The role of local promoters in helping microentrepreneurs engage in digital business training

Abstract

Policymakers face the challenge of delivering business training programs that are high-quality, scalable, and cost-effective. This paper examines the impact of Exper-tienda, a free, smartphone-based business training application designed for Colom-bian microentrepreneurs. Using a randomised controlled trial (RCT) and leveraging local promoters from nearby universities, we evaluated the program's uptake and its effects on business practices, financial inclusion, and formalization. The study involved 994 microentrepreneurs across 10 Colombian cities, with data collected through administrative records and follow-up surveys one year after the intervention. The intervention increased app take-up by 3.97 percentage points, with no evidence of spillover effects across geographical boundaries. However, usage data reveals that the program struggled to engage users, as evidenced by low levels of interaction with the course. Moreover, we found no significant impacts on financial inclusion, formalization, business practices, or other key business outcomes. A high and unexpected attrition rate limited our ability to detect small effects, which are likely given the low levels of interaction with the app. This study is among the first to evaluate a mobile-based training intervention aimed at established microentrepreneurs who lack direct connections to the implementing organisation, providing important insights for the design and implementation of scalable digital training solutions.

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Eurasian Business Review
https://doi.org/10.1007/s40821-025-00293-y
REGULAR ARTICLE
The role oflocal promoters inhelping microentrepreneurs
engage indigital business training
PaulRodríguez‑Lesmes1 · LuisH.Gutiérrez1 ·
JuanCarlosUrueña‑Mejía1,5 · AndrésFelipeOrtiz2,3·
IvánDaríoMedinaRojas2 · MauricioRomero4
Received: 9 March 2024 / Revised: 6 December 2024 / Accepted: 16 January 2025
© The Author(s) 2025
Abstract
Policymakers face the challenge of delivering business training programs that are
high-quality, scalable, and cost-effective. This paper examines the impact of Exper-
tienda, a free, smartphone-based business training application designed for Colom-
bian microentrepreneurs. Using a randomised controlled trial (RCT) and leveraging
local promoters from nearby universities, we evaluated the program’s uptake and
its effects on business practices, financial inclusion, and formalization. The study
involved 994 microentrepreneurs across 10 Colombian cities, with data collected
through administrative records and follow-up surveys one year after the intervention.
The intervention increased app take-up by 3.97 percentage points, with no evidence
of spillover effects across geographical boundaries. However, usage data reveals that
the program struggled to engage users, as evidenced by low levels of interaction
with the course. Moreover, we found no significant impacts on financial inclusion,
formalization, business practices, or other key business outcomes. A high and unex-
pected attrition rate limited our ability to detect small effects, which are likely given
the low levels of interaction with the app. This study is among the first to evalu-
ate a mobile-based training intervention aimed at established microentrepreneurs
who lack direct connections to the implementing organisation, providing important
insights for the design and implementation of scalable digital training solutions.
Keywords Financial inclusion· Business practices· Formality· Digital training·
Microbusiness
JEL Classification C93· D22· O10· O17
Extended author information available on the last page of the article

Eurasian Business Review
1 Introduction
Microfirms are ubiquitous in developing economies, making them a primary focus
for policymakers, international financial organizations like the World Bank and
IADB, non-governmental organizations, and academics (Woodruff, 2018). These
firms often face significant barriers to growth, such as limited access to capital,
inefficient business practices, and low productivity. Moreover, they tend to gener-
ate low-quality jobs, contributing to broader socioeconomic challenges. To address
these issues, a common policy response has been the provision of training programs
aimed at improving the productivity and management capabilities of these micro-
firms (Bruhn et al., 2018; McKenzie, 2021; McKenzie & Woodruff, 2014; Wood-
ruff, 2018).
Historically, business training programs have taken three main forms. The first
and most common are standard training courses, such as those offered by the Inter-
national Labour Organization (ILO) under its Start and Improve Your Business pro-
gram. These programs focus on basic business skills, providing structured curricula
to participants. A second approach integrates mentorship from experienced entre-
preneurs or includes peer-to-peer interactions and personalized business consulting
(Anderson & McKenzie, 2022; Brooks etal., 2018; Bruhn etal., 2018; Dalton etal.,
2021; Fafchamps & Quinn, 2017; Iacovone et al., 2022). More recently, a third
approach has emerged, focusing on psychological training to enhance participants’
personal initiative, aiming to instil proactive behaviours and long-term goal setting
(Campos etal., 2017; Eller etal., 2022).1
Despite their potential, scaling these programs remains a significant challenge
due to high costs and low participant engagement. One promising alternative is the
use of telecommunications technologies to deliver training more affordably and at
scale. For instance, business owners can receive business tips and customized advice
via SMS or mobile applications (McKenzie, 2021). While mobile-based interven-
tions can lower costs, they often suffer from low take-up due to various barriers.
Microentrepreneurs frequently cite lack of time, low motivation, and distrust in
external programs as key reasons for their reluctance to engage with training content
(Woodruff, 2018).
In this context, the use of local promoters presents a promising solution to over-
come these barriers. Local promoters, such as undergraduate or recently graduated
students from nearby universities, possess valuable knowledge of the community
and can build trust more effectively than external agents (Hussam et al., 2022).
Their familiarity with the local context enables them to address the specific con-
cerns and needs of microentrepreneurs, fostering a sense of security and legitimacy
(Adams & Sandarupa, 2021; Kolavalli, 2023). Furthermore, local promoters can
provide hands-on support in installing and using the training application, reducing
the technological barriers that often hinder participation. By leveraging their social
1 Early assessments of the effectiveness of traditional training courses were unfavourable (McKenzie &
Woodruff, 2014; Woodruff, 2018) More recently, McKenzie (2021) and McKenzie etal. (2021) present a
more positive nuance view of their effectiveness.

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and geographical proximity, local promoters can serve as a critical link between the
program and its target audience, potentially boosting take-up rates significantly.
Our research explores this approach by implementing a local-promoters-based
strategy to install and register in Expertienda, a smartphone application delivering
short, interactive business training lessons. The lessons cover key topics, including
business management, customer service, financial health, and marketing and sales.
This unassisted remote learning course was designed to be free and easily acces-
sible, but its success depends on achieving high adoption and sustained engagement
among microentrepreneurs.
This study addresses three main objectives. First, it investigates whether engag-
ing local promoters can effectively increase the take-up of Expertienda. Second,
it examines the presence of spillover effects, testing whether the app’s adoption
spreads more widely in areas with higher treatment density. Third, it assesses the
app’s impact on key business outcomes, such as financial inclusion, formalization,
and the adoption of improved business practices.
To achieve these objectives, we conducted a randomised control trial (RCT)
involving 994 microentrepreneurs across 10 Colombian cities. The intervention, car-
ried out in 2021, was followed by surveys and administrative data collection one
year later. The study design leverages the geographical proximity of treated and
control units to measure potential spillovers and the reinforcement effects of local
networks.
Our research contributes to the entrepreneurship literature in several ways. First,
it evaluates the effectiveness of low-cost, mobile-based training interventions for
microentrepreneurs, a relatively unexplored area. Unlike previous studies target-
ing low-income populations or microfinance clients (e.g., (Attanasio etal., 2019;
Moreno Sánchez et al., 2018)), our study focuses on more established microen-
trepreneurs with higher income and education levels. This distinction allows us to
assess the scalability and applicability of mobile training in a different demographic
context. Our research is also different from Estefan etal. (2023), whose interven-
tion is directed to microentrepreneurs contractually linked to a franchise where
standardisation and training rules can be imposed; and to Davies etal. (2024) who
conducted a training program based on traditional classes (i.e., not microlearning
or other approaches) but delivered through online video conferencing. To the best
of our knowledge, this is one of the first research of conducting an RCT with an
application targeting established microentrepreneurs without a direct link with the
implementing party apart from geographical proximity.
Second, our study is one of the first to explicitly incorporate mechanisms to detect
geographical spillovers in the adoption of digital training. By varying the intensity
of treatment across different areas, we test whether non-participating businesses gain
indirect exposure to the app and its benefits. Previous research on regulatory compli-
ance (DeAndrade etal., 2013) found no evidence of spillovers from enforcement
visits, but we hypothesize that ‘positive’ interventions, like digital training, might
foster greater diffusion through social networks.
Finally, our study is related to the broader literature on the effectiveness of busi-
ness training programs in improving firm outcomes. Existing evidence suggests that
adopting better business practices can enhance firm performance, expand customer

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bases, and improve access to financial services (Campos etal., 2017; McKenzie &
Woodruff, 2017). Unfortunately, an unexpectedly high attrition rate, particularly
driven by shutdowns following COVID-19, allows us to detect only large impacts in
terms of firms’ outcomes.
The remainder of the paper is organized as follows. Section2 introduces the theo-
retical framework and describes the training program. Section3 outlines the inter-
vention. Section 4 presents the experimental design and empirical strategy. Sec-
tion5 presents the main findings, and Sect.6 concludes.
2 Context
2.1 The Expertienda application
Microfirm owners often report limited interest or availability for traditional training
programs, coupled with low motivation and a reluctance to pay for such services
(Woodruff, 2018). Given these barriers, designing accessible and engaging learning-
centric courses is crucial. Effective strategies include: (i) incorporating customized
and adaptive content tailored to users’ existing knowledge, (ii) delivering concise,
easily digestible lessons, and (iii) employing gamification techniques to maintain
user engagement.2
The development of Expertienda was spearheaded by Fundación Capital, also
known for its work on the LISTA app (Attanasio etal., 2019).3 The application is
freely accessible on the Google Play Store, ensuring broad availability. The entire
course can be completed in approximately 1.5h, consisting of sessions under five
minutes, featuring text and video content.
The curriculum is divided into four core modules: Business Management, Cus-
tomer Service, Financial Health, and Marketing and Sales. Each module covers spe-
cific topics through multiple sessions. Additionally, Expertienda includes tools such
as a wage and legal payment calculator and a directory of suppliers commonly used
by microbusinesses.
2.1.1 Development process
The creation of Expertienda followed a structured four-step approach:
1. Benchmarking: Analysing existing online and traditional business training pro-
grams.
2 Gamification is the attempt to boost systems, services, organisations, and activities by getting similar
experiences to those experienced when playing games to motivate and engage. Apart from school-level
applications, it has effectively boosted entrepreneurship among high school students (Lafortune et al.,
2022) There are no studies in the context of firm owners.
3 See https:// funda cionc apital. org/.

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2. Ethnographic Research: Complementing quantitative surveys to understand the
training needs, technological capabilities, and digital literacy of the target audi-
ence.
3. Co-creation Methodology: Collaborative workshops involving designers,
researchers, and entrepreneurs to refine course content.
4. Digital Solution Development: Finalizing the app’s functionality and user experi-
ence.
Baseline and ethnographic studies identified that most target users relied on Android
smartphones with basic internet connectivity, with limited access to other devices
such as iPhones or laptops. Consequently, Expertienda was optimized for Android
and made available on the Google Play Store.
2.1.2 Course content
Table 1 outlines the course modules, detailing their topics, session structure, and
related business concepts. This holistic design ensures that users acquire practical
knowledge and tools to improve their business practices, enhance customer service,
and achieve greater financial inclusion.
2.2 Theoretical framework
Formal, in-person business training has demonstrated effectiveness in improv-
ing the performance of small firms in low- and middle-income countries (McKen-
zie & Woodruff, 2014). However, the potential of its lower-cost alternative-digital
training-remains less explored, although emerging evidence from various sectors is
promising (Estefan etal., 2023; Chang, 2016). Digital training offers scalability and
flexibility, but understanding its efficacy in enhancing business outcomes for micro-
entrepreneurs is crucial.
A significant challenge with traditional educational interventions is the lack of
interest and engagement among microentrepreneurs. In our sample, fewer than 20%
of baseline respondents had participated in any training over the past two years,
and 41% expressed no interest in receiving training. This highlights a critical bar-
rier: traditional training often fails to align with the immediate and practical needs
of business owners. However, evidence suggests that microentrepreneurs are more
inclined to adopt training when it leverages localized, self-developed knowledge and
provides rapid, actionable insights (Kelliher etal., 2014; Reinl & Kelliher, 2014).
Hypothesis 1: the intervention utilising local promoters increases Expertienda
usage.
Entrepreneurs frequently occupy central positions within their social networks,
enabling them to leverage the flow of ideas, knowledge, and capital (Stuart & Soren-
son, 2005). Technology diffusion literature indicates that social networks facilitate
the spread of innovations (Young, 2006; Acemoglu etal., 2011). In this study, we
focus on geographical proximity as the simplest form of social networking (Carlino

Eurasian Business Review
Table 1 Topics included in Expertienda and relationship with potential outcomes
Module Topics Sessions Related concept
Module 1: Business management Why do some businesses grow more than others? Implement planning, organization, direction, and control Business practices
Apply the cycle: what is done, how it’s done, ensure it’s done,
and evaluate how it was done
What is a priority in my business? Prioritizing tasks based on urgency and importance
Set short, medium, and long-term objectives
Keep detailed financial records (financial status, profits, debts,
savings)
Use technology to improve efficiency
Control inventories to optimize profitability and sustainability
How to apply the administrative process? Efficiently manage suppliers (producers, wholesalers, retailers)
Select reliable and beneficial suppliers for the business
Module 2: Customer Service Creating competitive customer service strategies Improve customer experience Formal sector
Actively listen and advise customers
Develop service strategies for employees and workers
Implement customer service standards (accessibility, accurate
information, transparency, kindness, efficiency)
Handle negative aspects constructively (learn from mistakes,
find solutions)
Identify loyalty opportunities
Practice assertive communication
Module 3: Financial Health Making sound financial decisions Carefully evaluate the need for loans (required amount, interest
rates, payment terms)
Financial inclusion
Encourage savings for better financial control and access to
banking products

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Table 1 (continued)
Module Topics Sessions Related concept
Use digital tools for financial management (digital wallets and
e-money)
Implement digital payments to increase sales and security
Maintaining effective accounting Record daily operations and keep receipts Business practices
Follow the accounting cycle and perform periodic balance
sheets
Keep payments and financial obligations up to date
How to improve business profitability? Calculate and analyze profitability regularly
Make informed decisions based on financial data
Develop an investment plan considering amount, rate of return,
time, and requirements
Module 4: Marketing and Sales Ideas to promote your Business Build your brand, delight your customers, design innovative
promotions, host events for your community, and offer per-
sonalized recommendations for promotions and new products
Business practices
Social network: Whatsapp, Facebook, among others
Design a marketing plan with goals and objectives

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& Kerr, 2015; Lengyel etal., 2020).4 However, even within these networks, infor-
mation flow can be limited. For instance, shop owners may remain unaware of rel-
evant activities in neighbouring businesses (DeAndrade etal., 2013).
Hypothesis 2: Course take-up increases with the geographic density of the
treatment.
Business training programs frequently aim to enhance business performance
by promoting better business practices, increasing formalization, and improving
financial inclusion. Expertienda was specifically designed to target these areas, as
reflected in its course content (see Table1).
Hypothesis 3: Expertienda’s users improve their business performance indicators.
Below, we define each of the concepts related to business performance.
2.2.1 Business practices
Managerial capital is a critical determinant of firm growth and a key predic-
tor of productivity disparities among organizations (Bloom etal., 2010; Bloom &
VanReenen, 2010; Bruhn etal., 2010). For microfirms, enhanced managerial prac-
tices can help overcome constraints such as limited access to financing (Bruhn etal.,
2010). Empirical studies show that the adoption of effective business practices-
such as financial tracking, inventory management, and goal-setting-correlates with
improved productivity and sales (Bloom & VanReenen, 2007; Anderson & McKen-
zie, 2022; Campos etal., 2017; Fabling & Grimes, 2007; Forth & Bryson, 2019;
McKenzie & Woodruff, 2017; Maes etal., 2005; McKenzie & Puerto, 2021).
Given this, we anticipate that microestablishments utilizing Expertienda will
adopt a higher number of effective business practices.
2.2.2 Financial inclusion
Access to financial products is strongly linked to firm performance (Beck & Demir-
güç-Kunt, 2006; Fowowe, 2017; Gorodnichenko & Schnitzer, 2013; Levine, 2005;
Nizam etal., 2021; Van etal., 2021; Wellalage & Locke, 2016). Yet, there is no uni-
versal agreement on which products-savings, credit, or insurance-constitute finan-
cial inclusion. Most studies measure inclusion through composite indexes reflecting
product availability, knowledge, and usage (Demirgüç-Kunt & Klapper, 2013; Bara-
jas etal., 2020; Girón etal., 2021; Nuzzo & Piermattei, 2020). Barriers to financial
product adoption often stem from supply-side constraints like information asym-
metries (Stiglitz & Weiss, 1981, 1992) or demand-side perceptions regarding cost
and benefits (Nuzzo & Piermattei, 2020; Salignac etal., 2016).
With rapid advancements in mobile banking and digital wallets, the scope of
financial inclusion has expanded, providing new opportunities for microentrepre-
neurs. We expect that Expertienda users will be more inclined to utilize financial
instruments, particularly mobile money.
4 We also measured social links among microentrepreneurs. However, as it is a sample and not a census,
we cannot compute position indicators such as network centrality.

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2.2.3 Formality
A business is considered formal if it complies with all regulatory requirements.
However, degrees of informality vary widely (Perry, 2007; Trebilcock, 2005; Ulys-
sea, 2018; Gutierrez & Rodriguez-Lesmes, 2023). Following Gutierrez and Rodri-
guez-Lesmes (2023), we define extensive informal firms as those which do not com-
ply with the registry of the business with both commercial and tax authorities. In
contrast, intensive informal firms comply with such requirements but hire workers
without lawful obligations.
Expertienda aims to demystify formalization, highlighting its benefits and guid-
ing users through compliance procedures. By improving awareness and reducing
barriers to formalization, we anticipate enhancing formality among participating
firms.
3 Intervention
3.1 Target population
The intervention targeted microbusinesses in ten neighbourhoods near the Minuto
de Dios University (Uniminuto) campuses. Uniminuto is a decentralized private
institution focused on serving low- and middle-income students. The selected cities-
Barranquilla, Bello, Bogotá, Bucaramanga, Girardot, Ibagué, Neiva, Pereira, Soa-
cha, and Zipaquirá-represent a diverse urban population, with each city having at
least 100,000 residents.
The intervention began with an economic census of microbusinesses in these
neighbourhoods. This census allowed us to collect a representative sample and ran-
domize the intervention, enabling the estimation of spillover effects. Businesses
whose operations or focus made the Expertienda content less relevant were excluded
from the study.5
3.2 Baseline census andsurvey
Baseline data collection was conducted in November 2019. Using detailed city
maps, we identified polygons containing at least 300 microbusinesses per neighbour-
hood, as estimated via Google Maps. The baseline survey covered all businesses
within these polygons, identifying 3,194 establishments. Around half of these busi-
nesses participated in a more comprehensive survey. Respondents did not receive a
financial incentive for participation in the study.
The surveyed businesses were located in a mix of commercial zones and resi-
dential areas characterized by low- to medium-income households. Most businesses
were small, family-owned operations with one or two employees (often including
5 Exclusions included community pharmacies, franchises, travel agencies, shops selling white goods
(e.g., refrigerators, washing machines), and nightclubs.

Eurasian Business Review
the owner), reflecting a typical business model in many Latin American countries
(Ramos-Menchelli & Sverdlin-Lisker, 2023).
3.3 The treatment: promotion ofExpertienda using local promoters
The intervention aimed to encourage microbusiness owners to install and use the
Expertienda application. Local undergraduate students and recent graduates from
Uniminuto were employed as program promoters. Their community ties were
expected to mitigate trust issues, as business owners might otherwise be wary of
scams or extortion.
Each promoter was assigned to visit businesses, explain the purpose of Exper-
tienda, and assist owners in installing and registering for the app. Follow-up calls
were made 10 days later to check usage and provide further assistance if needed.
After four months, another round of follow-ups was conducted by a different group
of Uniminuto students to track progress.
The intervention, initially planned for late 2020, was postponed to April-July
2021 due to the COVID-19 pandemic.6 The randomisation process was updated
during a telephonic follow-up to ensure operational businesses were included. Ulti-
mately, the intervention sample comprised 994 microbusinesses.
3.4 Follow‑up survey
The follow-up survey took place between April and May 2022, approximately one
year after the intervention. This process involved two steps:
1. Census of local businesses to identify those in operation.
2. Reinterviewing baseline businesses and adding others to meet area-specific quo-
tas.
Survey data were complemented with administrative records from the Expertienda
backend, which provided detailed usage statistics for registered users. This allowed
us to evaluate both app installation and sustained engagement (defined as usage of at
least 5min).
3.5 Measurement ofconcepts
The intervention was designed to impact three key areas: business practices, for-
malization, and financial inclusion. Baseline and follow-up surveys measured these
areas as follows:
6 The timing of the intervention was adjusted in response to the evolving conditions caused by COVID-
19 lockdowns (Carranza etal., 2022) Appendix A details these adjustments.

Eurasian Business Review
3.5.1 Business practices
Both surveys collected data on 30 business practices through self-completion ques-
tionnaires with binary responses. For the impact analysis, we selected a subset of
these practices that were targeted in the curriculum, influenced by the co-creation
focus groups, based on their relevance and ease of adoption. Impacts were analysed
using an index derived from these variables (see Table2). We explore an alternative
index constructed with the total 30 items with similar results as those that will be
presented below.
We explore some additional characteristics that are not part of the official list of
business practices but that would indicate that firms responded to the training: using
the internet for their business operation, having social networks, or simply having a
sign that indicates the name of the business outside the premises.
3.5.2 Formality
Formality was assessed using variables related to both extensive and intensive infor-
mality. These included business and tax registration, record-keeping, and compli-
ance with labour regulations (see Table2). A simple average index was used for
interpretative ease, though alternative methods such as principal component analysis
yielded consistent results.
3.5.3 Financial inclusion
Financial inclusion metrics extended beyond traditional indicators (bank accounts,
loans, insurance) to include knowledge and use of electronic wallets. These digital
tools have lowered barriers to financial participation, requiring only a mobile phone
number for transactions. An index summarizing these variables provided a compre-
hensive measure of financial inclusion.
3.5.4 Total score
A composite score averaging the three indexes was used as the primary outcome
variable. Additional variables, such as profits and client numbers, were analysed but
deemed less likely to change within the study’s time frame.
3.5.5 Final outcomes
While business practices could be considered as intermediate outcomes, ideally
those changes should be reflected in either profits or firm growth. We have sev-
eral proxy variables for this: the number of clients and firm workers observed by
enumerators at the time of the visit, self-reported profits, and whether the firm per-
formed some sort of investment (e.g., painting the premises).
We consider it unlikely that these final outcomes could be affected in the short
run.

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4 Experimental design
This randomised controlled trial (RCT) was designed to estimate the causal effects
of two factors: (i) the promotion effort on the uptake of the course, including both
direct and indirect effects, and (ii) the impact of the course on the targeted outcomes.
Below, we detail the randomization procedure and the empirical strategy.
4.1 Randomisation
In Latin America, cities are densely populated, and walking remains a prevalent
mode of transportation for daily activities, underscoring the importance of neighbor-
hoods in urban life (Loukaitou-Sideris, 2020). This context suggests that interven-
tions targeting microestablishments could propagate through peer interactions, espe-
cially when facilitated by a freely accessible mobile application compatible with
Table 2 Components of indicator variables
Note: The table was computed over the baseline sample (N=994) in ten cities of Colombia
Indicator Variable Mean at
baseline
(%)
Formality 0.540
Firms reports to be formal 74.7
Keeps accounting records 21.3
Business registry 74.0
Tax registry 79.5
Has the required approvals to operate 54.0
All of the workers received social insurance benefits 20.7
Business practices 0.572
With your records, can you know your current amount of cash 69.4
Do you keep records of all of your transactions 64.8
Have you visited your competitors to know their prices? 36.7
Have you attracted clients with special sales? 56.3
Have you tried to bargain prices with providers 59.0
Financial inclusion 0.175
Separate account for the business 15.6
Has some type of insurance 13.7
Has savings 20.9
Has any loan 17.4
Has a loan with a bank 8.3
Knows about electronic wallets 25.8
Use an electronic wallet 12.9
Total score 0.425

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most devices.7 Such features could significantly streamline promotional efforts by
governments, trade associations, or other organizations.
The randomisation procedure involved three key steps:
4.1.1 Step 1: Cluster formation
The ten neighbourhoods were split into clusters of shops (146 clusters) based on
geographical proximity (Fig. 1 shows an example of 2 cities), each of them of
around 50 ms, with around 8 microestablishments on average per cluster.8 The
number of clusters (and their size) was based on power calculations of a multilevel
design. The minimum detectable difference on the Total Score, with a 0.80 power
at the 95% confidence level, with three arms of 49 clusters of 8 shops each, was of
0.05-
−
0.31 standard deviations. Such calculations were based on a mean of 0.42,
a standard deviation of 0.16, and with intra-cluster correlation of 0.19, the values
observed at the baseline. In the discussion section, we present details on how the
power is affected by attrition.9
4.1.2 Step 2: Treatment allocation
In the second step, the treatment allocation at the individual level was designed to
ensure that we could have treated [control] units with several treated neighbours
and treated [control] units with few control neighbours. This way, it is possible to
disentangle direct and indirect effects based on location. The design is similar to
Sinclair et al. (2012).10 We assume that spillover effects if exist, would be small
and restricted to just one of a few blocks. This is based on the following observa-
tion: 64% of the respondent said that they do not have regular contact with any other
entrepreneur in the area, 22% with only one, 8% with two, and the remainder 6%
with three or more.
8 We adapted the clustering script by Wesley (2013). The algorithm is based on the coordinates of each
shop and the number of desired shops per cluster.
9 The calculation was done with the command clustersampi in Stata 17 (Hemming & Marsh, 2013).
10 The levels in their experiment are the neighbourhood, the household, and the individual. The authors’
non-interference assumption is that the treatment assignments of units in other neighbourhoods do not
matter. What determines which potential outcome is revealed is a combination of three things: (1) An
individual’s treatment assignment, (2) The treatment assignment of his or her housemate, (3) The treat-
ment assignment of others in the neighbourhood.
7 Spillovers arise whenever one unit is affected by the treatment status of another unit. This could be
because of the ‘contamination’ of the control group (i.e., control units receive the treatment) or because
equilibrium effects occur (ex., the growing sales of the treated store affect the income of the control store
due to demand displacement). The assumption that there are no spillovers is known as the non-interfer-
ence assumption, part of the Stable Unit Treatment Value Assumption (or SUTVA) usually invoked in
causal inference. In our exercise, ‘contaminated’ control units would not be receiving the same treatment,
rather a word-of-mouth promotion, but still this could violate SUTVA and for this reason our design
carefully allocated the treatment to minimize concerns while measuring this propagation channel.

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In practice, the clusters were randomly assigned to three potential expositions
to the treatment.11 In the first arm, no units were treated (all control, N = 166
microestablishments/22 clusters), in the second, only 50% were treated (half-half,
N=567/83), and in the third all units were treated (all treated, N=280/41). Given
this, the treatment at the individual level was randomly assigned for the second
arm.12 In the example of our diagram, cluster 1 is a all treated, cluster 2 a half-half,
and cluster 3 a all control. As a result, microestablishments A and B are selected
for treatment, and among C and D, the last one is randomly selected to be treated as
well. Microestablishments C, E, and F are control units and were not visited by the
field team promoting Expertienda.
4.1.3 Step 3: Exposure classification
Each microestablishment was classified based on its exposure to treated neighbours,
defined by a 50-metre buffer:
• Treated in high intensity (TH): Unit received treatment, and at least 50% of their
neighbours received treatment.
Fig. 1 Randomisation process: Example in two cities. Note: The maps present Ibagué on the left side and
Girardot on the right side. The stars show the treated units, in circles the control units, and the different
colours show the belonging to a different cluster
12 The same randomisation script was following, with 200 repetitions, similar blocks, and the same
covariates but defined at shop-level.
11 The randomisation was based on the command randomisation in Stata 17, blocking by region of the
country (South-Centre, North-West) and on the size shop. It runs 1,000 versions, from which it chooses
the one with the best balance across covariates (the average per cluster of the three indicators, size of the
shop (perceived area), education level of the owner, type of businesses (convenience stores, food and
bars, beauty salons, and alike services, and others), commercial density of the street).

Eurasian Business Review
• Treated in low intensity (TL): Unit received treatment, and less than 50% of their
neighbours received treatment.
• Control in high intensity (CH): Unit did not received treatment, but at least 50%
of their neighbours received treatment.
• Control in low intensity (CL): Unit did not receive treatment, and less than 50%
of their neighbours received treatment (pure control group).
Appendix Figure A1 presents a simplified diagram of six shops to illustrate the pro-
cedure. In Fig.1, which depicts the two cities, treated units are marked with stars,
clusters are distinguished by different colours, and the exposure classification is
shown for select units to demonstrate the outcomes of the design.
Notice that if the effects for TH and TL groups are equivalent, it suggests no rein-
forcement among treated units. Similarly, no effect for the CH group would indicate
minimal contamination of controls. When these conditions hold, a simple treated-
versus-control analysis is valid.
4.2 Empirical specification
We estimate the impact of incentivising entrepreneurs to install Expertienda by esti-
mating the following Eqs.(1 and 2).
In both equations,
Yij
denotes the outcome of interest for microestablishment i
located in block j. In Eq. (1), Treated indicates if the microestablishment was
selected for treatment. Instead, Eq.(2) considers the intensity of treatment in the
surrounding area as defined in Sect.3.1.13 In both equations,
Y(BL)
ij
corresponds to the
measurement at the baseline of the outcome. The matrix
Xij
represents a vector of
control variables, including gender, education level, a dummy for internet usage for
business, a dummy for having premises in a commercial district, and fixed effects of
city and economic activity (see TableD1 for further explanation of the variables).
Finally,
𝜖ij
corresponds to the error term. In both cases, standard errors are clustered
at the geographical cluster level.
Equation(1) tells us the individual treatment assignment. Instead, Eq.(2) allows
us to compare if there is a differential effect depending on the treatment status of
their neighbourhoods, as explained above.
When analysing Expertienda outcomes, such as registering as a user in the appli-
cation or actual usage time in minutes, the estimates reflect the Average Treatment
Effect on the Treated (ATT). However, for final outcomes, the estimates correspond
to an Intention-to-Treat (ITT) framework, as the majority of microentrepreneurs did
(1)
Y
ij =𝛽1Treatedij +𝛽2Y
(BL)
ij
+Xij𝜸1+𝜖1
i
(2)
Y
ij =𝛽3THij +𝛽4TLij +𝛽5CHij +𝛽6Y
(BL)
ij
+Xij𝜸2+𝜖2
i
13 As explained before, the High/Low area is defined for each unit i, using a buffer of 50ms. It might
match with the geographical cluster j, but this is not always the case.

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not install the application. To evaluate the impact of Expertienda on the primary
outcomes, we use a Local Average Treatment Effect (LATE) estimation, employing
an Instrumental Variable (IV) approach. In this approach, usage is instrumented by
treatment assignment, capturing the effect on those who received the intervention
and were successfully persuaded by the facilitators to install the application.
Attrition corrections are essential in this study to address the high dropout rate
that is expect for work with microbusinesses, which can bias the results and limit
the validity of the conclusions. When participants drop out in non-random ways,
the remaining sample may no longer be representative of the population, leading to
distorted estimates of the treatment effects. To mitigate this issue, we use two key
methods: Inverse Probability Weighting (IPW) and Lee Bounds Estimation (Lee,
2009). IPW adjusts the analysis by assigning weights to the observations based on
their likelihood of remaining in the study, thereby compensating for the missing
data. Lee Bounds, on the other hand, provide a range of possible treatment effects
under optimistic and pessimistic assumptions about the missing data’s relationship
with the outcomes. By applying these corrections, we aim to produce more reliable
and robust estimates of the treatment effects, accounting for the challenges posed by
attrition.
4.3 Qualitative analysis
The decision to enrol in the course can be analysed through the lens of Davis (1989)
Technology Acceptance Model (TAM), which posits that individuals are more likely
to adopt a technology if they perceive it to be beneficial, easy to use, and afford-
able. For small business entrepreneurs, uncertainty about these factors often leads to
resistance (Suhartanto & Leo, 2018). Additionally, individual characteristics, such
as educational background and cultural constraints, can further heighten resistance
to adopting new technologies (Anggadwita etal., 2015).
To investigate these dynamics further, the project incorporated an ethnographic
study, which examines social interactions, behaviours, and perceptions within
groups, organisations, and communities (Brewer, 2000). To gain insights into appli-
cation usage, we conducted in-depth interviews with treated entrepreneurs, includ-
ing both those who adopted the technology and those who did not. The sample com-
prised 40 microentrepreneurs from Bogotá, Soacha, Zipaquirá, Girardot, and Ibagué.
Appendix C1 provides the guiding questions used in these interviews.
5 Results
5.1 Baseline characteristics andbalance
The randomisation process successfully achieved balance across a wide range of
baseline characteristics. Table3 summarises baseline differences, examining indi-
vidual assignment to Expertienda, assignment to the three randomisation arms, and

Eurasian Business Review
the constructed high/low exposure groups. Panel A presents results for the entire
baseline sample, while Panel B focuses on the reinterviewed sample (the next sub-
section describes the attrition process). For the vast majority of variables, no signifi-
cant differences are observed.
Key characteristics of the businesses (see Table3) include: 60% female own-
ership, 34% of owners holding tertiary education degrees (either professional or
vocational), and only 6% with prior entrepreneurial experience. The predominant
business types were convenience stores (31%), small restaurants (31%), and beauty/
health services (15%). Approximately 37% operated on commercial streets, with
premises averaging 5ms in width and 20 square meters in area. While nearly all
businesses owned smartphones, only 50% used the internet for business purposes
before the COVID-19 pandemic.14
Table4 extends this analysis to the outcomes outlined in the conceptual frame-
work, again showing no substantial differences across groups. However, control
units in high-intensity areas tend to have smaller premises. To account for this, these
characteristics will be included as controls in our main specifications.
5.2 Attrition
Attrition rates in studies of microfirms are typically high. First, microfirms often
have low survival rates (Cader & Leatherman, 2011). Second, even if firms remain
operational, they may relocate outside the study’s geographical boundaries. Third,
firm owners may simply refuse to participate in follow-up interviews. Based on
results from a similar study in Brazil, we anticipated a re-interview rate of 50–60%
(DeAndrade etal., 2013).
However, the emergence of COVID-19 significantly impacted this expectation.
While the intervention began after most mobility restrictions were in place, the
study was conducted during the economic recovery, and the lingering effects of the
lockdowns likely disrupted many businesses.
Figure2 illustrates that, from the original 994 businesses, only 228 were success-
fully re-interviewed, resulting in a re-interview rate of just 22.9%.
We investigate whether firm survival and survey responses were influenced by the
intervention. Columns 1 and 2 of Table5 show no evidence of differential response
rates between treated and control units. The coefficient in column 1 indicates that
fewer treated units were surveyed at follow-up, but the difference is not large enough
to be significant at the 10% level. This suggests that there is no differential attrition
due to the treatment.
Columns 3 and 4 examine whether firms were untraceable during the follow-
up census. Of the original 994 firms, enumerators located 536 during the follow-
up microestablishment census, which involved listing all businesses in the area.
This implies that 308 firms declined to participate in the follow-up survey. These
14 Gutiérrez etal. (2020, 2023) and RodriguezLesmes etal. (2020) provide further details about the
surveys. Urueña-Mejía etal. (2023) compares the microentrepreneurs’ characteristics to those found in
national representative studies.

Eurasian Business Review
Table 3 Balance on characteristics of the businesses measured at baseline
Outcome variable (1) (2) (3) (4) (5) (6) (7) (8)
Mean N Obs/ Cluster Treatment Arm 2 Arm 3 TH TL CH
Panel A. Entire baseline sample
 Owner has tertiary education 0.34 994
−
0.005 0.030
−
0.037
−
0.010 0.043 0.019
146 (0.030) (0.040) (0.048) (0.035) (0.049) (0.046)
 Female owner 0.60 994
−
0.041
−
0.020
−
0.061
−
0.028
−
0.035 0.028
146 (0.037) (0.044) (0.052) (0.044) (0.049) (0.052)
 Located in a commercial zone 0.37 994 0.007
−
0.013 0.079 0.021 0.050 0.051
146 (0.061) (0.108) (0.129) (0.082) (0.079) (0.072)
 Activity 1: convenience store 0.31 994
−
0.014
−
0.048 0.007
−
0.041
−
0.007
−
0.048
146 (0.033) (0.040) (0.053) (0.043) (0.045) (0.044)
 Activity 2: prepared food 0.31 994
−
0.034
−
0.069
−
0.077
−
0.068
−
0.090
−
0.095**
146 (0.034) (0.054) (0.061) (0.042) (0.055) (0.045)
 Activity 3: health, beauty, other services 0.15 994 0.039 0.104*** 0.081* 0.062* 0.047 0.048
146 (0.025) (0.036) (0.041) (0.033) (0.047) (0.042)
 Use internet for business 0.50 994 0.043 0.052 0.041 0.050 0.094* 0.043
146 (0.034) (0.042) (0.053) (0.042) (0.056) (0.049)
 Number of workers 1.56 994 0.001 0.119
−
0.003
−
0.060 0.016
−
0.106
146 (0.106) (0.154) (0.199) (0.149) (0.157) (0.128)
 Large commercial space 0.42 994 0.031
−
0.010 0.036
−
0.006
−
0.021
−
0.100*
146 (0.037) (0.055) (0.066) (0.050) (0.051) (0.051)
 Total depth of commercial space (m) 5.66 994
−
0.021 0.016 0.102
−
0.418
−
0.694
−
1.141**
146 (0.487) (0.738) (1.020) (0.640) (0.677) (0.493)
 Total width of commercial space (m) 4.70 994
−
0.116 0.467 0.365
−
0.081
−
0.466
−
0.138
146 (0.352) (0.500) (0.731) (0.464) (0.393) (0.472)

Eurasian Business Review
Table 3 (continued)
Outcome variable (1) (2) (3) (4) (5) (6) (7) (8)
Mean N Obs/ Cluster Treatment Arm 2 Arm 3 TH TL CH
 Owner born in the same municipality 0.66 994
−
0.006
−
0.009
−
0.002
−
0.001
−
0.004 0.012
146 (0.033) (0.042) (0.051) (0.044) (0.055) (0.055)
Panel B. Reinterviewed sample (microestablishments that were interviewed at follow-up)
 Owner has tertiary education 0.23 228 0.111* 0.080 0.019 0.044 0.046 0.021
110 (0.065) (0.058) (0.066) (0.045) (0.061) (0.050)
 Female owner 0.54 228 0.087
−
0.012
−
0.073
−
0.038
−
0.024 0.031
110 (0.075) (0.042) (0.049) (0.039) (0.052) (0.053)
 Located in a commercial zone 0.57 228 0.043
−
0.089 0.206 0.111 0.107 0.051
110 (0.095) (0.124) (0.135) (0.090) (0.092) (0.082)
 Activity 1: convenience store 0.35 228
−
0.011 0.017 0.090 0.039 0.044
−
0.002
110 (0.071) (0.048) (0.062) (0.042) (0.050) (0.049)
 Activity 2: prepared food 0.18 228 0.036
−
0.026
−
0.039
−
0.023
−
0.076
−
0.062
110 (0.054) (0.054) (0.059) (0.041) (0.057) (0.044)
 Activity 3: health, beauty, other services 0.21 228
−
0.084 0.022
−
0.011
−
0.025
−
0.006
−
0.026
110 (0.058) (0.037) (0.042) (0.030) (0.048) (0.039)
 Use internet for business 0.54 228
−
0.119
−
0.018
−
0.075
−
0.060 0.027
−
0.048
110 (0.076) (0.057) (0.068) (0.045) (0.065) (0.055)
 Number of workers 2.15 228
−
0.756*
−
0.001
−
0.070
−
0.696*
−
1.167**
−
0.049
110 (0.440) (0.405) (0.421) (0.397) (0.448) (0.883)
 Large commercial space 0.44 228 0.047
−
0.008 0.052 0.023
−
0.019
−
0.084
110 (0.064) (0.059) (0.073) (0.050) (0.056) (0.056)
 Total depth of commercial space (m) 6.57 222
−
0.537
−
0.811
−
0.843
−
1.415 0.395
−
1.741
110 (0.854) (1.448) (1.448) (1.052) (1.219) (1.211)

Eurasian Business Review
Table 3 (continued)
Outcome variable (1) (2) (3) (4) (5) (6) (7) (8)
Mean N Obs/ Cluster Treatment Arm 2 Arm 3 TH TL CH
 Total width of commercial space (m) 5.34 228
−
0.348
−
1.588
−
1.108
−
1.118 0.350
−
1.305
110 (0.689) (1.174) (1.245) (0.824) (1.221) (0.942)
 Owner born in the same municipality 0.70 228
−
0.031
−
0.010 0.025 0.004 0.001
−
0.008
110 (0.073) (0.045) (0.049) (0.038) (0.055) (0.057)
Note: Column 1reports the mean value of each outcome variable (listed in each row) for non-treated units. Column 2 provides the number of observations and clusters
included in the analysis, determined by the specific dependent variable. Column 3 displays the regression coefficient for the treatment variable. Columns 4 and 5 show the
differences across treatment assignment groups: Arm 1 (all treated), Arm 2 (half treated), and Arm 3 (none treated). Columns 6 to 8 present the coefficients for the fol-
lowing exposure classification categories: treated in a high-treatment area (TH), treated in a low-treatment area (TL), and non-treated in a high-treatment area (CH). The
reference group is non-treated units in low-treatment areas (CL). All models include the same control variables. Clustered standard errors (at ‘cluster’ level) are shown in
parentheses. Significance levels are indicated as follows: *0.1, **0.05, ***0.01

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columns reveal that enumerators identified fewer treated firms than control firms in
the follow-up census. However, among those located, the reinterview rate was con-
sistent across treatment and control groups (Columns 5 and 6).
Table 4 Balance on outcome variables measured at baseline
Note: Column 1 reports the mean value of each outcome variable (listed in each row) for non-treated
units. Column 2 provides the number of observations and clusters included in the analysis, determined by
the specific dependent variable. Column 3 displays the regression coefficient for the treatment variable.
Columns 4 and 5 show the differences across treatment assignment groups: Arm 1 (all treated), Arm 2
(half treated), and Arm 3 (none treated). Columns 6 to 8 present the coefficients for the following expo-
sure classification categories: treated in a high-treatment area (TH), treated in a low-treatment area (TL),
and non-treated in a high-treatment area (CH). The reference group is non-treated units in low-treatment
areas (CL). All models include the same control variables. The predicted total index is derived from a
model that explains the total index using the following variables: firm size, premises size, building type,
and owner characteristics, including age, gender, education level, personal initiative, cognitive reflection
test scores, and perseverance level. Clustered standard errors (at ‘cluster’ level) are shown in parentheses.
Significance levels are indicated as follows: *0.1, **0.05, ***0.01
Outcome variable (1) (2) (3) (4) (5) (6) (7) (8)
Mean N Obs/ Cluster Treatment Arm 2 Arm 3 TH TL CH
Panel A. Entire baseline sample
 Total index 0.42 994 0.016 0.037* 0.017 0.013 0.026
−
0.001
146 (0.013) (0.021) (0.024) (0.016) (0.022) (0.017)
 Formality index 0.51 994 0.002 0.032
−
0.007
−
0.014 0.037
−
0.008
146 (0.019) (0.030) (0.034) (0.022) (0.029) (0.028)
 Business practices
index
0.58 994 0.030 0.047 0.025 0.034 0.012
−
0.003
146 (0.021) (0.034) (0.038) (0.025) (0.034) (0.030)
 Financial inclusion
index
0.17 994 0.018 0.031* 0.033 0.019 0.031 0.009
146 (0.014) (0.019) (0.022) (0.018) (0.026) (0.022)
 Predicted total
index
0.42 994 0.002 0.005 0.008 0.004 0.002 0.004
146 (0.005) (0.007) (0.009) (0.006) (0.007) (0.006)
Panel B. Reinterviewed sample (microestablishments that were interviewed at follow-up)
 Total index 0.39 228 0.021 0.034* 0.016 0.010 0.025 0.001
110 (0.025) (0.020) (0.024) (0.016) (0.022) (0.017)
 Formality index 0.49 228 0.020 0.030
−
0.009
−
0.017 0.033
−
0.008
110 (0.039) (0.030) (0.033) (0.022) (0.029) (0.028)
 Business practices
index
0.55 228 0.005 0.043 0.026 0.033 0.016 0.002
110 (0.045) (0.033) (0.037) (0.025) (0.033) (0.029)
 Financial inclusion
index
0.16 228 0.038 0.030 0.031 0.015 0.028 0.008
110 (0.025) (0.018) (0.022) (0.018) (0.026) (0.022)
 Predicted total
index
0.42 228
−
0.003 0.005 0.008 0.004 0.002 0.004
110 (0.009) (0.007) (0.009) (0.006) (0.007) (0.006)

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The follow-up survey comprised 228 firms across 110 clusters, with an increased
intra-cluster correlation of 0.3402. On average, each treatment arm included approx-
imately 37 clusters, with two firms per cluster. Consequently, the minimum detecta-
ble effect size increased to 0.09
−
0.56 standard deviations, nearly double the original
detectable difference.
While this reduction in statistical power limits the ability to detect small treat-
ment effects on business outcomes, the finding in Columns 3 and 4 raises a potential
concern. It suggests that Expertienda may have influenced firm attrition, either by
contributing to firm closure or inducing significant changes that prevented enumera-
tors from locating the firms.15 Alternatively, there may have been selection bias in
the treatment allocation, correlated with firm mortality or transformation.
A specific field-related issue may have contributed to this outcome. In two cities-
Barranquilla and Bucaramanga-the survey firm reported an increase in extortion in
certain neighbourhoods where the treatment was implemented. This led to a higher
likelihood of firms being sold or moved away. When these two cities were excluded
from the analysis, the estimated difference was halved and became statistically insig-
nificant. Results from this reduced sample, presented in the appendix, show no sub-
stantial differences.
Building on the differential attrition discussed earlier, which may affect internal
validity, we also examine how the reinterviewed sample compares to the original
baseline sample. Differences between these samples can raise concerns about the
study’s external validity.
Table6 indicates that the reinterviewed sample consists of firms with less edu-
cated owners who are less likely to use the Internet for business purposes. These
firms are more commonly located on commercial streets, more likely to operate as
convenience stores, and tend to have smaller premises.
This pattern aligns with the impact of COVID-19 lockdowns, which permitted
convenience stores to remain operational while restricting other types of businesses
Carranza et al. (2022). Convenience stores, typically small “mom-and-pop” estab-
lishments operating from owner-occupied premises, were better positioned to with-
stand the economic shock. However, these characteristics may also make such firms
less inclined to engage with training programmes, suggesting that any observed
impacts on business outcomes likely represent a lower bound of the potential effects
in ‘normal’ circumstances.
5.3 Take‑up ofExpertienda
Table7 presents evidence showing that the intervention significantly increased the
use of Expertienda among registered users. Columns (1) to (4) are based on the
sample of businesses that participated in the randomisation process at the time of
the intervention.
Column (1) reports a 3.97 percentage point increase in take-up, driven by the
facilitators’ efforts. This result is consistent with the 3.6% average conversion rate
15 Firms often change their name or primary business activity, particularly in response to crises such as
COVID-19.

Eurasian Business Review
for mobile app advertising reported by Kurzweg (2023). Given that the baseline
take-up rate is 3.3%, the intervention accounts for nearly all the users from the sam-
ple who registered for the application. When usage is defined more strictly-such as
spending at least five minutes in the app (e.g., completing at least one-course mod-
ule in a single session)-Column (3) shows a 2.3 percentage point increase.
Columns (2) and (4) offer no evidence of spillover effects: treated units in both
high- and low-intensity areas exhibit statistically similar coefficients, with slightly
smaller point estimates in low-intensity areas. Additionally, there is no indication of
“contamination” among control units or differences in take-up rates among untreated
businesses based on the treatment status of their neighbours.
Columns (5) and (6) use an alternative measure from administrative data, focus-
ing on whether respondents recall hearing about Expertienda. The results are quali-
tatively consistent with those derived from the initial take-up measure. Furthermore,
excluding control variables from the model (TableD2 in the appendix) and restrict-
ing the data to the reinterviewed sample (TableD3) yield similar results.
Beyond demonstrating the intervention’s effectiveness in increasing course take-
up, the table also reveals key characteristics of entrepreneurs more likely to enrol in
such programmes.
There are no significant differences in enrolment based on gender or age. Inter-
estingly, individuals with tertiary education are less likely to enrol, suggesting that
higher education does not necessarily correlate with greater interest in this type
of program. This socio-demographic pattern may be explained by the inclusion of
internet usage for business, which is often linked to the entrepreneur’s socio-eco-
nomic profile and appears to be a key predictor of enrolment.
Other factors, such as baseline outcome indexes (formality, financial inclusion,
and business practices), personality traits like perseverance, the business’s loca-
tion in a commercial area (indicating initial investment levels), or the owner’s prior
entrepreneurial experience, do not significantly predict enrolment. These findings
suggest that take-up of general training is more closely related to digital readiness
than to other business or personal characteristics.
We also explored potential heterogeneity in the intervention’s impact. The effect
seems concentrated among businesses already using the internet for commercial
activities, with less impact for owners with education levels above secondary. Other
factors, such as the owner’s gender, age, and baseline business practices, did not pro-
duce statistically significant interactions. However, given the large standard errors
for the interaction terms, it is difficult to rule out the possibility of heterogeneous
effects. For estimates, see TableD4 in the appendix.
5.4 Usage ofExpertienda
During the study period, a total of 252 users engaged with the Expertienda appli-
cation, of which 49 were part of the experiment. It was observed that some users
shared the app with others outside the study, although no additional promotional
actions were taken. This suggests the possibility of spillover effects among firms,

Eurasian Business Review
though not at the geographical level, as most of the other businesses were located
outside the study neighbourhoods.
Fig. 2 Sample size over the steps of the intervention. Note: The diagram illustrates the sample sizes at
various stages of the study. It begins with the total number of micro-establishments selected for inter-
views and randomisation, displaying the number of businesses on the left and the number of clusters on
the right. The diagram then progresses through the subsequent stages of each analysis arm
Table 5 Differential attrition rate: follow-up contact and treatment status
Note: Columns (1) and (2) present results based on the sample of micro-establishments from the baseline
randomisation that were identified at the time of the intervention. Columns (3) and (4) correspond to the
sample of baseline randomisation microbusinesses that were not located during the follow-up. Columns
(5) and (6) report findings from the survey, which tracks the original firms identified in the field. Clus-
tered standard errors (at ‘cluster’ level) are presented in parentheses. Significance level: *0.1, **0.05,
***0.01
(1) (2) (3) (4) (5) (6)
Surveyed at FU Not found at FU Surveyed at FU
conditional on
being found at FU
Treated
−
0.0425 0.101***
−
0.0149
(0.0286) (0.0346) (0.0467)
TH: treated in high intensity
−
0.0249 0.114** 0.0175
(0.0351) (0.0442) (0.0611)
TL: treated in low intensity
−
0.0185 0.0406
−
0.0187
(0.0469) (0.0581) (0.0754)
CH: non-treated in high intensity 0.0469
−
0.0114 0.0509
(0.0456) (0.0545) (0.0700)
Observations 994 994 994 994 536 536
R squared 0.0686 0.0696 0.0527 0.0545 0.0764 0.0777
Dependent variable average 0.221 0.221 0.461 0.461 0.410 0.410
Dependent variable std. dev 0.415 0.415 0.499 0.499 0.492 0.492

Eurasian Business Review
Most users interacted with the Expertienda application for less than 20 min
(Fig.3). Usage time varied by content type, with the majority spent on the salary
calculation tool, as shown in panel B of the figure. Notably, no users completed all
the modules, with none engaging for more than one hour, given that the course is
expected to take at least 1.5h to complete.
5.5 Impact onbusiness performance
Table 8 shows the ITT on the performance of business outcomes. None of the
treatments’ coefficients are significant.16
Table 6 Balancing test results: comparison of final and initial sample for statistical differences
Note: Columns (1) and (2) present results based on the sample of microbusinesses from the baseline ran-
domisation that were identified at the time of the intervention. Column (3) corresponds to the sample of
baseline randomisation micro-establishments that were reinterviewed. Clustered standard errors (at ‘clus-
ter’ level) are presented in parentheses. Significance level: *0.1, **0.05, ***0.01
Outcome variable (1) (2) (3)
Mean N Obs/Cluster Reinterviewed
Panel A. Balance at intervention
 Owner has tertiary education 0.40 994
−
0.104***
146 (0.037)
 Female owner 0.56 994 0.031
146 (0.039)
 Located in a commercial zone 0.43 994 0.196***
146 (0.042)
 Activity 1: convenience store 0.24 994 0.112***
146 (0.040)
 Activity 2: prepared food 0.26 994
−
0.058*
146 (0.031)
 Activity 3: health, beauty, other services 0.16 994
−
0.010
146 (0.030)
 Use internet for business 0.52 994
−
0.066*
146 (0.039)
 Number of workers 1.68 220 0.000
104 (0.000)
 Large commercial space 0.54 994
−
0.079**
146 (0.036)
 Owner born in the same municipality 0.68 994 0.004
146 (0.037)
16 For the sample without Barranquilla and Bucaramanga, there is a positive effect on the formal-
ity dimension, but it is significant only at the 90% level (TableD5 in the appendix). Table D7 presents
results on the specific variables constituting the indexes. There is a positive effect on reducing the inten-
sive margin of informality (an increase of 15.8 percentage points on the probability of complying with
labour regulations), increasing access to insurance products (13.6 percentage points), and on the usage of

Eurasian Business Review
Table 7 Local promoters intervention impact on take-up
Note: Columns 1, 3 and 5 presents the regression coefficient for the treatment variable as well as con-
trols variables such as gender, education, age, internet, localization, formalization, Business practices,
financial inclusion, experience as entrepreneur, and fixed effects of activity and city. Columns 2, 4 and
6 present the coefficients for the categorization of treated in the high-treatment area (TH), treated in the
low-treatment area (TL), and non-treated in the high-treatment area (CH), with the same control vari-
ables. Standard errors in parentheses. Significance level: *
p
<
0.1
, **
p
<
0.05
, ***
p
<
0.01
(1) (2) (3) (4) (5) (6)
Expertienda registered
user
More than 5min using
the app
Heard of Exper-
tienda
Treated 0.0398*** 0.0233*** 0.110**
(0.00870) (0.00681) (0.0491)
TH: treated in high intensity 0.0383*** 0.0210** 0.115*
(0.0108) (0.00824) (0.0687)
TL: treated in low intensity 0.0247 0.0181 0.100
(0.0174) (0.0152) (0.0740)
CH: non-treated in high intensity
−
0.0114
−
0.00717 0.00219
(0.00730) (0.00551) (0.0544)
Female owner
−
0.00157
−
0.00145
−
0.00911
−
0.00906 0.0580 0.0571
(0.0117) (0.0117) (0.00913) (0.00914) (0.0425) (0.0430)
Owner has tertiary education
−
0.00881
−
0.00861
−
0.0228**
−
0.0227** 0.0326 0.0325
(0.0149) (0.0149) (0.0106) (0.0105) (0.0539) (0.0543)
Age 31–42
−
0.00951
−
0.00990 0.00455 0.00406 0.0493 0.0442
(0.0160) (0.0163) (0.0115) (0.0117) (0.0802) (0.0779)
Age 43–58 0.0188 0.0194 0.0193 0.0192 0.0678 0.0621
(0.0185) (0.0188) (0.0135) (0.0137) (0.0790) (0.0760)
Age more than 58 0.0109 0.0109 0.00938 0.00917 0.148 0.142
(0.0230) (0.0231) (0.0168) (0.0168) (0.0931) (0.0939)
Use internet for business 0.0271* 0.0273* 0.0339*** 0.0340***
−
0.0284
−
0.0286
(0.0143) (0.0144) (0.0119) (0.0119) (0.0465) (0.0468)
Located in a commercial zone 0.0152 0.0158 0.0168 0.0170
−
0.0487
−
0.0479
(0.0156) (0.0157) (0.0123) (0.0124) (0.0524) (0.0530)
Formality index
−
0.00505
−
0.00385 0.00599 0.00618
−
0.0644
−
0.0637
(0.0189) (0.0191) (0.0133) (0.0136) (0.0886) (0.0885)
Business practices index 0.0286 0.0282 0.00845 0.00838 0.0270 0.0251
(0.0204) (0.0205) (0.0164) (0.0165) (0.0833) (0.0839)
Financial inclusion index
−
0.0128
−
0.0124
−
0.0356*
−
0.0354* 0.204* 0.204*
(0.0329) (0.0329) (0.0209) (0.0209) (0.110) (0.110)
Owner has experience as entre-
preneur
−
0.0136
−
0.0136
−
0.00728
−
0.00725
−
0.0353
−
0.0359
(0.0199) (0.0199) (0.0159) (0.0159) (0.0537) (0.0543)
Observations 994 994 994 994 228 228
R squared 0.0558 0.0566 0.0474 0.0477 0.151 0.151
Dependent variable average 0.0332 0.0332 0.0191 0.0191 0.101 0.101
Dependent variable std. dev 0.179 0.179 0.137 0.137 0.302 0.302

Eurasian Business Review
Table9 considers the analysis correcting for attrition. Column 1 presents the
estimates with the IPW adjustment, which are a measure of the average treatment
effect. Columns 2 and 3 presents the Lee bounds. The results suggest that while
there may be minor benefits in specific dimensions like formal practices and digi-
tal adoption, the intervention had no substantial overall effect on business perfor-
mance or growth. High attrition limits the robustness of these findings, highlight-
ing the need for cautious interpretation.
5.6 Instrumental variables approach
Finally, Table10 shows the results of instrumenting actual usage with the treat-
ment allocation. This exercise results in a LATE, that is, the average impact on
those who actually installed the application conditional on being convinced to
do so. We find no significant results among the outcomes of interest. Column
4 of the table presents the first stage F statistic. The value is above 12 in most
cases, which does not indicate weak instruments, but it is not strong enough to get
relatively small standard errors. Hence, it is difficult to draw solid conclusions.
Similar results are found when considering the sample without Barranquilla and
Bucaramanga (TableD6 in the appendix).
5.7 Qualitative analysis
Some of the reasons reported by the entrepreneurs on why they decided to follow
the program were:
– to learn more about technology and legal issues inbusinesses, but also out of
curiosity, as it was free,
– to provide support to students in completing the survey.
And some of the reasons why shopkeepers did not want to participate were:
– lack of time, mistrust of the manipulation of digital solutions (data privacy
issue), and
– lack of knowledge of the purpose of the application (tangible or real benefit).
These concerns are similar to those typically reported with any training. In contrast,
we observed quantitatively that using the Internet as part of the business operation
was the central predictor of take-up (aside from the intervention). This was the case
for 50% of the businesses at baseline, a number that grew to 57% at follow-up, but
mostly due to the lessons coming from COVID restrictions. Hence, this limitation
decreases over time but is likely to become a larger barrier for some entrepreneurs.
electronic wallets (12.8 percentage points). These effects have large confidence intervals but are signifi-
cant at the 95% level.
Footnote 16 (Continued)

Eurasian Business Review
There were general perceptions in both directions on the general experience with
Expertienda. It has positive attitudes such as:
– ‘Itis helpful, and I learned a lot from the tips for managing expenses’,
– ‘Expertienda is an interactive application; it gives interesting and basic trade
tips’,
– ‘...it was very explanatory that application’,
– ‘It was good to work on the platform’.
However, some users have less favourable perceptions:
– ‘I did not use Expertienda because it tells you lies’,
– ‘I downloaded it, I was managing it, and I put much care, then I did not give it so
much importance and deleted it’,
– ‘I almost do not like applications.’
We conclude that Expertienda faced the traditional problems of most training
courses in the literature, where individuals do not find a good reason for finishing the
training. Figure3 shows that most users completed just a few lessons (less than ten
minutes), and few of them completed the entire course (those above 40min). In this
sense, it is far from attaining the gains from coach-based or role-based experiences.
6 Discussion
First, the results indicate that the intervention successfully engaged entrepreneurs
to install the app (H1). However, these results are likely a lower bound, as the
COVID-19 pandemic contributed to sample attrition, leaving a group that was
less inclined to participate in training, particularly digital-based training. Despite
initial engagement, no participants completed the course, and most reviewed
only a few sessions. Both the qualitative findings and usage statistics suggest that
Expertienda encountered challenges commonly faced by training programs in the
literature. Many individuals lacked sufficient motivation to adopt the technology
and complete the training (Suhartanto & Leo, 2018). This mirrors a broader trend
in online education, where completion rates for MOOCs remain low (typically
below 10%) and have shown little improvement over time (Reich & Ruipérez-
Valiente, 2019). Although Expertienda’s curriculum was designed to be simple
and concise, the student and recent graduate facilitators were largely ineffective at
persuading users to complete the training or make substantial progress through it.
The usage of strategies more intensive in rewards for completion is suggested for
the future research.
We observed that the application was used by substantially more people than
those who were directly invited. Yet, this diffusion process was not related to geo-
graphical proximity. As a result, we do not have conclusive evidence in terms of
the existence of spillovers on the take-up (H2). What we can conclude is that if a
policymaker wants to target a particular geographical area (e.g., a business cluster

Eurasian Business Review
located in a given neighbourhood), there is a need for specific efforts to cover the
entire set of businesses to incentivise businesses to share the course.
Fig. 3 Expertienda usage statistics. Note: Time is measured in minutes. Data was collected in the back-
end platform of the application

Eurasian Business Review
Costs are notoriously low compared with other types of training. Our fixed
development costs were around 252.89 USD per potential user, while variable
costs were 4.85 USD per potential user, considering we aimed to treat 644 entre-
preneurs (TableB1). In comparison, traditional training like Campos etal. (2017)
intervention costs 756 USD per unit, and the virtual but comprehensive one of
Estefan etal. (2023) costs 440 USD (further details in Appendix table B2). The
big advantage is that the cost per person decreases rapidly: if we targeted the
3,194 microbusinesses in the selected neighbourhoods, the fixed costs would drop
Table 8 ITT results of the Expertienda intervention
Note: Column 1 presents the mean of each outcome of interest (each row) for non-treated units. Column
2 presents the number of observations and clusters included. Column 3 presents the regression coefficient
for the treatment variable, including the observed length and depth of the premises, and fixed effects of
activity and city. Finally, columns 4 to 6 present the coefficients for the categorisation of treated in the
high-treatment area (TH), treated in the low-treatment area (TL), and non-treated in the high-treatment
area (CH) (the base is non-treated in the low-treatment area (CL)), with the same control variables. Clus-
tered standard errors in parentheses. Significance level: *0.1, **0.05, ***0.01
Outcome variable (1) (2) (3) (4) (5) (6)
Mean N Obs/ Cluster Treatment TH TL CH
Score total 0.44 228 0.031 0.052
−
0.022 0.008
104 (0.028) (0.040) (0.040) (0.044)
Score Dim 1. Formal sector 0.46 228 0.071 0.056 0.025
−
0.041
104 (0.044) (0.055) (0.058) (0.063)
Score Dim 2. Management
practices
0.56 228
−
0.007 0.040
−
0.061 0.044
104 (0.050) (0.068) (0.076) (0.067)
Score Dim 3. Financial inclu-
sion
0.33 228 0.030 0.061
−
0.029 0.020
104 (0.030) (0.047) (0.054) (0.056)
How many clients (observed) 5.04 228
−
0.270
−
1.518
−
1.960 −2.543**
104 (0.924) (1.398) (1.316) (1.217)
Computed profits (10 USD) 60.47 228
−
38.781 59.302
−
14.090 153.100
104 ( 82.942) ( 48.442) ( 45.332) (147.663)
Use internet for business 0.57 228 0.084 0.144
−
0.022 0.042
104 (0.073) (0.116) (0.138) (0.123)
Some investment 2 years 0.68 228
−
0.057
−
0.072
−0.352
***
−
0.149
104 (0.081) (0.094) (0.114) (0.103)
How many employees
(observed)
1.63 222
−
0.059
−
0.143
−
0.137
−
0.073
104 (0.117) (0.127) (0.216) (0.184)
Has Social Networks 0.11 228
−
0.036
−
0.030
−
0.032
−
0.035
104 (0.034) (0.032) (0.040) (0.037)
The shop has a sign with its
name
0.87 228
−
0.007
−
0.032 0.060 0.024
104 (0.061) (0.046) (0.040) (0.038)

Eurasian Business Review
to 52 USD; getting closer to the 22 USD reported by Attanasio et al. (2019).
Hence, a program in this line could be a substantially cheaper option for the
1,313,201 microbusinesses in Colombia that hold a business registry according to
the 2021 official statistics (DANE, 2021).
Second, no evidence exists that the course modified the targeted outcomes
(H3), even among those who installed the application. Yet, we should be careful
about this interpretation.
The unexpectedly high attrition rate (nearly 80% compared to the anticipated
50%), largely driven by shutdowns following COVID-19, significantly hinders
our ability to infer the effects of the treatment on outcomes measured via the
follow-up survey. As discussed in the attrition section, the reduced sample size
limits our power to detect effects, allowing us to identify only those that are at
least twice as large as initially expected. Consequently, subtle changes cannot be
captured in our study.
Table 9 Impact on business outcomes adjusting for attrition
Note: Column (1) presents the Average Treatment Effect (ATE) estimates. Column (2) shows the lower
bound of the Lee Bounds, which is an estimate of the treatment effect under an assumption of non-attri-
tion (data loss unrelated to outcomes). Finally, column (3) presents the upper bound of the Lee Bounds,
which provides an upper estimate of the same effect, with a more optimistic assumption about the rela-
tionship between missing data and outcomes. Clustered Standard errors (at ‘cluster’ level) in parentheses.
Significance level: *
p
<
0.1
, **
p
<
0.05
, ***
p
<
0.01
Outcome Inverse probability
weighting
Lee bounds
(1) (2) (3)
ATE Lower Upper
Score total 0.0175
−
0.0169 0.0562
(0.68) (
−
0.48) (1.59)
Score Dim 1. Formal sector 0.0852* 0.0430 0.141*
(2.54) (0.87) (2.45)
Score Dim 2. Business practices
−
0.0470
−
0.101 0.0170
(
−
1.19) (
−
1.86) (0.23)
Score Dim 3. Financial inclusion 0.0150
−
0.0435 0.0572
(0.44) (
−
0.82) (1.06)
How many clients (observed)
−
0.612
−
2.235*
−
0.0634
(
−
0.87) (
−
2.27) (
−
0.07)
Computed profits (10 USD)
−
55.85
−
84.97
−
39.62
(
−
0.89) (
−
1.35) (
−
0.62)
Use internet for business 0.0570 0.0111 0.135
(0.84) (0.13) (1.30)
Some investment 2 years
−
0.114
−
0.168
−
0.0440
(
−
1.74) (
−
1.94) (
−
0.45)
How many employees (observed)
−
0.237*
−
0.283* 0.0137
(
−
2.03) (
−
2.27) (0.14)

Eurasian Business Review
Moreover, any potential impact is likely minimal, given the limited engagement
most users had with the application. Therefore, the substantial attrition rate intro-
duces a critical limitation to the study’s power, making it challenging to validate
these results with confidence.
Third, there was a high refusal rate of reinterviews at follow-up (57.4%), which
could be triggered by specific COVID concerns or simply that firm owners do not
perceive a benefit of responding to a long survey. Hence, there is a clear need to
compensate business owners for their time.
Future research could explore strategies to enhance both take-up and comple-
tion rates by leveraging the experience and goodwill of Colombia’s Chambers of
Table 10 Instrumenting Expertienda usage with treatment assignment
Note: Column 1 presents the mean of each outcome of interest (each row) for non-treated units. Column
2 presents the number of observations and of clusters included (determined by the specific dependent
variable). Column 3 presents the coefficient for the shop being in a high treatment area relative to being
in a low treatment one in a regression that also includes the observed length and depth of the premises
and fixed effects of activity and city. Finally, column 4 presents the Kleibergen–Paap rk Wald F statistic
to test for the strength of the instrument in the model. Clustered standard errors in parentheses. Signifi-
cance level: *0.1, **0.05, ***0.01
Outcome variable (1) (2) (3) (4)
Mean N Obs/Cluster Registered user Kleiber-
gen–Paap rk
Wald F
Score total 0.44 228 0.291 12.61
104 (0.276)
Score Dim 1. Formal sector 0.46 228 0.666 12.61
104 (0.451)
Score Dim 2. Management practices 0.56 228
−
0.064 12.61
104 (0.441)
Score Dim 3. Financial inclusion 0.33 228 0.281 12.61
104 (0.292)
How many clients (observed) 5.04 228
−
2.546 12.61
104 (8.150)
Computed profits (10 USD) 60.47 228
−
365.599 12.61
104 (699.118)
Use internet for business 0.57 228 0.790 12.61
104 (0.676)
Some investment 2 years 0.68 228
−
0.536 12.61
104 (0.747)
How many employees (observed) 1.63 222
−
0.526 12.89
104 (1.012)
Has social networks 0.11 228
−
0.339 12.61
104 (0.319)
The shop has a sign with its name 0.87 228
−
0.063 12.61
104 (0.541)

Eurasian Business Review
Commerce. Their involvement could help local promoters boost participation and
sustain engagement among microentrepreneurs. Additionally, these initiatives could
be further strengthened by incorporating financial incentives for course completion,
providing a tangible motivation for participants to stay committed.
7 Conclusions
Improving the quality of microfirms is particularly challenging, as many operate
informally, often circumventing business or labor regulations (Ulyssea, 2018). This
informality is often a deliberate strategy, allowing firms to remain competitive by
avoiding labour costs. Many informal positions are viable only within this informal
framework, as formalization per se does not necessarily lead to productivity gains
(Benhassine etal., 2018; De Mel etal., 2008). However, this strategy comes at the
cost of offering low-quality jobs in the informal sector.
Empirical evidence suggests that firms that choose to formalize-by adhering to
labour regulations and covering associated costs-can enhance job quality (Gutierrez
& Rodriguez-Lesmes, 2023; Johannes etal., 2009; Rand & Torm, 2012). Moreover,
these studies indicate that formalization is associated with a productivity premium,
highlighting potential benefits for both workers and businesses.
Numerous studies have examined the impact of business training courses for
microentrepreneurs. Many report no significant positive effects on business perfor-
mance (Drexler etal., 2014; Fiala, 2018; Karlan & Valdivia, 2011). However, others
find that such training can increase profits, survival, or growth over the long term
(Blattman etal., 2016; McKenzie & Puerto, 2021) or even the short term (De Mel
etal., 2014; Field etal., 2016; Mano etal., 2012). The use of digital tools offers a
promising avenue to expand the reach of these programs, as demonstrated by Attan-
asio etal. (2019), Davies etal. (2024), and Estefan etal. (2023). Nonetheless, sig-
nificant challenges remain.
Our intervention was designed for a diverse group of entrepreneurs, encompass-
ing various ages, literacy levels, and stages of business development-ranging from
newly established to long-standing enterprises. Participants were not part of any
specific social program and had no prior connection to the application’s designers
or facilitators, except for geographical proximity. This setup mirrors the challenges
faced by large-scale business training programs.
Our findings demonstrate that increasing program take-up at a low cost is feasi-
ble by leveraging local facilitators. However, the primary challenge lies in sustain-
ing participant engagement, even when the program includes an application tailored
to the needs of the target population. Ensuring that entrepreneurs remain engaged,
achieve meaningful learning outcomes, and internalize effective business practices
without continuous involvement from coaches remains an open question.
Supplementary Information The online version contains supplementary material available at https:// doi.
org/ 10. 1007/ s40821- 025- 00293-y.

Eurasian Business Review
Acknowledgements This study is registered in the AEA RCT Registry, and the unique identifying num-
ber is AEARCTR-0006120. Helpful comments from Applied Microeconomics Workshops at Universidad
del Rosario and Universidad de los Andes are gratefully acknowledged, in particular to Santiago Saave-
dra, Julia Seither, Stanislao Maldonado, and Juan Vargas. This project received ethical approval from the
ethics committee of Minuto de Dios University.
Funding Open Access funding provided by Colombia Consortium. Financial Support from the program:
The intervention grew out of a regional initiative, the Colombia Cientifica-Alianza EFI Research
Program, with code 60185 and contract number FP44842-220-2018, funded by the World Bank.
Data availability Data is publicly available at https:// resea rchda ta. urosa rio. edu. co/.
Declarations
Conflict of interest The authors declare that they have no Conflict of interest.
Ethics approval We are using data, which was collected under the approval of the ethics and research board
of Corporación Universitaria Minuto de Dios.
Consent to participate Not applicable.
Consent for publication Not applicable.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License,
which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long
as you give appropriate credit to the original author(s) and the source, provide a link to the Creative
Commons licence, and indicate if changes were made. The images or other third party material in
this article are included in the article’s Creative Commons licence, unless indicated otherwise in
a credit line to the material. If material is not included in the article’s Creative Commons licence and
your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need
to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://
creativecommons.org/licenses/by/4.0/.
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Authors and Aliations
PaulRodríguez‑Lesmes1 · LuisH.Gutiérrez1 ·
JuanCarlosUrueña‑Mejía1,2,5 · AndrésFelipeOrtiz2,3·
IvánDaríoMedinaRojas2 · MauricioRomero4
* Juan Carlos Urueña-Mejía
juan.uruena1@uexternado.edu.co
Paul Rodríguez-Lesmes
paul.rodriguez@urosario.edu.co
Luis H. Gutiérrez
Luis.gutierrez@urosario.edu.co
Andrés Felipe Ortiz
andresf.ortiz@uniminuto.edu
Iván Darío Medina Rojas
imedina@uniminuto.edu
Mauricio Romero
mauricio.romero@fundacioncapital.org
1 School ofEconomics, Universidad del Rosario, Calle 12 C No. 4-69, 111711Bogotá, Colombia
2 Corporación Universitaria Minuto de Dios, Carrera 74 No. 81C-05, Bogotá, Colombia
3 Universidad de la Salle, Carrera 74 No. 81C-05, Bogotá, Colombia
4 Fundación Capital, Carrera 74 No. 81C-05, Bogotá, Colombia
5 Department ofMathematics, Universidad Externado, Bogota, Colombia