/10.1016/j.eswa.2016.04.001