Luiz Gustavo Medeiros Barbosa et al., Impact of COVID-19 on SMEs in Brazil and managerial perception drivers: a novel neural model based on entropy-weighted utility functions (2024)

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Article by Luiz Gustavo Medeiros Barbosa, Peter Fernandes Wanke, Jorge Junio Moreira Antunes and Saulo Barroso Rocha in Cad. EBAPE.BR, v. 22, 2024, on how managers of small and medium enterprises in Brazil perceived the COVID-19 shock. Over 6000 SMEs answered twelve rounds of surveys from 2020 to 2021. The authors weight business criteria with SWARA and information entropy, build utility functions and use neural network regressions to find what drove perceptions. They find the more resilient firms were 5-10 years old and in services or construction, and that loan success was the second most impactful criterion for keeping activity going.

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ARTICLE
Impact of COVID-19 on SMEs in Brazil and managerial
perception drivers: a novel neural model based on
entropy-weighted utility functions
Luiz Gustavo Medeiros Barbosa ¹
Peter Fernandes Wanke ²
Jorge Junio Moreira Antunes ²
Saulo Barroso Rocha ³
¹ Fundação Getulio Vargas (FGV EBAPE) / Escola Brasileira de Administração Pública e de Empresas, Rio de Janeiro – RJ, Brazil
² Universidade Federal do Rio de Janeiro (COPPEAD UFRJ) / Instituto de Pós-Graduação e Pesquisa, Rio de Janeiro – RJ, Brazil
³ Universidade Federal Fluminense (UFF) / Departamento de Empreendedorismo e Gestão, Niterói – RJ, Brazil
Abstract
Departing from the inconclusive results of the scant literature on the COVID-19 impact on Small and Medium Enterprises (SMEs), this paper proposes a novel
evaluation model for addressing this issue through managerial perceptions. Over 6000 SMEs responded to twelve rounds of surveys from 2020 to 2021 during the
pandemic, allowing to track the evolution over time of the perceived impact of the pandemic on small businesses. A novel entropy-weighted utility function approach
is proposed here, followed by artificial neural network regression to map the variables related to the SME’s businesses that most foster the perceived utility of
each business criterion during the pandemic. First, weights of business-related criteria were computed using Stepwise Weight Assessment Ratio Analysis (SWARA),
sorting their relative importance – or perceptions - based on information entropy ranks derived from questionnaires collected. Transfer entropy measurements
also helped in unveiling the hidden cause-effect relationships among criteria. Second, business utility functions for each criterion were computed using Complex
Proportional Assessment based on SWARA weights. Third, neural network regressions were used to explain the managerial perceptions on each business criterion
during the pandemic, considering each business variable. Our expected and unexpected results suggest that more resilient SMEs in Brazil are 5-10 years old and
operating in the services and construction sectors. Moreover, loan success is the second most impactful criterion, deeply impacting the continuity of economic
activity levels, and it is not impacted by any other business criteria. Implications for policymakers and governmental actions are highlighted.
Keywords: SME. Business-related variables. Utility functions. Information entropy. COVID-19 impact

Impacto da COVID-19 nas PMEs no Brasil e drivers de percepção gerencial: um novo modelo neural baseado
em funções de utilidade ponderadas pela entropia
Resumo
Partindo dos resultados inconclusivos da escassa literatura sobre o impacto do COVID-19 nas pequenas e médias empresas (PMEs), este artigo propõe um novo modelo
de avaliação para abordar esse problema por meio de percepções gerenciais. Para atingir esse objetivo, mais de 6.000 PMEs responderam doze rodadas de pesquisas de
2020 a 2021, durante a pandemia, permitindo assim acompanhar a evolução do impacto percebido da pandemia nas pequenas e médias empresas. Uma nova abordagem
de função de utilidade ponderada pela entropia é proposta aqui, seguida por regressão de rede neural para mapear quais variáveis relacionadas aos negócios das PMEs
impulsionam mais a utilidade percebida de cada critério de negócios durante a pandemia. Primeiro, os pesos dos critérios relacionados aos negócios foram calculados
usando a análise de proporção de avaliação de peso passo a passo (SWARA), classificando sua importância relativa - ou percepções - com base nas classificações de
entropia de informações derivadas de dados coletados. As medições de entropia de transferência também ajudaram a revelar as relações de causa e efeito entre os
critérios. Em segundo lugar, as funções de utilidade comercial para cada critério foram calculadas usando a Avaliação Proporcional Complexa com base nos pesos
SWARA. Terceiro, regressões de redes neurais foram usadas para explicar as percepções gerenciais sobre cada critério de negócios durante a pandemia à luz de cada
variável de negócios. Nossos resultados, esperados e inesperados, sugerem que as PMEs mais resilientes no Brasil são aquelas com 5 a 10 anos de idade operando nos
setores de serviços e construção. Além disso, o sucesso do empréstimo é o segundo critério de maior impacto, impactando profundamente a continuidade dos níveis
de atividade econômica; e não é afetado por nenhum outro critério de negócio. Implicações para formuladores de políticas e ações governamentais são destacadas.
Palavras-chave: PME. Variáveis relacionadas ao negócio. Funções utilitárias. Entropia da informação. Impacto da COVID-19.

Impacto de la COVID-19 en las pymes en Brasil y factores impulsores de la percepción gerencial: un nuevo
modelo neuronal basado en funciones de utilidad ponderadas por entropía
Resumen
Con base en los resultados no concluyentes de la escasa literatura sobre el impacto de la COVID-19 en las pequeñas y medianas empresas (pymes), este artículo
propone un nuevo modelo de evaluación para abordar este problema a través de las percepciones gerenciales. Para lograr este objetivo, más de 6.000 pymes
respondieron a doce rondas de encuestas de 2020 a 2021, durante la pandemia, lo que permitió monitorear la evolución del impacto percibido de la pandemia en
las pequeñas y medianas empresas. Aquí se propone un nuevo enfoque de función de utilidad ponderada por entropía, seguido de una regresión de red neuronal
para mapear qué variables relacionadas con el negocio de las pymes impulsan más la utilidad percibida de cada criterio comercial durante la pandemia. Primero,
los pesos de los criterios relacionados con el negocio se calcularon utilizando un análisis de relación de evaluación de peso paso a paso (SWARA), clasificando su
importancia relativa ‒o percepciones‒ en función de las calificaciones de entropía de la información derivada de los datos recopilados. Las mediciones de entropía
de transferencia también ayudaron a revelar las relaciones de causa y efecto entre los criterios. En segundo lugar, las funciones de utilidad comercial para cada
criterio se calcularon mediante una evaluación proporcional compleja basada en los pesos SWARA. En tercer lugar, se utilizaron regresiones de redes neuronales
para explicar las percepciones gerenciales de cada criterio comercial durante la pandemia a la luz de cada variable comercial. Nuestros resultados, esperados e
1 inesperados, sugieren que las pymes más resilientes en Brasil son aquellas que tienen de 5 a 10 años, que operan en los sectores de servicios y construcción.
Además, el éxito del préstamo es el segundo criterio de mayor impacto, que afecta profundamente la continuidad de los niveles de actividad económica; y no se
ve afectado por ningún otro criterio comercial. Se destacan las implicaciones para los formuladores de políticas y las acciones gubernamentales.
Palabras clave: Pymes. Variables relacionadas con el negocio. Funciones de utilidad. Entropía de la información. Impacto de la COVID-19.

Article received on December 01, 2022, and accepted on August 18, 2023.
[Original version]
DOI: https://doi.org/10.1590/1679-395120220273x

Cad. EBAPE.BR, v. 22, nº 1, Rio de Janeiro, e2022-0273, 2024 ISSN 1679-3951 1-20
Impact of COVID-19 on SMEs in Brazil and managerial perception drivers: Luiz Gustavo Medeiros Barbosa
a novel neural model based on entropy-weighted utility functions Peter Fernandes Wanke
Jorge Junio Moreira Antunes | Saulo Barroso Rocha

INTRODUCTION

Evidence shows that elsewhere in most developed and developing economies, SMEs employ the largest proportion of the
workforce. In Brazil, these businesses account for approximately eighteen million formal companies, employing most of
the workforce, from agricultural products to the cultural sector (Barbosa et al., 2022). Besides, Brazil had 8,863 exporting SMEs
in 2017, which represented 40.8% of the country’s exporting companies in the year, with 17.8% referring to micro-enterprises
and 23.1% to small businesses (Serviço de Apoio às Micro e Pequenas Empresas Brasileiras [SEBRAE], 2022).
Some studies evaluating the impacts of COVID-19 for SMEs were carried out for the Brazilian context (Bretas & Alon, 2020;
Dweck, 2020; Pereira & Patel, 2022; Rediske et al., 2022; Reis et al., 2021), that operate in different sectors; with a focus on
commerce and services (Marques et al., 2021), on educational institutions (A. D. S. M. Costa et al., 2020; B. G. S. Costa et al.,
2022; Dias & Ramos, 2022), on the strategies used (Wecker et al., 2020). Thus far, however, it has not been made clear how
SME business-related variables impact on the perceived utility of business-criteria, particularly during the COVID-19 pandemic.
Precisely, this research focused on five major business-criteria to capture the managerial perceptions of the pandemic impact
to SME performance: business impact (whether it remained without operational changes or was affect either by temporary
or permanently closure) (Bartik et al., 2020; Latham, 2009); business operation (whether its economic activity level increased,
decreased or remained stable) (Dess & Robinson, 1984; S. Singh et al., 2016) ; employee dismissal (whether its jobs were spared
during the pandemic or not); loan success (whether it could borrow working capital from banks to sustain their operation
or not); and crisis duration (how long pandemic impacts were perceived to last, despite lockdowns, governmental support
etc.) (Brown et al., 2020; Deyoung et al., 2015). On the other hand, a comprehensive number of business-related variables,
encompassing socio-demographic issues both related to the SMEs and the respondents themselves were targeted as possible
perception drivers. As regards the respondents, their academic level, and their respective age; as regards the SMEs, their
relative size, time in business, business type, economic sector, and the respective Brazilian State where they are located
(Lim et al., 2020; Schepers et al., 2021).
The distinctive methodological approach offered by this research is twofold. First, by unveiling, through the transfer entropy
approach, the cause-effect and feedback relationships among major business-criteria, based on the distributional profile
of the respondents’ perceptions. Information entropy is a well-stablished concept related to the reliability of a dataset
(Núñez et al., 1996). The maximal entropy principle states that the probability distribution which best represents the current
state of knowledge for a given business-criteria is the one with largest entropy (Peter et al., 2010) . Second, and differently
from previous research, this paper aims at answering how socio-demographic, business-related, variables impact on the
perceived utility of distinct business-criteria in Brazilian SME. By computing the information entropy of the distribution
of perceptions for each criterion, it becomes possible to focus on the most meaningful criteria for policy making, and their
socio-demographic drivers, for which it is not possible to be ascertained a priori.
The impact of the COVID-19 pandemic on SMEs has led to reflection and attention on the SME ecosystem and has attracted the
awareness of academics and practitioners (Bretas & Alon, 2020; Cepel et al., 2020; A. D. S. M. Costa et al., 2020; B. G.
S. Costa et al., 2022; Habachi & Haddad, 2021; Kamaldeep, 2021; Pereira & Patel, 2022; Reis et al., 2021;). Most of this
literature on COVID-19 and SMEs reveals an understanding of how companies have responded to or been impacted by
the effects of COVID-19 (Bretas & Alon, 2020; A. D. S. M. Costa et al., 2020; Dejardin et al., 2023; Dweck, 2020; Habachi &
Haddad, 2021; Kamaldeep, 2021; Ma et al., 2021; Pereira & Patel, 2022; Rediske et al., 2022; Reis et al., 2021). In other
words, these studies tend to describe the dynamics of COVID-19 and its effects on SMEs, mostly based on descriptive
studies. Although the body of research has generated relevant results on the subject, the success, or difficulties of SMEs
during the pandemic has not yet been understood, with undeveloped aspects regarding the effect of the pandemic on
SMEs from emerging countries.
Spurred on by the research gaps, this original study reports on a series of survey data collected in Brazilian SME by means
of a novel neural-MCDM (multi-criteria decision making) model structured in three stages (Sheng-Hshiung et al., 1997; T. C.
Wang & Lee, 2009). This model is proven capable of deriving unbiased utility functions for distinct business-criteria based

Cad. EBAPE.BR, v. 22, nº 1, Rio de Janeiro, e2022-0273, 2024 2-20
Impact of COVID-19 on SMEs in Brazil and managerial perception drivers: Luiz Gustavo Medeiros Barbosa
a novel neural model based on entropy-weighted utility functions Peter Fernandes Wanke
Jorge Junio Moreira Antunes | Saulo Barroso Rocha

on information entropy levels captured from the respective respondent´s perceptions. In fact, information entropy is the
cornerstone method used in this research to assess the perceived importance of each business-criteria, based on weights
computed using the recent SWARA model. Compared with other methods, information entropy provides the benefits of lower
bias and higher robustness to unconsidered assumptions, which can lead to a more comprehensive interpretation of the
results as regards how the utility of distinct attributes, as derived by COPRAS (Zavadskas & Kaklauskas, 1996), are perceived
by distinct demographic groups. Results indicate that analyzing each criterion in an isolated fashion, crisis duration, business
operation and employee dismissal appears as the most relevant criterions, as expected due to the economic moment caused
by the pandemic. The two least relevant criteria, loan success and business impact, relate to actions that could be taken to
keep SMEs running even despite lockdown interruptions. Most SMEs suffered from business interruptions that may have
caused operational changes, thus yielding lower economic activity. Besides, while most of them did not find financial support
in banking loans for working capital, they are so diminished in size (self-entrepreneurs) that employee dismissal presented a
limited impact on explaining the lower utility function levels. In general, our paper contributes to our understanding of the
impact of COVID-19 on the small business ecosystem in Brazil. This survey on the impact of the COVID-19 pandemic on
the operations of small and medium-sized enterprises (SMEs) in Brazil is, to date, the most comprehensive and representative
in the sector. The study involved 7,000 companies from different segments and regions. The rest of this paper includes four
sections. Literature review is presented in Section 2, while methodology is presented in Section 3. Section 4 focuses on the
analysis and discussion of results, and conclusions are elaborated in Section 5.

IMPACT OF COVID-19 ON SMES

In March 2020, along with the rest of the world, Brazil was in the agony of the COVID-19 pandemic. Organizations have
responded to the shutdown of the global economy in multiple ways, having to make decisions in a context of uncertainty
about the duration of the crisis and potential public policies to support business. It is clear, exemplified and documented that
the crisis caused by COVID-19 has led to the disruption of business operations, supply chain and management models. And
COVID-19 pandemic demonstrated that small and medium-sized enterprises (SMEs) are mostly susceptible to crises and shocks
(Fasth et al., 2022; Kurland et al., 2022; Miklian & Hoelscher, 2022; Organization for Economic Co-operation and Development
[OECD], 2021; Puthusserry et al., 2022). Demand and supply-side interruption, business contraction and restricted access
to loan and trade credit are just some of the consequences SMEs face from exogenous shocks (Miklian & Hoelscher, 2022).
Decisions made during a crisis are described as complex since they have a propensity to contain paradoxes, such as having to
be made carefully but quickly (Vargo & Seville, 2011), affecting operations, performance, and survival (Ozanne et al., 2022;
Puthusserry et al., 2022). Still, as more evidence is gathered and reported about the experience of COVID‐19 among SMEs,
we gradually develop our understanding of the policies, preparatory steps and procedures that are best suited in a global
type of crisis such as COVID‐19 (Fasth et al., 2022).
The pandemic’s length also affects smaller firms more strongly as they lack adequate resources to tolerate extended periods
of disturbance with many closings once they drain their operating finances (Brown et al., 2020; Cowling et al., 2020). The
diverse collection of small and medium-sized enterprises is often more vulnerable than large firms under diverse shock settings
(Deyoung et al., 2015). While all exogenous shocks bring a degree of economic effect, their scale and magnitude can differ,
for example, in the range of the time needed to ‘return to normal’ (Miklian & Hoelscher, 2022). Time is money even for SMEs,
and unlike large firms, SMEs do not have satisfactory access to the capital markets and thus have a much more restricted
menu of diverse sources of external finance. There are only two economically important alternatives for SMEs: bank loans and
trade credit (Carbó-Valverde et al., 2016). Credit rationing is a common phenomenon faced by firms in Brazil (Maffioli et al.,
2017; Maia et al., 2019; Zambaldi et al., 2011), one that has negative consequences for long-term investments. In Brazil,
public credit plays a vital role in supporting firms: state-owned banks account for half of the outstanding credit (Maffioli et al.,
2017). The relation of past budgetary crisis to SMEs (Carbó-Valverde et al., 2016) indicates that the financial crisis was
associated with a credit crunch that affected the SME sector by increasing the number of credit constrained firms. Thus, a
well-developed local financial system increases the availability of bank loans and reduces the need of SMEs to hold cash as
a precautionary buffer against adverse shocks (Fasano & Deloof, 2021).

Cad. EBAPE.BR, v. 22, nº 1, Rio de Janeiro, e2022-0273, 2024 3-20
Impact of COVID-19 on SMEs in Brazil and managerial perception drivers: Luiz Gustavo Medeiros Barbosa
a novel neural model based on entropy-weighted utility functions Peter Fernandes Wanke
Jorge Junio Moreira Antunes | Saulo Barroso Rocha

More specifically, the COVID-19 pandemic had a significant impact on small and medium-sized enterprises (SMEs), leading to a
decrease in sales, an increase in costs, and uncertainty, resulting in rising unemployment rates, amplifying the consequences of
the tragedy caused by the pandemic (Dweck, 2020; Klein & Todesco, 2021; Puthusserry et al., 2022). The COVID-19 pandemic
led to a decrease in sales for SMEs in several sectors, including tourism, retail, and hospitality. This was due to business
closures and travel restrictions. Fasano and Deloof (2021) found that Italian SMEs that were most affected by the pandemic
had an average decrease of 50% in sales. Machado et al. (2022) found that Brazilian food exports to the United Kingdom fell by
an average of 40% during the pandemic. The pandemic also led to an increase in costs for SMEs, as a result of mobility restrictions,
store closures, and a decline in productivity. Wecker et al. (2020) found that Brazilian SMEs faced an average increase of 20%
in costs during the pandemic. In addition to these impacts, the pandemic period brought uncertainty to business in general,
making it difficult to make decisions and plan. This was due to uncertainty about the duration of the pandemic, the impact
of the pandemic on the economy, and consumer behavior. Nicolletti et al. (2020) found that European SMEs were more likely
to report uncertainty about the future of their business during the pandemic.
Governments can take measures to support SMEs, in order to prevent them from closing down and losing jobs.
Cowling et al. (2020) argued that governments need to take measures to support SMEs to prevent them from closing and
losing jobs. Providing lines of credit and other types of financing to help SMEs cover their expenses and keep their businesses
running. Providing tax breaks and other types of financial relief to help SMEs reduce their costs. Offering training and technical
support to help SMEs adapt to the new realities of the market and become more resilient, and helping SMEs connect with
customers and suppliers to help them maintain their sales and operations (Cowling et al., 2020; Habachi & Haddad, 2021;
Klein & Todesco, 2021; Maia et al., 2019). SMEs are responsible for a large part of the economy and employment, and their
success is essential for the post-COVID-19 economic recovery.
In addition to studies on the direct impact of COVID-19 on the operational performance of small and medium-sized enterprises
(SMEs), some researchers have addressed different perspectives of organizations during the pandemic. SMEs that adopted
new innovations with external support were more likely to survive the pandemic (Adam & Alarifi, 2021). This is in line with
the research where it was found that the pandemic accelerated the digitalization of companies, as SMEs were forced to adopt
new technologies to remain competitive (Klein & Todesco, 2021). SMEs that adopted digital transformation were more likely to
survive the pandemic and emerge stronger. According to Doerr et al. (2021), companies with a stronger technological capacity
were more likely to recover from the pandemic than companies with a weaker technological capacity. Technological
capacity as defined in Bernades et al. (2019).
Clampit (2021), Dejardin et al. (2023), and Wecker et al. (2020) presented studies on the impact of dynamic capabilities on
SME performance during the COVID-19 crisis. SMEs with stronger dynamic capabilities had a better performance during the
pandemic, therefore, SMEs that invest in dynamic capabilities are better prepared to face challenges and take advantage
of opportunities in times of crisis (Dejardin et al., 2023). This is also in line with Wecker et al. (2020): “crisis management
strategies can help companies to develop and improve their dynamic capabilities”, and Clampit (2021) where “SMEs with
stronger dynamic capabilities were more likely to maintain their performance during the COVID-19 pandemic.” The three main
dynamic capabilities that were found to be important for SME performance stability were sensing, seizing, and reconfiguring
(Clampit et al., 2021). The studies converge to the conclusion that dynamic capabilities and crisis management strategies are
essential for the success of companies in the post-COVID-19 era.
New research on the impact of COVID-19 on organizations is likely to emerge in the coming years, covering both the supply and
demand sides. This research focused on studies that analyzed the operational impact dimension and its underlying variables.
We will discuss the methodology in the following section.

Cad. EBAPE.BR, v. 22, nº 1, Rio de Janeiro, e2022-0273, 2024 4-20
Impact of COVID-19 on SMEs in Brazil and managerial perception drivers: Luiz Gustavo Medeiros Barbosa
a novel neural model based on entropy-weighted utility functions Peter Fernandes Wanke
Jorge Junio Moreira Antunes | Saulo Barroso Rocha

METHODOLOGY

Research sample and data collection procedures]
Brazilian Support Service for Micro and Small Enterprises (SEBRAE) and Fundação Getulio Vargas (FGV) conducted surveys
between March 2020 and September 2021. SEBRAE and FGV conducted twelve waves of web surveys, interviewing approximately
7,000 SMEs in each one, corresponding to 85.857 observations. Table 1 presents the number of SMEs interviewed in each
wave of the survey. The list of variables used are available in (Serviço de Apoio às Micro e Pequenas Empresas Brasileiras
[SEBRAE], 2022).

Table 1
Number of SMEs

Ed. 1 2 3 4 5 6 7 8 9 10 11 12 Total

n 9,105 6,080 10,384 7,403 6,470 6,506 7,586 6,033 6,138 6,228 7,820 6,104 85,857

When Mar Apr May Jun Jul Aug Sep Oct Nov Mar May Jun

Source: Elaborated by the authors.

The variables analyzed were grouped into Business-criteria and business-related variables. Business-criteria consisted
of the following sub-unit of analysis: business-impact, business-operation, crisis duration, employee-dismissal, and loan
success. Business-related variables comprised the following socio-demographic aspects: state, sector, business-size,
business-time, business-type, years (age), academic level.
Business-impact. Economic recessions represent a period that threatens the survival of all firms. This is particularly the case
for SMEs and start-up firms, which have been shown to fail at a much higher rate compared with their larger, more established
peers (Latham, 2009). SMEs have experienced from a shortage of production inputs because of distortions that affected supply
chains, which negatively impacted their sales. Thus, in this research, business-impact is a variable with a 4-point scale, taking
a value of one if SME permanently closed business, two for temporary closed business, three for business with operational
changes, and four for business without operational changes.
Business-operation. Organizational performance (OP) lies at the heart of an organization’s survival. it must be reiterated that
measuring OP is a complex task, as literature and real-life experience of scores of researchers shows, given the accessibility to
reliable financial data and other performance measures (S. Singh et al., 2016). To face this problem, the value of performance
measures, obtained from top management teams, is an alternative way to capture firms’ performance (Dess & Robinson,
1984). To capture performance of SMEs in pandemic context, we employed growth in sales variation, with the following
attributes: Lesser, Equal, or Greater.
Loan success. Small and medium enterprises face strong asymmetric information problems when trying to access credit. In
previous economic crises, the supply of credit via loan to small and medium-sized companies was drastically reduced due to
the increase in lender risk aversion (Deyoung et al., 2015). A reduction in SME credit supply could exacerbate the economic
downturn by denying SMEs the short-term credit necessary to finance supplies and retain employees.
Crisis duration. Crisis duration is entrepreneurs’ perception of how long it will take for the economy to return to normal.
Employee dismissal. Employee dismissal refers to information about employees who had their employment contracts
terminated during the pandemic.
Business-related variables are the sociodemographic variables of the SMEs interviewed, namely: state, sector, business-size,
business-time, business-type, years, and academic level. The proposed model used these variables, specifically in Neural
Network Regression, as presented in the next section.

Cad. EBAPE.BR, v. 22, nº 1, Rio de Janeiro, e2022-0273, 2024 5-20
Impact of COVID-19 on SMEs in Brazil and managerial perception drivers: Luiz Gustavo Medeiros Barbosa
a novel neural model based on entropy-weighted utility functions Peter Fernandes Wanke
Jorge Junio Moreira Antunes | Saulo Barroso Rocha

Proposed model
Multiple Attribute Decision Making (MADM) is a research field focused on the assessment of different alternatives when
considering multiple attributes (Sheng-Hshiung et al., 1997; T. C. Wang & Lee, 2009). The most common models applied to
compute the weightings of these attributes include the Entropy Method (Sheng-Hshiung et al., 1997; R. K. Singh & Benyoucef,
2011), Information Entropy Weight (IEW) (Zhang et al., 2011), Analytic Hierarchy Process (AHP) (Dağdeviren et al., 2009;
Sheng-Hshiung et al., 1997; Yu et al., 2011), Fuzzy AHP (Gumus, 2009; Sun, 2010; J. W. Wang et al., 2009) and Rough AHP
(Aydogan, 2011). More recently, SWARA emerges a general tool that is used for calculating attribute weights within the ambit
of performance measurement, as well as the respective resulting importance levels (Keršuliene et al., 2010).
Liang and Ding (2003) focus specifically on respondents to determine the weightings of attributes, based on perceptual
Likert scales. However, the inherent uncertainty and subjectivity of such scales can result in weighting errors, yielding biased
conclusions as regards the relative importance of each attribute. In this sense, information entropy can be conceptualized as
a probabilistic measure of uncertainty. Depending on the socio-demographic group, the randomness level at given attribute
may vary, and this variation can be captured by calculating the information entropy for each sub-unit of analysis. The greater
the information entropy value, the greater the randomness within the range of respondents and, therefore, the greater the
inherent discriminatory power of a given attribute (Núñez et al., 1996).
In this paper, information entropy is used to set the initial importance order of business-criteria in SWARA, through which
unbiased weights are computed. These weights serve subsequently as inputs to COPRAS, which differently from other
MADM methods, helps in establishing a partial utility degree for each business-criteria in Brazilian SMEs (Kaklauskas et al.,
2006; Zavadskas et al., 2007). Readers should recall that utility functions are a well-known economic concept applied in
MADM (Dyer et al., 1992). Precisely, utility is an important concept that measures perceptions or preferences over a set of
business-criteria (Kassem & Hakim, 2016; Rezaeisaray et al., 2016). The COPRAS utility function approach is the most simply
and easily understood by academics and practitioners since it does not require any stronger restrictions on the preference
structures than the aggregation formula, straightforwardly establishing the relation between business-criteria and partial
value function amounts (Gandhi et al., 2015, 2016; Janssen et al., 2017). The simplicity of the additive aggregation makes the
utility function approach particularly appealing for serving as inputs of subsequent multivariate analysis (de Almeida et al.,
2016). The following sub-sections dig further into the novel neural-MADM methods utilized in this paper to apprehend the
socio-demographic impacts on the perceived utility of distinct SMEs attributes.

SWARA
The SWARA steps used in this research are duly described next (Stanujkic et al., 2015).
Step 1: Sort business-criteria from the highest to the lowest based on the information entropy ranking for each criterion.
Step 2: Assign the null value for the preference of the first business-criteria. Allocate preferences to the second most important
business-criteria; repeat this step until the least important business-criteria is reached. These preferences are computed
by comparing a given business-criteria with the first one with highest entropy. Compute their pairwise relative importance,
denoted by , which shows the ratio of this comparison.
Step 3: Set-up pairwise efficiency criteria by:
1, j = 1 (8)
Kj =
S
 j + 1, j > 1

Step 4: Compute relative weights ( based on sorted pairwise efficiency with respect to the importance criterion rank:
(9)

Step 5: Compute final weights as , where denotes the weight of each criterion j.

Cad. EBAPE.BR, v. 22, nº 1, Rio de Janeiro, e2022-0273, 2024 6-20
Impact of COVID-19 on SMEs in Brazil and managerial perception drivers: Luiz Gustavo Medeiros Barbosa
a novel neural model based on entropy-weighted utility functions Peter Fernandes Wanke
Jorge Junio Moreira Antunes | Saulo Barroso Rocha

COPRAS
COPRAS was first introduced more than two decades ago by Zavadskas and Kaklauskas (1996). Since then, several different
researches have been published on possible alternative ways for combining SWARA and COPRAS (Zolfani & Bahrami, 2014;
Nakhaei et al., 2016; Valipour et al., 2017); SWARA and Fuzzy COPRAS (Bekar et al., 2016; Yazdani et al., 2011); and COPRAS
and other MCDMs (Aghdaie et al., 2012; Ecer, 2014; Fouladgar et al., 2012; Rezaeiniya et al., 2012; Zolfani et al., 2012). The
next lines briefly present the major steps of the COPRAS method applied in this research for deriving utility functions based
on different business-criteria importance weights (cf. previous section):
Step 1: Create a decision-making matrix X, containing m respondents and n business-criteria:
 a11  a1n 
 
X =     (10)
a  i 1, 2,...
 m1  a
= mn 
= n ; j 1, 2,..., m

Step 2: Normalize the decision matrix X by computing:
x
x ij = n ij
(11)
∑ x ij
j =1

Then the decision matrix will be:
 x 11  x 1n 
  (12)
X =    
x 
 m 1  x mn 
Step 3: Compute the weighted normalized decision matrix by means of:
(13)
Therefore,

(14)

Step 4: Sum-up the larger values that are more preferable, named as P i :
k

P = ∑ x (15)
i
j =1
ij

Step 5: Sum-up the smaller values that are more preferable, named as R i :
k

R =∑x
i ij (16)
j= k +1

Then the number of business-criteria that should be minimized is given by the difference m-k.
Step 6: Minimize R i observing eq. (8):

R min min R
= = i ;i 1, 2,..., n (17)
i

Step 7: Compute the relative significance of each business-criterion Q i as given:
n
R min ∑ R i (18)
Q= P +
i i n
i =1
R min
Ri ∑
i =1 Ri

Cad. EBAPE.BR, v. 22, nº 1, Rio de Janeiro, e2022-0273, 2024 7-20
Impact of COVID-19 on SMEs in Brazil and managerial perception drivers: Luiz Gustavo Medeiros Barbosa
a novel neural model based on entropy-weighted utility functions Peter Fernandes Wanke
Jorge Junio Moreira Antunes | Saulo Barroso Rocha

Step 8: Identify the optimal business-criterion i, given by K, as is illustrated:
=K max
= Q i ; i 1, 2,..., n (19)
i

Step 9: Prioritize business-criteria in a descending order.
Step 10: Determine the utility degree N of each subsequent business-criterion i, given as:
Qi
N
= i ×100%
Q max (20)

Transfer entropy
The information flow between two business-criteria i and j can be measured combining both Shannon Entropy (Shannon,
1948a, 1948b) with Kullback-Leibler divergence (Kullback & Leibler, 1951) considering a Markov process with k and l levels
or factors, respectively (Schreiber, 2000). Assuming the probabilities distributions p(i) and p(j) for business-criteria i and j
respectively and the joint probability p(i,j), the information flow from business-criteria j to i is given by (Dimpfl & Peter, 2013):

(21)

which measure the deviation from generalized Markov process = at the marginal conditional

distribution odds-ratio log .

Since the information flow from i to j is measured analogously, it is possible to define the causation direction between two
given business-criteria based on the net information flow computed as the difference between flows from i to j and j to i. By
bootstrapping the inherent probability distributions for each factor/level in each criterion, it is possible to run this Markov
process n times and compute the statistical significance for the net information flow from one business criteria to another
(Peter et al., 2010).

Neural network regression
ANNs (Artificial Neural Networks) are used to analyze the responses for each business-criterion as a resultant of a series of
socio-demographic, business-related, variables while controlling for the respective utility function. Precisely, an ANN regression
is computed to unveil the non-linear impact of each socio-demographic, business-related, variable on the response factors
or levels asked in each business-criterion. When controlling these relationships between criteria and demographic variables,
higher (lower) values of perceived utility not only denote that a given business-criterion is regarded – as a whole – as more
(less) relevant by respondents, but also that the distribution of the responses of this business-criterion is more (less) scattered
or dispersed, thus making it more difficult to make a priori inferences based on socio-demographic variables without using
more sophisticated inference techniques. In this research, we particularly look at the MLP (Multi-Layer Perceptron) network
which has been the most used of ANNs architectures for forecasting (Mubiru & Banda, 2008). We also observed the Connection
Weight Approach (CWA) (Olden et al., 2004; Olden & Jackson, 2002) for accurately quantifying the relative importance of
each socio-demographic variable on the response levels or factors for each business-criterion.

Cad. EBAPE.BR, v. 22, nº 1, Rio de Janeiro, e2022-0273, 2024 8-20
Impact of COVID-19 on SMEs in Brazil and managerial perception drivers: Luiz Gustavo Medeiros Barbosa
a novel neural model based on entropy-weighted utility functions Peter Fernandes Wanke
Jorge Junio Moreira Antunes | Saulo Barroso Rocha

ANALYSIS AND DISCUSSION OF RESULTS

Density plots for the business-criteria weights computed using SWARA are depicted in Figure 1, based on the information
entropy distributions provided by respondents for each criterion. Analyzing each criterion in an isolated fashion, crisis
duration appears as the most relevant criterion, followed by business operation and employee dismissal as expected due
to the singular economic moment caused by the pandemic. These three most relevant criteria indicate that SME concerns
are mostly related to lockdown decisions and the consequent impact on economic activity and employment level. The two
least relevant criteria, loan success and business impact, relate to actions that could be taken to keep SMEs running even
despite lockdown interruptions. Besides, this importance imbalance among business-criteria is also reflected on the overall
utility function distribution: SMEs tend perceive such utility as low – most utility function values are below 0.50 – what in
some sort anticipates the nature of problem faced during the pandemic in light of the response levels/factors for each
business-criteria as depicted in Table 2. Most SMEs suffered from business interruptions that may have caused operational
changes, thus yielding lower economic activity. Besides, while most of them did not find financial support in banking loans
for working capital, they are so diminished in size (self-entrepreneurs) that employee dismissal presented a limited impact
on explaining the lower utility function levels.

Figure 1
Barplot for the business-criteria information entropy weights computed using SWARA

Cad. EBAPE.BR, v. 22, nº 1, Rio de Janeiro, e2022-0273, 2024 9-20
Impact of COVID-19 on SMEs in Brazil and managerial perception drivers: Luiz Gustavo Medeiros Barbosa
a novel neural model based on entropy-weighted utility functions Peter Fernandes Wanke
Jorge Junio Moreira Antunes | Saulo Barroso Rocha

Source: Elaborated by the authors.
Figure 2
COPRAS utility function results

Source: Elaborated by the authors.

Table 2
Descriptive statistics for the business-criteria and their respective response levels
Business Frequency distribution for each response/
criteria* factor level (number in brackets denote the response level)
Permanently Business with Business without
Business Temporary Closed
Closed 0.32% 30.22% Operational 56.93% Operational 12.53%
Impact (+) Business (2)
Business (1) changes (3) changes (4)
Business
Lesser (1) 85.63% Equal (2) 7.90% Greater (3) 6.47%
Operation (+)
Employee Without Business without With
39.85% 48.48% 11.67%
Dismissal (-) Dismissal (1) employees (2) Dismissal (3)
Loan Waiting Loan
Loan Denied (1) 79.03% 9.89% 11.08%
Sucess (+) Response (2) Approved (3)
Crisis Descriptives
Duration(-) Min 0 Max 365 Mean 11.89 SD 11.64
* Signs are related to the positive or negative impact of a given criteria on overall utility. They reflect the factor/response levels for each
criterion, observing intrinsic relations such as “the higher the better,” “the higher the worse” w.r.t. utility function values.
Source: Elaborated by the authors.

Cad. EBAPE.BR, v. 22, nº 1, Rio de Janeiro, e2022-0273, 2024 10-20
Impact of COVID-19 on SMEs in Brazil and managerial perception drivers: Luiz Gustavo Medeiros Barbosa
a novel neural model based on entropy-weighted utility functions Peter Fernandes Wanke
Jorge Junio Moreira Antunes | Saulo Barroso Rocha

Transfer entropy and neural network results for cause-effect relationships among business-criteria and business-related variables
in Brazilian SME are depicted in Figure 3. Table 3 also reports on the best ANN architecture found for each regression, after
cross-validating the originally trained models with a randomly selected 20% of the sample. One may easily note that business
operation is the most critical criteria: it impacts three other criteria (crisis duration, employee dismissal and business impact),
and it is only impacted by one (loan success). Greater economic activity not only impacts on the respondent´s perceptions
about the duration of lockdowns and the persistence of pandemic effects but can also revert decisions with respect to reduction
in workforce or even shutting down the business. Loan success is the second most impact criterion, deeply impacting the
continuity of economic activity levels; it could be considered a pure exogenous criterion since it is not impacted by any other
business-criteria. Consistent with Deyoung et al. (2015) and Maffioli et al. (2017), the availability of credit resources for SMEs
directly impacts the business operation.
On the other hand, business impact is purely endogenous, its perception is the resultant of the countervailing forces represented
by economic activity level; reduction of labor force; and successful working capital loans for sustaining business during the
pandemic. These pure exogenous and endogenous business criteria may explain why their perceived utility is high (COPRAS
function present a positive impact highlighted in green). Hence, more resilient SMEs – without operational changes – are
those with 5-10 years’ operating in the services and construction sectors. On the other hand, SMEs that suffered the most
with lockdowns are those related to food and technology industries. As regards banking support, food services SMEs were
more successful in borrowing working capital from banks than novel SMEs that operate in the gym, pet shop, and educational
services in general. It is important to note that, regardless of the business-criteria, the educational respondent profile, and
the state of location of the SME were also found to be pretty heterogeneous, results that suggest that perceptions and the
utility functions on the distinct business-criteria still depends on whether the SME is located in poorer or richer Brazilian
states or on whether the self-entrepreneurs are illiterate or not. This is crucial evidence of the impact of formal education on
the survival of SMEs during the COVID-19 pandemic crisis. The absence of adequate education to run a business can make
it difficult to deploy dynamic capabilities, or technological capabilities. This is an underlying and relevant variable in any
business model, in any sector. Education is important for small and medium-sized enterprises (SMEs) because it can help to
improve productivity, increase competitiveness, and create new jobs. Differences in local financial development particularly
affect corporate finance decisions of small and medium-sized firms (Fasano & Deloof, 2021). The full set of ANN results are
depicted in the Appendix.

Table 3
Best Neural Network architecture validation
Neurons L1 L2 Error Validation
Business-Criteria Layers
per Layer Regularization Regularization Measure Error
Business Impact 1 35 1.00E-07 1.00E-07 ACC 71.22%
Business Operation 2 5 1.00E-05 1.00E-07 ACC 76.37%
Employee Dismissal 4 30 1.00E-05 1.00E-05 ACC 70.08%
Loan Sucess 3 35 1.00E-06 1.00E-05 ACC 53.91%
Crisis Duration 3 5 1.00E-06 1.00E-05 MAE 0.53
Validation with 20% of total dataset observations. MAE stands for mean absolute error, while ACC stands
for accuracy, that is, the fraction of correct predictions. Readers should note that for the first four business-
criteria, a classification neural network model was performed to regress socio-demographic variables onto a
respective response level.
Source: Elaborated by the authors.

Cad. EBAPE.BR, v. 22, nº 1, Rio de Janeiro, e2022-0273, 2024 11-20
Figure 3
Results for the transfer entropy analysis (arrows among business-criteria) and for the ANN regressions (business-related variables) for each criterion

Impact of COVID-19 on SMEs in Brazil and managerial perception drivers:

Cad. EBAPE.BR, v. 22, nº 1, Rio de Janeiro, e2022-0273, 2024

a novel neural model based on entropy-weighted utility functions

Luiz Gustavo Medeiros Barbosa

Key: List of the five most relevant positive in green and negative in red. Peter Fernandes Wanke
Note: All results were controlled by COPRAS utility function scores.
Source: Elaborated by the authors.

Jorge Junio Moreira Antunes | Saulo Barroso Rocha

12-20
Impact of COVID-19 on SMEs in Brazil and managerial perception drivers: Luiz Gustavo Medeiros Barbosa
a novel neural model based on entropy-weighted utility functions Peter Fernandes Wanke
Jorge Junio Moreira Antunes | Saulo Barroso Rocha

CONCLUSIONS

The study aimed to propose a novel evaluation model for addressing the impact of COVID-19 on SMES through managerial
perceptions. A novel entropy-weighted utility function approach is proposed here, followed by artificial neural network
regression to map which SME business-related variables drivers the most the perceived utility of each SME business-criteria
during the pandemic. Neural network regressions were used to explain the managerial perceptions on each business
criterion during the pandemic considering each business variable, while controlling for the respective criterion utility.
The entropy-weighted utility function approach and the ANN regression were impactful in figuring out the SMEs business-
related variables that most drive the perceived utility of each SME business criterion during the pandemic for some reasons:
1) it considers the uncertainty and variability of data by incorporating entropy calculations. This helps in managing the complexity
of business-related variables and their impact on perceived utility. This type of approach could be used to any unpredictable
and rapidly changing situations; 2) by considering the weights (Olden & Jackson, 2002; Olden et al., 2004), decision-makers
can prioritize and focus on the variables that have the greatest impact on business outcomes; 3) By using ANN regression, the
business-related variables and their influence on the perceived utility can be mapped in a non-linear manner. But while
the proposed model offers valuable insights, there are certain limitations, such as: it requires a precise specification of the
utility function and the probability distribution of the outcomes, which may not be easy to elicit in real-world problems.
Forthcoming studies might conduct more research on these managerial perceptions issues to improve the proposed model,
additional granular examinations of isolated business type, or focus on the smallest SMEs (e.g., less than 5 employees).
Fasano and Deloof (2021) identified that the distribution of financial credit, with the purpose of lengthening payment terms,
to the supply chain of a given SME can be more effective than the resource directly allocated in the company, depending on
the context and SME’s operating sector. This was not investigated in this study and, if studied, this aspect might contribute
to the design of policies for SMEs. SMEs’ financial performance could be investigated considering business impact and
operational functions, including SME structure and owner capability. The role of education in building dynamic strategies
and technological capacity is critical for SMEs, especially in times of crisis. There is a gap on this subject in the literature on
strategy and business resilience for SMEs.
Finally, the model proposed in this article enables capturing intricate relationships that may not be easily identifiable through
traditional statistical methods. By understanding the described transformations in steps for SWARA and COPRAS, and how
the ANN was applied, researchers can assess whether this method is suitable for their research problem.

Cad. EBAPE.BR, v. 22, nº 1, Rio de Janeiro, e2022-0273, 2024 13-20
Impact of COVID-19 on SMEs in Brazil and managerial perception drivers: Luiz Gustavo Medeiros Barbosa
a novel neural model based on entropy-weighted utility functions Peter Fernandes Wanke
Jorge Junio Moreira Antunes | Saulo Barroso Rocha

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Cad. EBAPE.BR, v. 22, nº 1, Rio de Janeiro, e2022-0273, 2024 17-20
Impact of COVID-19 on SMEs in Brazil and managerial perception drivers: Luiz Gustavo Medeiros Barbosa
a novel neural model based on entropy-weighted utility functions Peter Fernandes Wanke
Jorge Junio Moreira Antunes | Saulo Barroso Rocha

Luiz Gustavo Medeiros Barbosa
ORCID: https://orcid.org/0000-0002-3172-5878
Professor from the Brazilian School of Public and Business Administration at Getulio Vargas Foundation (FGV EBAPE); Project Coordinator at Getulio
Vargas Foundation (FGV Projects). E-mail: luiz.barbosa@fgv.br

Peter Fernandes Wanke
ORCID: http://orcid.org/0000-0003-1395-8907
Full Professor and Coordinator in the Business Analytics and Economics Research Unit (BAE RU) from the COPPEAD Graduate School of Business at the
Federal University of Rio de Janeiro (UFRJ). E-mail: peter@coppead.ufrj.br

Jorge Junio Moreira Antunes
ORCID: https://orcid.org/0000-0003-3199-5912
Researcher in the Business Analytics and Economics Research Unit (BAE RU) from the COPPEAD Graduate School of Business at the Federal University
of Rio de Janeiro (UFRJ). E-mail: jorge.moreira@coppead.ufrj.br

Saulo Barroso Rocha
ORCID: https://orcid.org/0000-0001-5441-6747
Associate Professor at the Department of Entrepreneurship and Management at Federal Fluminense University (UFF). E-mail: saulorocha@id.uff.br

AUTHORS’ CONTRIBUTION
Luiz Gustavo Medeiros Barbosa: Conceptualization (Lead); Investigation (Lead); Project administration (Lead); Supervision (Lead); Validation (Lead); Writing
- original draft (Supporting).
Peter Fernandes Wanke: Formal Analysis (Lead); Methodology (Lead); Software (Supporting); Supervision (Lead); Writing- original draft (Supporting); Writing
- review & editing (Supporting).
Jorge Junio Moreira Antunes: Formal Analysis (Equal); Methodology (Supporting); Software (Lead); Writing - original draft (Lead); Writing - review & editing
(Supporting).
Saulo Barroso Rocha: Conceptualization (Supporting); Investigation (Supporting); Writing - review & editing (Lead).

DATA AVAILABILITY
The dataset supporting the results of this study is not publicly available.

EDITOR-IN-CHIEF
Hélio Arthur Reis Irigaray (Fundação Getulio Vargas, Rio de Janeiro / RJ – Brazil). ORCID: https://orcid.org/0000-0001-9580-7859

ASSOCIATE EDITOR
Fabricio Stocker (Fundação Getulio Vargas, Rio de Janeiro / RJ – Brazil). ORCID: https://orcid.org/0000-0001-6340-9127

REVIEWERS
Abimael Magno do Ouro Filho (Universidade Federal de Sergipe, Aracaju / SE – Brazil). ORCID: https://orcid.org/0000-0003-1308-9297
One of the reviewers did not authorize the disclosure of their identity.

PEER REVIEW REPORT
The peer review report is available at this URL: https://periodicos.fgv.br/cadernosebape/article/view/90536/85321

Cad. EBAPE.BR, v. 22, nº 1, Rio de Janeiro, e2022-0273, 2024 18-20
Impact of COVID-19 on SMEs in Brazil and managerial perception drivers: Luiz Gustavo Medeiros Barbosa
a novel neural model based on entropy-weighted utility functions Peter Fernandes Wanke
Jorge Junio Moreira Antunes | Saulo Barroso Rocha

APPENDIX

Table A
Relative importance of each business-variable on each business-criteria
(controlling for the respective utility function – COPRAS value)
Business Business Employee Loan Crisis
Business-variable
Impact Operation Dismissal Sucesssuccess Duration
Academic_Level_Graduate (Complete) 0.201 0.119 -0.007 0.297 1.339
Academic_Level_High School (Complete) 0.790 0.068 0.087 -0.274 -0.805
Academic_Level_High School
0.219 -0.084 -0.038 -0.150 15.871
(Incomplete)
Academic_Level_Primary Education
0.026 -0.253 -0.242 -0.221 -12.240
(Complete)
Academic_Level_Primary Education
0.350 0.085 0.235 0.094 -12.435
(Incomplete)
Academic_Level_Undergraduate
0.550 0.108 -0.032 -0.134 11.614
(Incomplete)
Business_Size_EPP 0.165 -0.035 -0.014 -0.016 -2.523
Business_Size_ME 0.375 -0.010 0.005 -0.251 2.478
Business_Size_MEI 0.288 -0.063 -0.193 0.295 -0.934
Business_Time_1 - 2 years -0.238 -0.073 -0.015 -0.282 0.671
Business_Time_2 - 5 years 0.605 0.047 -0.010 -0.055 1.377
Business_Time_5 - 10 years -0.033 0.187 0.075 -0.520 0.625
Business_Time_Less than 1 year 0.612 -0.007 0.131 0.170 -2.471
Business_Type_Agriculture 0.237 0.073 0.313 0.124 0.691
Business_Type_Automotive Workshops
0.115 0.011 -0.322 -0.082 2.149
and Parts
Business_Type_Beauty -0.076 -0.080 -0.356 0.079 0.297
Business_Type_Business Services -0.026 -0.026 -0.143 0.039 0.811
Business_Type_Construction 0.158 -0.019 0.196 0.233 -2.847
Business_Type_Craftsmanship 0.404 -0.059 -0.106 0.066 -6.203
Business_Type_Creative Economy 0.157 -0.056 0.017 -0.005 0.461
Business_Type_Education 0.128 0.041 0.178 -0.281 4.617
Business_Type_Energy 0.143 0.037 -0.029 0.090 2.176
Business_Type_Fashion 0.352 -0.046 0.243 -0.162 -1.260
Business_Type_Food Industry 0.216 -0.336 -0.125 0.001 4.314
Business_Type_Food Services -0.107 0.078 -0.014 0.314 3.534
Business_Type_Gyms and Physical
-0.322 0.057 -0.252 -0.434 -0.932
Activities
Business_Type_Health 0.164 0.055 0.006 0.095 -0.167
Business_Type_Logistics and
0.074 -0.112 0.117 -0.095 -1.878
Transportation
Business_Type_Other 0.296 0.000 0.191 -0.075 -5.681
Business_Type_Pet Shops and Veterinary
0.360 -0.117 -0.054 -0.359 -2.493
Services

(Continue)

Cad. EBAPE.BR, v. 22, nº 1, Rio de Janeiro, e2022-0273, 2024 19-20
Impact of COVID-19 on SMEs in Brazil and managerial perception drivers: Luiz Gustavo Medeiros Barbosa
a novel neural model based on entropy-weighted utility functions Peter Fernandes Wanke
Jorge Junio Moreira Antunes | Saulo Barroso Rocha

Business Business Employee Loan Crisis
Business-variable
Impact Operation Dismissal Sucesssuccess Duration
Business_Type_Technology Industry 0.038 -0.172 0.003 -0.124 2.268
Business_Type_Tourism 0.572 0.027 -0.110 0.073 -0.839
COPRAS 0.462 -0.094 -0.056 0.060 -6.281
Edition 0.119 -0.056 0.022 0.249 -4.791
Sector_Agriculture 0.125 -0.034 0.234 -0.236 0.191
Sector_Construction 0.214 0.109 0.063 -0.214 1.427
Sector_Industry 0.831 -0.049 -0.141 0.037 1.352
Sector_Services 0.005 0.115 0.170 0.238 4.925
Sex_Female 0.196 0.079 0.199 -0.077 0.590
Years_<= 35 yearsState_AC 0.3730.021 -0.135-0.063 0.231-0.024 0.132-0.155 0.482-0.965
Years_>= 56 yearsState_AL 0.3140.113 0.062-0.009 -0.054-0.021 0.1550.163 -0.705-5.372
State_AM 0.188 0.106 0.346 -0.057 0.019
State_AP 0.207 0.085 0.038 0.101 1.193
State_BA -0.229 -0.024 -0.145 0.019 -0.197
State_CE -0.378 0.090 -0.048 0.139 0.596
State_DF -0.070 0.014 -0.066 0.074 -0.992
State_ES -0.384 -0.139 0.030 0.061 -0.267
State_GO 0.652 -0.023 -0.065 -0.147 0.927
State_MA 0.486 0.058 -0.296 0.015 -0.606
State_MG 0.146 0.022 -0.095 0.217 0.693
State_MS 0.564 -0.034 0.020 0.063 -0.350
State_MT 0.064 0.061 -0.057 0.219 0.562
State_PA 0.255 0.009 -0.036 0.124 -0.084
State_PB 0.278 0.039 0.210 0.254 0.208
State_PE 0.288 -0.124 0.087 0.006 1.983
State_PI 0.110 0.053 -0.211 0.103 -2.268
State_PR 0.377 -0.016 0.011 -0.086 1.629
State_RJ 0.875 -0.001 0.141 -0.093 -0.549
State_RN -0.047 0.041 0.014 -0.167 3.192
State_RO 0.060 -0.109 0.123 0.131 -2.513
State_RR -0.276 0.069 -0.010 -0.007 0.878
State_RS 0.061 0.060 -0.211 0.047 0.697
State_SC 0.045 -0.005 -0.012 0.004 0.479
State_SE 0.023 0.082 -0.094 -0.050 0.129
State_TO 0.015 -0.050 0.158 0.143 3.000
Years_<= 35 years 0.373 -0.135 0.231 0.132 0.482
Years_>= 56 years 0.314 0.062 -0.054 0.155 -0.705

* State information not shown in table.
Source: Elaborated by the authors.

Cad. EBAPE.BR, v. 22, nº 1, Rio de Janeiro, e2022-0273, 2024 20-20

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