Bank of Morocco – CEMLA – IFC Satellite Seminar at the ISI World Statistics Congress

on “Financial Inclusion”
Marrakech, Morocco, 14 July 2017

Measuring financial inclusion: a multidimensional index 1

Noelia Cámara, BBVA Research,
and David Tuesta, CAF- Bank of Development for Latin America

1 This paper was prepared for the meeting. The views expressed are those of the authors and do not necessarily
reflect the views of the BIS, the IFC or the central banks and other institutions represented at the meeting.
Measuring financial inclusion: a multidimensional index

Noelia Cámara 1 and David Tuesta 2

Abstract

We use demand and supply-side information to create a composite index that measures the extent of
financial inclusion at country level, for 137 developed and less-developed countries. We postulate that
the degree of financial inclusion is determined by three dimensions: usage, barriers and access to the
financial system. Let assume that a latent structure exists behind the covariation of a set of correlated
indicators associated to the financial inclusion concept. It allows estimating a comprehensive measure
of the degree of financial inclusion by assigning weights endogenously, with a two-stage Principal
Component Analysis. Our composite index is easy to interpret and compute.
Keywords: net financial inclusion, underlying structure, inclusion barriers
JEL classification: C43, G21, O16

Contents

Measuring financial inclusion: a multidimensional index .......................................................................................... 1

1. Introduction.......................................................................................................................................................................... 2

2. Financial Inclusion Dimensions and Data Sources ................................................................................................ 3

2.1 Usage ............................................................................................................................................................................ 5
2.2 Barriers ......................................................................................................................................................................... 6
2.3 Access ............................................................................................................................................................................. 7

3. Principal Component Analysis as an Indexing Strategy ..................................................................................... 8

3.1 First Stage PCA ......................................................................................................................................................... 9
3.2 Second Stage PCA ................................................................................................................................................ 10

4. Results ................................................................................................................................................................................. 11
4.1 Financial Inclusion Dimensions ....................................................................................................................... 11
4.2 Multidimensional Financial Inclusion Index ............................................................................................... 15

5. Conclusions and Policy Recommendations .......................................................................................................... 19

Appendix .................................................................................................................................................................................... 22

References ................................................................................................................................................................................. 23

1
Financial Inclusion Unit, BBVA Research Department (noelia.camara@bbva.com)
2
CAF- Bank of Development for Latin America (DTUESTA@caf.com)

Measuring financial inclusion: a multidimensional index 1

1. Introduction

Issues relating to financial inclusion are a subject of growing interest and one of the major
socioeconomic challenges on the agendas of international institutions, policymakers, central banks,
financial institutions and governments. The United Nations’ declared objective of achieving universal
financial access by 2020 is another example of financial inclusion being recognized as fundamental for
economic growth and poverty alleviation. 3 The World Bank’s latest estimates state that nearly half of
the adult population in the world does not have a bank account in a formal financial institution.
However, the concept of financial inclusion goes beyond single indicators, such as percentage of bank
accounts and loans or number of automated teller machines (ATMs) and bank branches. In the
literature, the attempts to measure financial inclusion through multidimensional indices are scarce
and incomplete. To the best of our knowledge, literature lacks a comprehensive indicator that can
bring together information on financial inclusion by using a statistically sound weighting methodology
and takes into account both demand and supply-side information. Our study aims to fill this gap.
The major contribution of this paper is the construction of a multidimensional financial inclusion
index covering 138 countries for the periods 2011 and 2014. The weights of the index are obtained
from a two-stage Principal Component Analysis (PCA) for the estimation of a latent variable. First, we
apply PCA to estimate the group of three sub-indices (i.e. dimensions) representative of financial
inclusion. Second, we apply again PCA to estimate the overall financial inclusion index by using the
previous sub-indices as causal variables. Our index improves existing financial inclusion indices in
several ways. First, we use a parametric method that avoids the problem of weighting assignment.
Second, we offer a harmonized measure of financial inclusion for a larger set of countries, 137
developed and less-developed countries, that allows comparisons across countries and over time.
Finally, we provide a comprehensive definition of financial inclusion combining information from 20
indicators from both demand and supply-side data sets, and from two perspectives: banked and
unbanked population. It is the first time that a composite index uses a demand-side data set at
individual level to measure the level of financial inclusion across countries. We identify two problems in
the current financial inclusion indices. First, existing attempts to build financial inclusion indices rely
only on supply-side country level data and come up with inaccurate readings of financial inclusion due
to bias generated by the existence of measurement errors in the usage indicators. Supply-side
indicators, particularly the number of accounts or loans, can overestimate the inclusiveness of financial
systems since one person can have more than one account or loan. It is a very common practice in
developed countries. Second, assigning exogenous weights to indicators is often criticized for lack of
scientific rigor because exogenous information is imposed.
The lack of a harmonized measure that includes multidimensional information to define financial
inclusion is a pitfall that confounds the understanding of several related problems. The
multidimensional measurement of financial inclusion is important in several aspects. First, a measure
that aggregates several indicators into a single index aids in summarizing the complex nature of
financial inclusion and helps to monitor its evolution. A good index is better at extracting information.
Second, a better measure of financial inclusion may allow us to study the link between financial

3
The Global Financial Development report for 2014, by the World Bank (2013), is the second report that focuses on the
relevance of financial inclusion. It offers an overview of financial inclusion status and problems based on new evidence
about financial sector policy. The Maya Declaration is another example that evidences the importance of financial inclusion.
It consists of a set of measurable commitments by developing countries’ governments to enhance financial inclusion. There
are more than 90 countries in the agreement and they represent more than 75 per cent of the unbanked population.
Finally, the G20 also express its interest in promoting financial inclusion in non-G20 countries through the Global
Partnership for Financial Inclusion (GPFI). This platform, officially launched in Seoul in 2010, recognizes financial inclusion
as one of the main pillars of the global development agenda endorsed in its Financial Inclusion Action Plan.

2 Measuring financial inclusion: a multidimensional index

inclusion and other macroeconomic variables of interest (i.e. economic growth, financial stability, etc.).
Third, information by dimension helps to better understand the problem of financial inclusion. It can
be a useful tool for policy making and policy evaluation.
There are two commonly used approaches to constructing composite indices: non-parametric and
parametric methods. The first ones assign the importance of indicators by choosing the weighs
exogenously, based on researchers’ intuition. There is evidence that indices are sensitive to subjective
weight assignment, since a slight change in weights can alter the results dramatically (Lockwood,
2004). 4 Sarma (2008, 2012) and Chakravarty and Pal (2010) are examples of financial inclusion indices
that apply this methodology to usage and access indicators from supply-side country level data sets. In
contrast, parametric methods assign the importance of indicators (weights) in the overall index
endogenously, based on the information structure of sample indicators. Specifically, through the
covariation between the indicators related to the common structure. There are two parametric analyses
commonly used for indexing: PCA and Common Factor Analysis. Amidzic et al. (2014) proposes a
measure of financial inclusion based on a Common Factor Analysis. However, the indicators used to
define financial inclusion only include limited supply-side information at country level. From an
empirical point of view, PCA is preferred over Common Factor Analysis as an indexing strategy because
it is not necessary to make assumptions on the raw data, such as selecting the underlying number of
common factors (Steiger, 1979). This paper offers a multidimensional financial inclusion index with
endogenous weights estimated by Principal Componets.
The rest of the paper is organized as follows. In section 2, we describe the data and the rationale
for our chosen indicators as well as for the use of sub-indices that measure financial inclusion
dimensions. Section 3 describes the methodology for constructing our composite index from multi-
dimensional data. Section 4 discusses the results of the sub-indices as well as the composite financial
inclusion index. Finally, Section 5 concludes.

2. Financial Inclusion Dimensions and Data Sources

How to measure financial inclusion is a topic of concern among researchers, governments and policy
makers. To date, financial inclusion measurement has been mainly approached by the usage and
access to the formal financial services by using supply-side aggregate data (e.g. Honohan (2007);
Sarma (2008, 2012); Chakravarty and Pal (2010) and Amidzic et al. (2014)). However, the way supply-
side information is collected is not precise to capture the extent of financial inclusion since it does not
inform on the real population that is covered by access to the formal financial system or using financial
services. In terms of access, a broad availability (i.e. more ATMs and bank branches) does not mean
necessarily that a system is inclusive per se since the geo-location of points of service is unknown. In
terms of usage, figures such as number of deposits are overestimated, especially in developed
countries. These pitfalls should be solved by using additional information from the demand side when
it comes to usage. There are only two studies that rely on demand-side data. The first one, developed
by Demirgüc¸-Kunt and Klapper (2013 and 2015), focus on several financial inclusion-related indicators
individually. 5 However, monitoring different indicators individually, although useful, does not offer a
comprehensive understanding of the level of financial inclusion across countries. In the second study,
Dabla-Norris et al. (2015) focuses on the Latin America and the Caribbean countries and builds on a
previous version of our financial inclusion index by including a similar index for SMEs.

4
There is also a problem with weight reassignment when new indicators are included into an existing index.
5
Didier and Schmuckler (2014) analyses individual indicators of the Enterprise Survey but they do not explore a composite
indicator.

Measuring financial inclusion: a multidimensional index 3

 In brief, the few attempts to measure financial inclusion through composite indices are either
limited in terms of countries or incomplete in terms of information and subject to methodological
problems. In addition, current attempts also lack information on financial exclusion
We collate nine definitions for financial inclusion to stablish the dimension structure of our index.
Accordingly, we define an inclusive financial system as one that maximizes usage and access, while
minimizing involuntary financial exclusion. 6 Involuntary financial exclusion is measured by a set of
barriers perceived by those individuals who do not participate in the formal financial system. It
includes the barriers to financial inclusion through the obstacles perceived by people prevented from
using formal financial services and it is considered a proxy for the quality of financial inclusion. Thus,
we postulate that the degree of financial inclusion is determined by three dimensions: usage, barriers
(i.e. quality) and access (Figure 1). These dimensions are, at the same time, determined by a set of 20
indicators including demand-side individual level indicators for the cases of usage and barriers, and
supply-side country level indicators for access.
Combining information on the three dimensions is important since having access does not implies
a straightforward usage as it is conditioned by other socio-economic factors such as income,
regulatory framework or cultural habits that make individuals use these kinds of services in a particular
manner. Access can be considered a necessary but not sufficient condition for measuring the
inclusiveness of a financial system. Likewise, we consider the use of formal financial services as an
output of financial inclusion rather than a comprehensive measure of the inclusiveness of a financial
system in itself. Our hypothesis is that focusing only on usage and access leads to limited
measurement of financial inclusion because we do not have information about the quality conditions
of the financial inclusion process or the number of financially excluded people. In this context,
demand-side individual surveys that gather information on the perceived reasons why people fail to
use formal financial services add significant information about the degree of inclusiveness of a
financial system. Adding this information on the unbanked aims to assess financial inclusion by
introducing the concept of "net financial inclusion". It approaches financial inclusion measurement
from a double perspective. From the banked side, by measuring the actual use of formal financial
services, namely, inclusion output of financial systems. And, from the unbanked, by incorporating the
extent of excluded population in the financial inclusion assessment.

6
For the CGAP financial inclusion means that all working age adults have effective access to credit, savings, payments and
insurance from formal service providers. Effective access involves convenient and responsible service delivery, at a cost
affordable to the customer and sustainable for the provider with the result that financially excluded customers use formal
financial services rather than existing informal options.

4 Measuring financial inclusion: a multidimensional index

 Multidimensional Financial Inclusion Index
Figure1

Source: Own elaboration

To compute the index, we take advantage of the largest demand-side harmonized dataset at
individual level, the World Bank’s Global Findex (2011 ad 2014). It offers a homogeneous measure of
indicators for individuals’ use of financial products across economies. This survey collects information
about 150,000 nationally representative and randomly selected adults from 140 countries in 2011 and
137 in 2014, around the world. Data available at individual, rather than household, level is also an
advantage that improves accuracy and comparability of the analyses. This database fills an important
gap in the financial inclusion data landscape. We also use supply-side aggregate data on access from
the International Monetary Fund’s Financial Access Survey (2015). This is a source of supply-side data
that offers information on an unbalanced panel of 189 countries, covering the period 2004-2015.

2.1 Usage

To assess the extent of usage of the formal financial services by individuals, we try to proxy the utility
derived of using such services by considering the use of different products: holding at least one active
financial product that allows making and receive payments and storage money, having a savings
account and having a loan in a formal financial institution. Taking advantage of the information in the
Global Findex data set, we can measure the usage dimension of formal financial services.
We built the indicator to account for people using at least one formal financial service that allows
making and receive payments and storage money by adding information from several questions in the
Global Findex. We consider as formal financial service users for this indicator the percentage of
respondents who report having an account (by themselves or together with someone else) at a bank
or another type of financial institution. Account at a financial institution includes respondents who
report having an account at a bank or at another type of financial institution, such as a credit union,
microfinance institution, cooperative, or the post office (if applicable), or having a debit card in their
own name. It includes an additional 2.77 percent and 2.04, for 2014 and 2011 respectively, of
respondents who report not having any of the previous products but receive wages, government

Measuring financial inclusion: a multidimensional index 5

transfers, or payments for agricultural products into an account at a financial institution in the past 12
months; pay utility bills or school fees from an account at a financial institution in the past 12 months;
or receive wages or government transfers into a card in the past 12 months. Often, these individuals
are not aware that they have a bank account. 7 In addition, we consider as banked those individuals
who reported not having a bank account because someone else in the family already has one. They are
contemplated as indirect users of formal financial services. 8 Finally, in order to account only for active
financial products, we define dormant accounts and subtract them from the usage indicator by
removing the percentage of respondents with an account at a bank or another type of financial
institution who report neither a deposit into nor a withdrawal from their account in the past 12
months. The savings and loan indicators represent the percentage of adult population that saves and
has a loan in a formal financial institution respectively. The upper panel in Table 1 shows descriptive
statistics of the indicators that we use to measure usage dimension, for 2014. For all the demand-side
indicators, data is aggregated at country level by computing the proportion of individuals in each
category and then applying the weighting scheme corresponding to the sample in each country.

2.2 Barriers

The barriers to financial inclusion, perceived by unbanked individuals, provide information about the
obstacles that prevent them from using formal financial services. This information offers an additional
angle to assess the extent of financial inclusion since it offers the number of financially excluded
individuals and the reasons perceived by these individuals for being excluded from the formal financial
system. There are two types of financial exclusion: voluntary or self-exclusion and involuntary. If we
treat financial inclusion as a behavioral issue, individuals need to decide whether to participate in the
formal financial system given their budget constraints and utility function. One possibility is that some
individuals do not have a demand for formal financial services, leading them to self- exclusion because
of cultural reasons, lack of money or just because they are not aware of the benefits of these types of
services. This choice can be shaped by imperfect information about the utility of financial services for
managing risk, savings for the future and affordability of different investments such as education or
buying a house. However, exclusion can also be due to other market imperfections such as the lack of
access to financial services or an inappropriate product range that does not satisfy people’s needs. The
latter obstacles that hinder financial inclusion may be associated with the category of involuntary
exclusion so that people cannot satisfy their demand.
In order to measure the degree of inclusiveness of financial systems, from the unbanked
perspective, we take into account only the information about barriers that represent involuntary
exclusion such as distance, lack of the necessary documentation, affordability and lack of trust in the
formal financial system. The question about perceived barriers is formulated in the Global Findex
questionnaire in such a way that individuals can choose multiple reasons for their not having a bank
account.
According to the Global Findex data set, almost 20 percent and 16, for 2011 and 2014 respectively,
of the unbanked population cites distance as one of the reasons that prevents them from having an
account. This reason is observed more frequently in developing countries where access points are
remote. Documentation requirements are also cited as a perceived barrier for financial inclusion by
almost 20 percent of the unbanked in 2011 and 19 percent in 2014. Affordability is the second most

7
Since we want to compute and index including both developed and less-developed countries we cannot take into account
the usage of financial services for enterprises due to the lack of harmonized information for developed countries. This
information is only available for less-developed countries in the World Bank’s Enterprise Survey.
8
We do not consider people with insurance since this information is only available for less-developed countries.

6 Measuring financial inclusion: a multidimensional index

cited obstacle for financial inclusion, after only lack of money, and prevented 25 percent of the
unbanked from using formal financial services in 2011 (same figure for 2014). Finally, the lack of trust
in the financial system is cited by 13 percent of adults in 2011 and 10 percent in 2014. All these
variables are introduced in our analysis in their negative form so that the fewer people reporting the
barrier, the greater the inclusiveness of the financial system.

2.3 Access

Access to formal financial services represents the possibility for individuals to use them. However,
greater access does not necessarily imply a higher level of financial inclusion. There is a threshold for
access since, when it reaches a certain level, a marginal increase does not necessarily generate a
financial inclusion increase. It may enhance frequency in the use of financial services, by improving
intensive margin of usage but does not necessarily increase extensive margin, in terms of higher
percentages of accounts held or any other financial service. However, greater access is expected to
foster financial inclusion when access levels are below the threshold, via greater availability, if financial
services meet the needs of the population. Also, when increasing access is generated from different
financial companies, more intense competition may increase the consumption of financial services via
prices too, even above the threshold.
We construct the access dimension with supply-side data at country level from three basic
indicators: automated teller machines (ATMs) (per 100,000 adults), commercial bank branches (per
100,000 adults) and banking agents (per 100,000 adults). Banking agents, also known as banking
correspondents, are non-financial commercial establishments that offer basic financial services under
the name of a financial services provider, facilitating access points to the formal financial system. The
establishments are spread across diverse sectors (grocery shops, gas stations, postal services,
pharmacies, etc.), as long as they are brick-and-mortar stores whose core business involves managing
cash. In its most basic form, banking correspondents carry out only transactional operations (cash in,
cash out) and payments but, in many cases, they have evolved as a distribution channel for the banks
‘credit, saving and insurance products Cámara et al. (2015). 9
This three indicators account for the physical points of services offered by the institutions
belonging the formal financial system such as commercial banks, credit unions, saving and credit
cooperatives, deposit-taking microfinance and other deposit takers (savings and loan associations,
building societies, rural banks and agricultural banks, post office giro institutions, post office savings
banks, savings banks, and money market funds). Information on ATMs and bank branches is collected
by financial services providers though the International Monetary Fund’s Financial Access Survey (FAS).
Data on banking agents are gathered by Cámara et al. (2015). 10
Since banking agents do not exist in all the countries, we add up banking agents to the number of
bank branches in order to not to bias the analysis. Thus, we use a single indicator which contains
information of the number of bank branches and banking agents together. Although banking agents
play an important role in enhancing access, distance is still one of the reasons why people do not
participate in the formal financial system. In 2014 perceived distance as a barrier for financial inclusion

9
The key difference with respect to other financial channels such as in-store branches or kiosks is that, in the banking
correspondent business model, financial services are provided by the employees of the commercial establishment itself,
not by the bank´s employees or machines. This outsourcing strategy leads to an improvement in efficiency for banks that
makes it sustainable to focus on low-income clients with costly efficient access channels.
10
Data on adult population come from the World Development Indicators provided by the World Bank.

Measuring financial inclusion: a multidimensional index 7

 decreased by 5 percent on average but it decreases for the group of developed countries. 11 Both
technology and regulation are contributing greatly to extend availability of access points. However,
these advances might not be perceived with the same intensity by financially excluded people in the
developing world yet.

Descriptive Statistics
Table 1

Variable Obs. Mean Std. Dev Min Max

Usage
Account 137 61.00 27.00 8.00 100

Loan 137 11.60 5.15 1.31 26.43

Savings 137 24.46 16.85 0.90 68.84

Access
ATMs/100,000 pop. 137 56.18 52.46 0.49 270.13
Branches and agents /100,000 pop. 137 20.82 17.91 0.66 89.73
Barriers
Distance 137 17.06 11.65 0.00 49.16
Affordability 137 26.32 14.59 0.00 59.81
Documentation 137 18.60 11.98 0.00 49.47
Lack of trust 137 18.83 12.10 0.00 57.45

Source: Own elaboration

3. Principal Component Analysis as an Indexing Strategy

Financial inclusion is an unobservable concept which cannot be measured quantitatively in a

straightforward way. However this variable is supposed to be determined by the interaction of a number
of causal variables. We assume that behind a set of correlated variables we can find an underlying
latent structure that can be identified with a latent variable as is the case of financial inclusion. Two
important issues arise in the estimate of any latent variable: the selection of relevant causal variables
and the estimation of parameters (weights). Regarding the first issue, it is not possible to apply
standard reduction of information criterion approaches for the selection of variables. For the second,
since financial inclusion is unobserved, standard regression techniques are also unfeasible to estimate
the parameters. The weight assignment to the indicators or sub-indices is critical to maximize the
information from a data set included in an index. A good composite index should comprise important
information from all the indicators, but not be strongly biased towards one or more of these indicators.
Thus, we seek to determine the best weighted combination of indicators that define our underlying
structure by applying two-stage principal components methodology to estimate the degree of financial
inclusion as an indexing strategy.

11
Distance is a problem that affects mainly less-developed countries. In developed countries, the proportion of the unbanked
who perceive distance as a problem is only 10 per cent.

8 Measuring financial inclusion: a multidimensional index

 Our dataset contains causal variables which summarize the information for the degree of financial
inclusion. As explained in the previous section, each causal variable relates to different dimensions that
define financial inclusion. The purpose of dividing the overall set of indicators into three sub-indices is
twofold. On the one hand, the three sub-indices have a meaning so, we get additional disaggregated
information that is also useful for policy making. On the other hand, for methodological purposes,
since the sub-indices contain highly correlated indicators within dimension, we estimate the sub-
indices first, rather than estimating the overall index directly by picking all the indicators at the same
time. This is a preferred strategy because it avoids weight’s biases towards indicators which exhibit the
highest correlation (Mishra, 2007). We minimize this problem by applying two-stage PCA (Nagar and
Basu, 2004). In the first stage, we estimate the three sub-indices: usage, barriers and access, which
defined financial inclusion. In the second stage, we estimate the weights for each dimension and the
overall financial inclusion index by using the dimensions as explanatory variables. Regarding the
number of variables included in our index, PCA is robust to redundant information.
Let consider that the latent variable financial inclusion is linearly determined as follows:

𝐹𝐹𝐹𝐹𝑖𝑖 = 𝜔𝜔1 𝑌𝑌𝑖𝑖𝑢𝑢 + 𝜔𝜔2 𝑌𝑌𝑖𝑖𝑏𝑏 + 𝜔𝜔3 𝑌𝑌𝑖𝑖𝑎𝑎 + 𝑒𝑒𝑖𝑖 (1)

where subscript 𝑖𝑖 denotes the country, and �Yiu , Yib , Yia � capture the usage, barriers and access
dimension respectively. Thus, the total variation in financial inclusion is represented by two orthogonal
parts: variation due to causal variables and variation due to error term (𝑒𝑒𝑖𝑖 ). If the model is well
specified, including an adequate number of explanatory variables, 𝐸𝐸(𝑒𝑒) = 0 and the variance of the
error term should be relatively small compared to the variance of the latent variable, financial inclusion.
Thus, we can reasonably assume that the total variation in financial inclusion can be largely explained
by the variation in the causal variables.

3.1 First Stage PCA

The first stage estimates the dimensions, that is, the three unobserved endogenous variables Yiu , Yib , Yia
and the parameters in the following equation system:

𝑌𝑌𝑖𝑖𝑢𝑢 = 𝛽𝛽1 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑖𝑖 + 𝛽𝛽2 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑖𝑖 + 𝛽𝛽3 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑖𝑖 + 𝑢𝑢𝑖𝑖 (2)

𝑌𝑌𝑖𝑖𝑏𝑏 = 𝜃𝜃1 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑖𝑖 + 𝜃𝜃2 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑖𝑖 + 𝜃𝜃3 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑖𝑖 + 𝜃𝜃4 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑖𝑖 + 𝜖𝜖𝑖𝑖 (3)

𝑌𝑌𝑖𝑖𝑎𝑎 = 𝛾𝛾1 𝐴𝐴𝐴𝐴𝐴𝐴𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 + 𝛾𝛾2 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏ℎ𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 + 𝑣𝑣𝑖𝑖 (4)

where account is a variable that represents the individuals who have at least one of the financial
products described in section 2.1, and savings and loan represent individuals who save and have a loan
in the formal financial system. Hence, the three dimensions are also indices that we estimate by
principal components as linear functions of the explanatory variables described in Table 1. Note that
the endogenous variables are unobserved so we need to estimate them jointly with the unknown
parameters: 𝛽𝛽, 𝜃𝜃 and 𝛾𝛾. Let 𝑅𝑅𝑅𝑅, (𝑝𝑝𝑝𝑝𝑝𝑝) be the correlation matrix of the 𝑝𝑝 standardize indicators for each
dimension. We denote 𝜆𝜆𝜆𝜆(𝑗𝑗 = 1, . . . , 𝑝𝑝) as the 𝑗𝑗 − 𝑡𝑡ℎ eigenvalue, subscript 𝑗𝑗 refers to the number of
principal components that also coincides with the number of indicators or sub-indices, 𝑝𝑝. 𝜑𝜑𝜑𝜑(𝑝𝑝𝑝𝑝1) is
the eigenvector of the correlation matrix. We assume that 𝜆𝜆1 > 𝜆𝜆2 > . . . > 𝜆𝜆𝜆𝜆 and denote 𝑃𝑃𝑘𝑘 (𝑘𝑘 =
1, . . . , 𝑝𝑝) as the 𝑘𝑘 − 𝑡𝑡ℎ principal component. We get the corresponding estimator of each dimension
according to the following weighted averages:

Measuring financial inclusion: a multidimensional index 9

 𝑝𝑝
∑𝑗𝑗,𝑘𝑘=1 𝜆𝜆𝑢𝑢 𝑢𝑢
𝑗𝑗 𝑃𝑃𝑘𝑘𝑘𝑘
𝑌𝑌𝑖𝑖𝑢𝑢 = 𝑝𝑝
∑𝑗𝑗=1 𝜆𝜆𝑢𝑢
(5)
𝑗𝑗

𝑝𝑝
∑𝑗𝑗,𝑘𝑘=1 𝜆𝜆𝑏𝑏 𝑏𝑏
𝑗𝑗 𝑃𝑃𝑘𝑘𝑘𝑘
𝑌𝑌𝑖𝑖𝑏𝑏 = 𝑝𝑝
∑𝑗𝑗=1 𝜆𝜆𝑏𝑏
(6)
𝑗𝑗

𝑝𝑝
∑𝑗𝑗,𝑘𝑘=1 𝜆𝜆𝑎𝑎 𝑎𝑎
𝑗𝑗 𝑃𝑃𝑘𝑘𝑘𝑘
𝑌𝑌𝑖𝑖𝑎𝑎 = 𝑝𝑝
∑𝑗𝑗=1 𝜆𝜆𝑎𝑎
(7)
𝑗𝑗

where 𝑃𝑃𝑘𝑘 = 𝑋𝑋𝜆𝜆𝑗𝑗 𝜆𝜆𝑗𝑗 represents the variance of the 𝑘𝑘 − 𝑡𝑡ℎ principal component (weights) and 𝑋𝑋 is
the indicators matrix. The weights given to each component are decreasing, so that the larger
proportion of the variation in each dimension is explained by the first principal component and so on.
Following this order, the 𝑝𝑝 − 𝑡𝑡ℎ principal component is a linear combination of the indicators that
accounts for the smallest variance. In brief, this method represents a 𝑝𝑝-dimensional dataset of
correlated variables by 𝑝𝑝 orthogonal principal components, with the first principal component
explaining the largest amount of information from the initial data. One issue using principal
component analysis is to decide how many components to retain. Although a common practice is to
replace the whole set of causal variables by only the first few principal components, which account for
a substantial proportion of the total variation in all the sample variables, we consider as many
components as the number of explanatory variables. Our concern is to estimate accurately financial
inclusion rather than reducing the data dimensionality so, we avoid discarding information that could
affect our estimates.

3.2 Second Stage PCA

The second stage of the principal component analysis computes the overall financial inclusion index by
replacing 𝑌𝑌𝑖𝑖𝑢𝑢 , 𝑌𝑌𝑖𝑖𝑏𝑏 𝑎𝑎𝑎𝑎𝑎𝑎 𝑌𝑌𝑖𝑖𝑎𝑎 in 𝐸𝐸𝐸𝐸. (1) and applying a similar procedure to that described in the first stage
(to estimate the vectors of parameters 𝜆𝜆). This produces the following estimator of the financial
inclusion index:

𝑝𝑝
∑𝑗𝑗,𝑘𝑘=1 𝜆𝜆𝑗𝑗 𝑃𝑃𝑘𝑘𝑘𝑘
𝐹𝐹𝐹𝐹𝑖𝑖 = 𝑝𝑝 (8)
∑𝑗𝑗=1 𝜆𝜆𝑗𝑗

The highest weight, 𝜆𝜆1 , is attached to the first principal component because it accounts for the
largest proportion of the total variation in all causal variables. Similarly, the second highest weight, 𝜆𝜆2 ,
is attached to the second principal component and so on. After some straightforward algebra, we can
write each component, 𝑃𝑃𝑃𝑃 of (8) as a linear combination of the three sub-indices (𝑝𝑝 = 3) and the
eigenvectors of the respective correlation matrices represented by 𝜑𝜑:

𝑃𝑃1𝑖𝑖 = 𝜑𝜑11 𝑌𝑌𝑖𝑖𝑢𝑢 + 𝜑𝜑12 𝑌𝑌𝑖𝑖𝑏𝑏 + 𝜑𝜑13 𝑌𝑌𝑖𝑖𝑎𝑎 (9)

𝑃𝑃2𝑖𝑖 = 𝜑𝜑21 𝑌𝑌𝑖𝑖𝑢𝑢 + 𝜑𝜑22 𝑌𝑌𝑖𝑖𝑏𝑏 + 𝜑𝜑23 𝑌𝑌𝑖𝑖𝑎𝑎 (10)
𝑃𝑃3𝑖𝑖 = 𝜑𝜑31 𝑌𝑌𝑖𝑖𝑢𝑢 + 𝜑𝜑32 𝑌𝑌𝑖𝑖𝑏𝑏 + 𝜑𝜑33 𝑌𝑌𝑖𝑖𝑎𝑎 (11)

so that the financial inclusion index can be expressed as:

10 Measuring financial inclusion: a multidimensional index

 𝑢𝑢 𝑏𝑏 𝑎𝑎
∑3
𝑗𝑗=1 𝜆𝜆𝑗𝑗 �𝜑𝜑𝑗𝑗1 𝑌𝑌𝑖𝑖 +𝜑𝜑𝑗𝑗2 𝑌𝑌𝑖𝑖 +𝜑𝜑𝑗𝑗3 𝑌𝑌𝑖𝑖 �
𝐹𝐹𝐹𝐹𝑖𝑖 = (12)
∑3
𝑗𝑗=1 𝜆𝜆𝑗𝑗

Rearranging terms, we can express the overall financial inclusion index as a weighted average of
the dimensions as in Eq. (1). The parameters 𝜔𝜔𝑘𝑘 are the relative weights (importance) of each
dimension in the final index, which are computed as: 12

∑3
𝑗𝑗=1 𝜆𝜆𝑗𝑗 𝜑𝜑𝑗𝑗𝑗𝑗
𝜔𝜔𝑖𝑖 = , 𝑘𝑘 = 1, 2, 3. (13)
∑3
𝑗𝑗=1 𝜆𝜆𝑗𝑗

4. Results

In this section, we present the estimated financial inclusion indices for 137 developed and less-
developed countries (see Table A1 in the appendix) by two-stage PCA for the years 2011 and 2014.
The correlation matrix for the causal variables used to measure financial inclusion is reported in
Table 2.

4.1 Financial Inclusion Dimensions

In the first stage, we compute the weights for the causal variables for each sub-index and estimate the
latent variables: usage, barriers and access that represent the dimensions of the financial inclusion
index. Since we construct the sub-indices as weighted averages of the principal components, it is
possible to gather the coefficients for each causal variable. These weights are derived by Eqs. (2 − 4)
and normalized such that their sum is 1.

12
In general the sum of the weights expressed by the formula above does not necessarily have to equal 1 due to the fact that
principal component methodology normalizes the mode of each eigenvector to 1. The weights therefore could be very
close to but not always equal to 1.

Measuring financial inclusion: a multidimensional index 11

 Correlation Matrix
Table 2

Variables [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]

Account 1 - - - - - - - - - -

Loan 0.53 1 - - - - - - - - -

Savings 0.81 0.57 1 - - - - - - - -

ATMs/100,000 pop. 0.68 0.33 0.54 1 - - - - - - -

Branches/100,000 pop. 0.55 0.25 0.31 0.56 1 - - - - - -

ATMs/1,000 Km2 0.35 0.11 0.34 0.60 0.20 1 - - - - -

Branches/1,000 Km2 0.44 0.00 0.35 0.45 0.56 0.64 1 - - - -

Distance -0.45 -0.25 -0.27 -0.39 -0.43 -0.21 -0.40 1 - - -

High cost -0.43 -0.29 -0.28 -0.34 -0.26 -0.26 -0.30 0.55 1 - -

Documentation -0.31 -0.23 -0.16 -0.31 -0.28 -0.05 -0.13 0.49 0.39 1 -

Lack of trust -0.18 -0.05 -0.30 0.01 0.08 -0.21 -0.26 0.03 0.31 -0.07 1

Source: Own elaboration

Notes: Total Pearson correlations for 2014 data

12 Measuring financial inclusion: a multidimensional index

 With regard to the weighting scheme, we observe that the contributions of the different indicators
barely change over time. For simplicity we only refer to the weights for 2014. For the usage dimension,
the indicator for loans has the highest weight (0.40), followed by having an account (0.33) and savings
(0.27) (see upper panel of Table 3). It is important to notice that although the weights are not evenly
distributed, none of the indicators is dominant; this is a desirable condition for an index. For the access
dimension, the ratios of ATMs have higher weight (0.61) than the bank branches and agents (0.39, see
middle panel of Table 3). It is because ATMs are highly present in more mature markets so differences
across countries are larger. 13 Finally, the lower panel of Table 3 shows the weights for the indicators in
the barriers dimension. For the first three indicators (distance, affordability and documentation), the
weights are also very similar, at 0.21, 0.25 and 0.25 respectively, and there only very small changes over
time. Lack of trust is the most important indicator in defining the barriers dimension, with a weight
close to 0.30.

Principal Components Estimates

Table 3
Usage Usage
Variable P C1 P C2 P C3 P C4 norm. weight
Account 0.5968 -0.4551 0.6608 - 0.33
Loan 0.5126 0.8499 0.1223 - 0.40
Savings 0.6172 -0.2658 -0.7041 - 0.27
Eigenvalues 2.2617 0.5579 0.1804 -
Access

Variable P C1 P C2 P C3 P C4 norm. weight

ATMs per 100,000 pop. 0.5204 0.0368 0.7283 -0.4443 0.61
Branches per 100,000 pop. 0.4546 0.7461 -0.0687 0.4816 0.39
Eigenvalues 2.5050 0.8044 0.5530 0.1377

Barriers

Variable P C1 P C2 P C3 P C4 norm. weight

Distance 0.5198 -0.3481 -0.2594 0.7358 0.21
Affordability 0.5357 -0.0126 -0.5986 -0.5955 0.25
Documentation 0.5184 -0.3407 0.7373 -0.2676 0.25
Trust 0.4172 0.8733 0.1757 0.1803 0.29
Eigenvalues 3.1286 0.5854 0.1501 0.1358

Source: Own elaboration.

Notes: The weights are normalized to sum 1. Figures refer to 2014 data

13
For a robustness check, we also include branches and ATMs ratios per square kilometre. However, similar access indicators
related to population are more powerful in measuring access since correlation with the rest of the indicators is much
higher.

Measuring financial inclusion: a multidimensional index 13

 Since weights are obtained from the information in the principal components and the
corresponding eigenvalues, it is worth studying the composition of these components to understand
the structure of our estimated indices. Table 4 shows, in a cumulative way and by dimensions, the
amount of the total variance explained by the different components. For the usage dimension, we
observe that the first component, which contains 75% of the total information in this dimension (see
Table 4) has an even contribution of the three indicators: account, loan and savings. This suggests that
these three indicators measure the same latent structure. However, only the indicator referring to loans
adds extra information through the second component. It might indicate that having a loan also
represents a stage of greater financial inclusion since most people who have a loan already have
another financial product, such as a bank account or pay-roll account. 14 As a result, having a loan may
be an accurate indicator to identify more consolidated stages of financial inclusion. When defining the
access dimension, as shown in the middle panel of Table 3, we again find an even contribution of the
two indicators to the first principal component since the coefficients in the eigenvector for this
component are similar. Finally, for the barriers dimension, we also find that the four indicators
contribute evenly to the first component, which accounts for almost 80 per cent of the total variation
in the data. Distance, affordability and documentation have their highest loadings in the first
component. Although lack of trust contributes to the first component, it has its highest weight in the
second component, which indicates that this variable also adds extra information, in a different
structure, from the first component. Lack of trust is a structural variable that can be related to not only
idiosyncratic financial system issues (efficiency of financial institutions, financial stability, episodes of
bank failures, etc.) but also to broader issues beyond the financial markets, such as governance,
cultural norms, economic crises or macroeconomic variables such as inflation.

Cumulative Variance Explained by Components

Table 4
Components Cumulative Variance
Usage
P C1 0.7539
P C2 0.9399
P C3 1
Access
P C1 0.6262
P C2 0.8273
P C3 0.9656
P C4 1
Barriers
P C1 0.7822
P C2 0.9285
P C3 0.9660
P C4 1
Source: Own elaboration
Notes: Figures refer to 2014 data

14
People who start to use formal financial services by having a loan, although they might exist, should be a very small
minority.

14 Measuring financial inclusion: a multidimensional index

 Table 5 shows the list of countries ranked by the degree of usage, access and barriers. 15 For a
more intuitive interpretation, the sub-indices are normalized to be between 0 and 1, where 1 indicates
the best relative position in the dimension related to financial inclusion and 0 the worse. The
computation of the sub-indices to estimate the dimensions can be useful information for policy-
makers and governments when designing financial inclusion strategies. The idea is that policy-makers
can obtain useful information to design interventions by using the information provided by weights in
such a way that optimize financial inclusion strategies.

4.2 Multidimensional Financial Inclusion Index

In the second stage, we apply PCA on the three sub-indices (usage, access and barriers) to compute
their weights in the overall index. Table 6 presents the composition of the principal components and
the normalized weights for each dimension or sub-index, for 2014. Results are similar for 2011. The last
column shows that PCA assigns the highest weight to access (0.42), followed by usage with a weight of
0.30 and barriers at 0.28. Thus, this information reveals that access is the most important dimension for
explaining the degree of financial inclusion. Supply of formal financial services contributes more than
number of users to explain the latent structure behind our pool of indicators, i.e. the degree of
financial inclusion. It can be explained because access represents a necessary, but not sufficient
condition, for using formal financial services.
In terms of the principal component structure, we observe that the first and most important
component, accounting for 76 per cent of the total variation in the data (see Table 7), has an even
contribution of the three dimensions. As explained previously, this has to hold to ensure that the three
dimensions measure the same latent structure which is interpreted as the degree of financial
inclusion. 16 Moreover, unlike usage and barriers, access allocates part of its information in the second
component, so this dimension not only contributes to the overall index through the first principal
component, but also adds extra information through the second component and gains importance in
explaining the overall index.
The first column of Table 8 shows the ranking position of countries according to their scores in the
financial inclusion index in 2014, from the highest to the lowest score. The third column represents the
ranking variations, from 2011 to 2014. As expected, developed countries have the most inclusive
financial systems. The first quarter of the ranking (positions 1 to 40) corresponds to developed
countries with few exceptions such as Brazil (4), Mongolia (20), Bangladesh (22), Colombia (36) and
Thailand (39). This group of low-income countries outperforms other middle income countries and
even some high-income countries. Brazil exhibits one of the best performances in the table. A factor
that contributes to this success is related to the important role that the public sector takes in the
financial system. The existence of social support programs, sponsored by the government through the
formal financial system, generates usage of formal financial services for a vulnerable part of the
population.

15
Using two-stage PCA, we can compute indices by countries as well as aggregated by regions. Due to space limitations, we
report the county-based analysis only.
16
Tables 4 and 7 show that, in most of the cases, only the first component explains more than 75 per cent of the causal
variables’ total variation (except for the access dimension that explains 62 per cent). Thus, the strategy of taking only the
first principal component may be a good approximation for estimating the dimensions and the degree of financial
inclusion as well.

Measuring financial inclusion: a multidimensional index 15

 Ranking of Countries by Dimension
Table 5
Usage Access Barriers
Country rank Country rank Country rank
Israel 1 Bangladesh 1 Norway 1
Sweden 2 Brazil 2 Sweden 2
Norway 3 Korea, Rep. 3 United Kingdom 3
Singapore 4 Colombia 4 Denmark 4
New Zealand 5 Peru 5 Netherlands 5
Mauritius 6 Russian Federation 6 Australia 6
Japan 7 Canada 7 France 7
France 8 Portugal 8 Japan 8
Luxembourg 9 United States 9 New Zealand 9
Denmark 10 Australia 10 Canada 10
United Kingdom 11 Chile 11 Finland 11
Finland 12 Spain 12 Belgium 12
Canada 13 Luxembourg 13 Switzerland 13
Australia 14 United Kingdom 14 Austria 14
Germany 15 Croatia 15 Singapore 15
Netherlands 16 Japan 16 Spain 16
Belgium 17 Costa Rica 17 Estonia 17
Mongolia 18 Austria 18 Malta 18
Austria 19 Slovenia 19 Ireland 19
United States 20 Israel 20 Germany 20
Ireland 21 Italy 21 Mongolia 21
Hong Kong SAR, China 22 Bulgaria 22 Korea, Rep. 22
Korea, Rep. 23 France 23 Luxembourg 23
Sri Lanka 24 Switzerland 24 Mauritius 24
Switzerland 25 Mongolia 25 Sri Lanka 25
Chile 26 Germany 26 Slovenia 26
Spain 27 Ireland 27 Greece 27
Slovak Republic 28 Belgium 28 Hong Kong SAR, China 28
Malta 29 Thailand 29 Latvia 29
Estonia 30 Estonia 30 Jordan 30
Latvia 31 New Zealand 31 Israel 31
Uruguay 32 Latvia 32 Croatia 32
Poland 33 Slovak Republic 33 Serbia 33
Slovenia 34 Ecuador 34 United States 34
Czech Republic 35 Poland 35 Lebanon 35
Croatia 36 Montenegro 36 China 36
Brazil 37 Lithuania 37 Thailand 37
Italy 38 Turkey 38 Cyprus 38
Bosnia and Herzegovina 39 Czech Republic 39 Ethiopia 39
Greece 40 China 40 United Arab Emirates 40
Cyprus 41 Hungary 41 Italy 41
Ecuador 42 Kazakhstan 42 Portugal 42
Portugal 43 Ukraine 43 Algeria 43
United Arab Emirates 44 South Africa 44 Kuwait 44
Lithuania 45 Greece 45 Venezuela, RB 45
China 46 Guatemala 46 Bosnia and Herzegovina 46
Thailand 47 Mexico 47 Brazil 47
Hungary 48 Romania 48 Vietnam 48
Bulgaria 49 Serbia 49 Poland 49
Kuwait 50 Pakistan 50 Macedonia, FYR 50
Malaysia 51 Malta 51 Belarus 51
Costa Rica 52 Cyprus 52 Czech Republic 52
Montenegro 53 Belarus 53 Tunisia 53
Macedonia, FYR 54 Saudi Arabia 54 Slovak Republic 54
Lebanon 55 Georgia 55 Costa Rica 55
Serbia 56 Panama 56 Lithuania 56

16 Measuring financial inclusion: a multidimensional index

 Ranking of Countries by Dimension
Table 5 cont
Usage Access Barriers
Country rank Country rank Country rank
Russian Federation 57 Denmark 57 Bhutan 57
Bolivia 58 Armenia 58 Saudi Arabia 58
Argentina 59 Bosnia and Herzegovina 59 Malaysia 59
Jamaica 60 Malaysia 60 Dominican Republic 60
Bhutan 61 Macedonia, FYR 61 Montenegro 61
Saudi Arabia 62 Kuwait 62 Hungary 62
Belarus 63 United Arab Emirates 63 Rwanda 63
South Africa 64 Argentina 64 Russian Federation 64
Dominican Republic 65 Lebanon 65 Myanmar 65
Turkey 66 Hong Kong SAR, China 66 Georgia 66
Namibia 67 Venezuela, RB 67 Jamaica 67
Romania 68 Singapore 68 Bulgaria 68
Venezuela, RB 69 Mauritius 69 Romania 69
Kazakhstan 70 Namibia 70 South Africa 70
Georgia 71 Netherlands 71 Kazakhstan 71
El Salvador 72 Belize 72 Uruguay 72
Colombia 73 Uruguay 73 India 73
Botswana 74 Gabon 74 Namibia 74
Ukraine 75 Indonesia 75 Kosovo 75
Kosovo 76 Sweden 76 Argentina 76
Kenya 77 Norway 77 West Bank and Gaza 77
Peru 78 Azerbaijan 78 Belize 78
Belize 79 Kosovo 79 Sudan 79
Rwanda 80 Albania 80 Nigeria 80
Panama 81 Honduras 81 Ecuador 81
Nigeria 82 Egypt, Arab Rep. 82 Yemen, Rep. 82
Guatemala 83 Dominican Republic 83 Colombia 83
Azerbaijan 84 India 84 Nepal 84
Indonesia 85 Jordan 85 Chile 85
Vietnam 86 Bolivia 86 Ghana 86
Algeria 87 Moldova 87 Bangladesh 87
India 88 Finland 88 Indonesia 88
Mexico 89 Botswana 89 Kenya 89
Honduras 90 El Salvador 90 Panama 90
Jordan 91 Philippines 91 Burundi 91
Nepal 92 Jamaica 92 Egypt, Arab Rep. 92
Ghana 93 Nicaragua 93 Zambia 93
Myanmar 94 Uzbekistan 94 Uzbekistan 94
Armenia 95 Tunisia 95 Albania 95
Nicaragua 96 Kenya 96 Mali 96
Bangladesh 97 Bhutan 97 Cote d’Ivoire 97
Gabon 98 Rwanda 98 Botswana 98
Tunisia 99 Angola 99 Azerbaijan 99
Albania 100 Sri Lanka 100 Zimbabwe 100
Angola 101 Kyrgyz Republic 101 Mauritania 101
Uganda 102 Zimbabwe 102 Pakistan 102
Philippines 103 West Bank and Gaza 103 Kyrgyz Republic 103
Cambodia 104 Vietnam 104 Burkina Faso 104
Kyrgyz Republic 105 Nigeria 105 Gabon 105
Mauritania 106 Cambodia 106 Bolivia 106
Zambia 107 Algeria 107 Ukraine 107
Ethiopia 108 Nepal 108 Benin 108
Uzbekistan 109 Tajikistan 109 Armenia 109
West Bank and Gaza 110 Zambia 110 Malawi 110
Moldova 111 Ghana 111 Moldova 111
Benin 112 Mauritania 112 Madagascar 112
Egypt, Arab Rep. 113 Sudan 113 Honduras 113

Measuring financial inclusion: a multidimensional index 17

 Ranking of Countries by Dimension
Table 5 cont
Usage Access Barriers
Country rank Country rank Country rank
Egypt, Arab Rep. 113 Sudan 113 Honduras 113
Togo 114 Cote d’Ivoire 114 Haiti 114
Congo, Rep. 115 Tanzania 115 Mexico 115
Tanzania 116 Mali 116 Cameroon 116
Sudan 117 Togo 117 Turkey 117
Malawi 118 Malawi 118 El Salvador 118
Burkina Faso 119 Senegal 119 Guatemala 119
Haiti 120 Benin 120 Congo, Rep. 120
Zimbabwe 121 Congo, Rep. 121 Angola 121
Cote d’Ivoire 122 Uganda 122 Uganda 122
Tajikistan 123 Iraq 123 Togo 123
Sierra Leone 124 Yemen, Rep. 124 Chad 124
Senegal 125 Burundi 125 Guinea 125
Cameroon 126 Cameroon 126 Sierra Leone 126
Afghanistan 127 Burkina Faso 127 Tajikistan 127
Congo, Dem. Rep. 128 Myanmar 128 Nicaragua 128
Mali 129 Madagascar 129 Peru 129
Iraq 130 Haiti 130 Senegal 130
Chad 131 Guinea 131 Tanzania 131
Pakistan 132 Ethiopia 132 Philippines 132
Burundi 133 Afghanistan 133 Iraq 133
Guinea 134 Sierra Leone 134 Congo, Dem. Rep. 134
Madagascar 135 Niger 135 Afghanistan 135
Yemen, Rep. 136 Congo, Dem. Rep. 136 Niger 136
Niger 137 Chad 137 Cambodia 137
Source: Own elaboration
Notes: Rankings are assigned according to the scores in each dimension of the financial inclusion index for
2014 data. Ranking for 2011 is available upon request.

Such way of facilitating money transfers is running in Brazil, Bangladesh, Mongolia and
Thailand. 17 Most importantly, Brazil has a huge banking agent network, pioneering in Latin America.
The same also happens with Bangladesh. Finally the role of state-owned banks, with the mandate of
fostering financial inclusion, is also an important driver. The second quarter of the ranking, down to
the position 40 to 80 is made up mostly of the Eastern European middle-income countries and some
Asian (Sri Lanka, China, United Arab Emirates, etc.) and fewer Latin American countries (Costa Rica,
Ecuador, Venezuela, Peru and Argentina, most of them below the 60th position).
The remaining positions after these two groups (81 to 137, less than the second half of the
ranking) consist of a heterogeneous group that includes countries from Latin America, Asia and all the
African countries in the sample except South Africa (63). The last ten countries, at the bottom of the
ranking, are low-income African countries. Most African countries in our sample perform poorly in
financial inclusion terms, with the only exceptions being South Africa, Nigeria (85) and Kenia (89).
Given the relevance of the access dimension in the financial inclusion index, the low levels of financial

17
Moreover, for Mongolia, the high level of financial inclusion may be due in large part to universal cash hand-outs from the
government’s Human Development Fund as well as pensions, health insurance and student tuition payments. Around 50%
of all bank account holders over the age of 15 cite receiving government payments as the most common use for a bank
account, according to the Global Findex database.

18 Measuring financial inclusion: a multidimensional index

inclusion in some African countries should improve by including data on e-money outlets, belonging
telecommunication companies, since this business model is widespread in the region. This argument
does not apply to Latin American countries since e-money is provided by companies that belong the
formal financial system.

Principal Component Estimates

Financial Inclusion Index

Table 6

Variable P C1 P C2 P C3 norm. weight

Usage 0.5775 -0.5758 0.5787 0.39

Access 0.5437 0.8001 0.2535 0.42

Barriers 0.609 -0.1682 -0.7752 0.28

Eigenvalues 2.2805 0.4855 0.2339

Source: Own elaboration

Notes: The weights are normalized to sum 1. Figures refer to 2014 data

Cumulative Variance Explained by Components

Financial Inclusion Index
Table 7

Components Cumulative variance

PC1 0.7602
PC2 0.9220
PC3 1
Source: Own elaboration
Notes: Figures refer to 2014 data.

5. Conclusions and Policy Recommendations

Financial inclusion is an essential ingredient of economic development and poverty reduction and it
can also be a way of preventing social exclusion. A person’s right to use formal financial services, to
prevent exclusion, must be a priority. However, efforts to measure financial inclusion are scarce and
incomplete. Financial inclusion is a multidimensional concept that cannot be captured accurately with
single indicators, but is determined by a much larger set of indicators than the few considered in
existing works. The nature of the financial systems is complex and heterogeneous. An inclusive
financial system needs particularly to encourage usage of financial services on the part of society’s
most vulnerable groups; that is, those most affected by obstacles to financial inclusion.
Existing financial inclusion composite indices are questionable since they choose arbitrary weights.
This paper proposes a two-stage PCA to measure the extent of financial inclusion for a country or
region. This methodology is statistically sound for index construction and robust to high dimensional
data. We measure financial inclusion through a composite index for 137 countries by using 20 causal

Measuring financial inclusion: a multidimensional index 19

variables as financial inclusion determinants for 2011 and 2014. This index is comparable across
countries and over time. Specifically, our index poses that the degree of financial inclusion is
determined by the maximization of usage and access to formal financial services, as well as by the
minimization of obstacles causing involuntary exclusion. Demand-side information to assess the usage
and barriers dimensions is key in determining the degree of financial inclusion. The dimension of
usage measures financial inclusion from the banked perspective, and barriers do so from the
perspective of the unbanked. Including information of financially excluded people helps to reveal a
comprehensive picture of the extent of financial system inclusiveness. Our major contribution is
twofold. First, we use a parametric method, robust to redundant information, to determine the
contribution of each indicator to our financial inclusion index. It has the advantage of not employing
any exogenous, subjective information. Second, we build a comprehensive index that includes both
demand- and supply-side information.
As shown by our estimates, access is the most important dimension for determining the level of
financial inclusion. It represents a necessary but not sufficient condition for using formal financial
services. However, due to data constraints, we are not able to measure access to the formal financial
system in a comprehensive way. We only measure physical access. Although remarkable effort has
been done in the last five years in terms of data production (i.e. availability and quality), there exist
important limitations. For instance, the traditional indicators used to measure access are currently
incomplete. New technology adopted by the financial sector goes beyond the traditional banking
access measured by number of physical access points. New mobile banking developments and the use
of financial services on the internet open up new channels for accessing formal financial services that,
under certain circumstances, overcome the distance as a barrier for access. Measuring these new
channels is not straightforward because of the lack of homogeneous measures for a wide range of
countries. 18 Although we cannot get an accurate proxy to take into account the new access channels,
we do include information on mobile and internet banking in the usage dimension. Efforts in such
direction yield relevant improvements on the analysis of financial inclusion’s causes and consequences.
Despite of this caveat, the creation of such an index is useful to shed some light on the
determinants of financial inclusion as well as its contribution to economic growth and development.
Our index is easy to interpret and compute. We believe that more granular information on the
different dimensions, in the form of disaggregated data by product, usage frequency and geo-locate
information on access points, world be useful for a more accurate assessment of financial inclusion
that leads policy recommendations.

18
The bias introduced for omitting this information might be different for developed countries and less-developed countries.
We cannot quantify this bias but we have some intuitive information about its direction. Although the lack of data to
measure financial service access via internet and smart phone underestimates access more for developed countries than
for less-developed countries, the effect on financial inclusion may be larger for less-developed countries than for
developed countries. The latter have greater access levels and, as such, increases in access may have a larger effect on less-
developed countries that start from lower levels. Likewise, less-developed countries benefit more from banking
correspondents as well as from basic mobile phones.

20 Measuring financial inclusion: a multidimensional index

Financial Inclusion Index Country Ranking, 2014
Table 8
Rank/137 Country Δ Rank/137 Country Δ Rank/137 Country Δ
1 Israel 32 47 Lithuania -7 93 Nepal -1
2 Korea, Rep 3 48 Bosnia and Herz. 3 94 Armenia -6
3 Canada 5 49 Bulgaria -4 95 Albania -18
4 Brazil 17 50 Serbia -4 96 Ghana 7
5 Japan 8 51 UAE -1 97 Mexico -6
6 Australia -5 52 Lebanon 3 98 Guatemala -26
7 United Kingdom 9 53 Montenegro -4 99 Egypt, Arab Rep. -18
8 Sweden 16 54 Kuwait -20 100 Gabon 11
9 Luxembourg -6 55 Hungary -16 101 Sudan 24
10 Norway N/A 56 Uruguay 2 102 Pakistan -5
11 New Zealand -1 57 Ecuador 4 103 Uzbekistan -20
12 France -7 58 Macedonia -6 104 Zambia 10
13 Singapore -10 59 Belarus -3 105 El Salvador -3
14 United States 1 60 Malaysia -7 106 Honduras -12
15 Spain -7 61 Saudi Arabia 1 107 Yemen, Rep 0
16 Germany 2 62 Venezuela 4 108 Kyrgyz Rep. 8
17 Austria 3 63 South Africa 5 109 Moldova -3
18 Belgium 1 64 Kazakhstan -1 110 Zimbabwe -11
19 Mauritius 13 65 Romania -6 111 Mauritania N/A
20 Mongolia 11 66 Georgia 5 112 Côte d'Ivoire N/A
21 Denmark 0 67 Jordan 6 113 Burundi 1
22 Bangladesh 42 68 Peru 11 114 Mali 6
23 Ireland -12 69 Bhutan N/A 115 Benin 11
24 Switzerland N/A 70 Argentina 5 116 Angola -16
25 Portugal -17 71 Dominican Rep. 0 117 Burkina Faso 0
26 Finland -1 72 Jamaica -7 118 Malawi -11
27 Croatia -3 73 Namibia N/A 119 Nicaragua -17
28 Netherlands -1 74 Vietnam 10 120 Uganda 10
29 Slovenia -12 75 Algeria 4 121 Madagascar 11
30 Estonia -1 76 Kosovo -5 122 Haiti N/A
31 Chile 23 77 Belize N/A 123 Congo, Rep -11
32 Russia 11 78 Tunisia 9 124 Cameroon -2
33 Latvia -5 79 Rwanda 14 125 Philippines -5
34 Hong Kong 8 80 India -2 126 Togo -1
35 Italy -5 81 Panama 18 127 Tajikistan -1
36 Colombia 21 82 Ethiopia N/A 128 Sierra Leone 4
37 Malta -23 83 Ukraine 1 129 Chad 6
38 Slovak Rep. -1 84 Indonesia 28 130 Guinea -6
39 Thailand -8 85 Nigeria 24 131 Tanzania -1
40 Poland 4 86 Turkey -22 132 Senegal -3
41 Sri Lanka 6 87 Myanmar N/A 133 Iraq -10
42 Greece -6 88 Bolivia 5 134 Congo, Dem. Rep. 0
43 Costa Rica -2 89 Kenya 7 135 Afghanistan 1
44 Czech Rep. -6 90 Botswana 18 136 Niger 1
45 China 3 91 Azerbaijan -1 137 Cambodia -30
46 Cyprus -33 92 W. Bank and Gaza -6
Source: Own elaboration
Notes: Positive (negative) numbers represents an improvement (deterioration) in financial inclusion’s relative position
between 2011 and 2140

Measuring financial inclusion: a multidimensional index 21

 Appendix
Countries
Table A1
Afghanistan Gabon New Zealand
Albania Georgia Nicaragua
Algeria Germany Niger
Angola Ghana Nigeria
Argentina Greece Norway
Armenia Guatemala Pakistan
Australia Guinea Panama
Austria Haiti Peru
Azerbaijan Honduras Philippines
Bangladesh Hong Kong SAR, China Poland
Belarus Hungary Portugal
Belgium India Romania
Belize Indonesia Russian Federation
Benin Iraq Rwanda
Bhutan Ireland Saudi Arabia
Bolivia Israel Senegal
Bosnia and Herzegovina Italy Serbia
Botswana Jamaica Sierra Leone
Brazil Japan Singapore
Bulgaria Jordan Slovak Republic
Burkina Faso Kazakhstan Slovenia
Burundi Kenya South Africa
Cambodia Korea, Rep0. Spain
Cameroon Kosovo Sri Lanka
Canada Kuwait Sudan
Chad Kyrgyz Republic Sweden
Chile Latvia Switzerland
China Lebanon Tajikistan
Colombia Lithuania Tanzania
Congo, Dem0. Rep0. Luxembourg Thailand
Congo, Rep0. Macedonia, FYR Togo
Costa Rica Madagascar Tunisia
Cte d’Ivoire Malawi Turkey
Croatia Malaysia Uganda
Cyprus Mali Ukraine
Czech Republic Malta United Arab Emirates
Denmark Mauritania United Kingdom
Dominican Republic Mauritius United States
Ecuador Mexico Uruguay
Egypt, Arab Rep0. Moldova Uzbekistan
El Salvador Mongolia Venezuela, RB
Estonia Montenegro Vietnam
Ethiopia Myanmar West Bank and Gaza
Finland Namibia Yemen, Rep0.
France Nepal Zambia
Netherlands Zimbabwe
Source: Own elaboration

22 Measuring financial inclusion: a multidimensional index

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Measuring financial inclusion: a multidimensional index 23

Bank of Morocco – CEMLA – IFC Satellite Seminar at the ISI World Statistics Congress on “Financial Inclusion”

Marrakech, Morocco, 14 July 2017

Measuring financial inclusion: a multidimensional index 1

Noelia Cámara, BBVA Research,
and David Tuesta, CAF- Bank of Development for Latin America

1 This presentation was prepared for the meeting. The views expressed are those of the authors and do not necessarily reflect the views of the BIS, the IFC or the central banks
and other institutions represented at the meeting.
 Measuring Financial Inclusion:
A Multidimensional Index
Noelia Camara(BBVA Research)
David Tuesta (CAF- Bank of Development for Latin America)
Bank Al-Maghrib – CEMLA – IFC Satellite Seminar
on Financial Inclusion
Morocco, July 2017
 Outline
1. Motivation

2. Contribution

3. Data

4. Econometric Strategy

5. Empirical results

6. Financial inclusion and geography

7. Conclusions
 1. Motivation: The challenge of
measuring the unobserved
• The use of formal financial services enhances economic growth and
welfare (Bencivenga y Smith, 1991 RES; Rajan y Zingales, 1998 AER;
Beck et al., 2000 JoFE; Levine et al., 2000 JoME; Townsend and
Ueda, 2006 RES; Ergungor, 2010 JoMCB)

• Financial inclusion as well as income, health or home is a basic

ingredient for individuals’ welfare

• While the importance of financial inclusion is well-established,

there is no formal consensus on its measurement
1. Motivation
• Individual indicators: + demand-side data (Demirguç-Kunt and
Klapper, 2013)

• Composite indices:
– Non-parametric methods: +supply-side data ( Sarma, 2008,
2012 and Chakravarty and Pal 2010). They assign the
importance of indicators by choosing the weighs exogenously

– Parametric methods (CFA): + supply-side data (Amidži´c et al.,

2014). The importance of indicators (weights) in the overall
index are determined endogenously
 2. This paper
• We present a country-level multidimensional index to measure the
degree of inclusiveness of financial systems. It is comparable across
countries and over time

• Our index uses demand and supply-side information of banked and

unbanked

• Weights are endogenously determined

• Access and barriers measure the degree of readiness for financial

inclusion while usage is considered as the output
 3. Data

• Demand-side: Usage and Barriers - Global Findex (2011 and 2014)

– The survey collects information about 150,000 nationally
representative and randomly selected adults from 148 countries
– Harmonized micro-data set

• Supply-side: Access
– Financial Access Survey (2011 and 2014): Annual data collected
by country authorities
– Data on banking correspondents : Camara et al., (2015)
 3. Data: Index structure
• Our index covers 140 and 137
countries for 2011 and 2014,
respectively

• It summarizes the information of 20 FI-

related indicators in an efficient way

• We define an inclusive financial system

as one that maximizes usage and
access, while minimizing involuntary
financial exclusion
 3. Data: Usage

• Account: adjusted number of account/card holders in a formal

financial institution or post office over the total population:
corrected by dormant accounts/cards

• Savings:
𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑖𝑖
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑖𝑖 =
𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑖𝑖
• Loans:
𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑖𝑖
𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝑖𝑖 =
𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑖𝑖
 3. Data: barriers
• Trust: percentage of unbanked who do not have a bank account
because they do not trust the formal financial system

• Affordability: percentage of unbanked who do not have a bank

account because they perceive them to be too expensive

• Distance: percentage of unbanked who do not have a bank account

because they perceive that access points are too far away

• Documents: percentage of unbanked who do not have a bank

account because they perceive that lack the necessary documents
 3. Data: access

• Access points:

– Access points with a human interaction: Number of commercial

bank branches and banking correspondents (per 100,000 adults)

– Access points with a machine interaction: ATMs (per 100,000

adults)
 4. Econometric strategy
• We assume that behind our set of correlated variables, we can find
an underlying structure that can be identified with a latent variable
that represents FI

• We need to estimate at the same time the parameters and the

latent variable. Standard regression techniques are unfeasible for
these purposes

• Two-step PCA
 4. Econometric strategy

• First step: estimation of the three dimensions(usage, access and

barriers)

𝑌𝑌𝑢𝑢𝑢𝑢 = 𝛽𝛽1 account𝑖𝑖 +𝛽𝛽2 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑖𝑖 +𝛽𝛽3 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑖𝑖 +𝑢𝑢𝑖𝑖

𝑌𝑌𝑎𝑎𝑖𝑖 = 𝛾𝛾1 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑖𝑖 +𝛾𝛾2 ATM𝑖𝑖 +𝑣𝑣𝑖𝑖

𝑌𝑌𝑏𝑏𝑖𝑖 = 𝛼𝛼1 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑖𝑖 +𝛼𝛼2 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑖𝑖 +𝛼𝛼3 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑖𝑖 +𝛼𝛼4 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑖𝑖 +𝑒𝑒𝑖𝑖

𝑖𝑖: denotes the country, (𝑌𝑌𝑢𝑢 𝑌𝑌𝑎𝑎 𝑌𝑌𝑏𝑏 ) is the dimension’s vector where the
subscripts 𝑢𝑢, 𝑎𝑎 and 𝑏𝑏 denote the dimensions
 4. Econometric strategy

• Second step: estimate of the dimension weights and the overall FI

index (dimensions are the explanatory variables)

𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝒊𝒊 = 𝜽𝜽𝟏𝟏 𝒀𝒀𝒖𝒖𝒊𝒊 + 𝜽𝜽𝟐𝟐 𝒀𝒀𝒂𝒂𝒊𝒊 + 𝜽𝜽𝟑𝟑 𝒀𝒀𝒃𝒃𝒊𝒊 + 𝝉𝝉𝒊𝒊

5. Results: Financial inclusion growth 2011 - 2014
5. Results: Financial inclusion growth 2011 - 2014
 5. Empirical results
60000

United States
50000
GDP per cápita PPP 2014

Austria Australia

40000

South Korea
Spain
30000 Israel

Greece
Chile
20000
Turkey

Iraq Brazil
South Africa Colombia
Mongolia
10000 Peru
El Salvador

Kenya Bangladesh
0
0 10 20 30 40 50 60 70 80 90 100

Financial Inclusion 2014

 5. Empirical results

0.8

0.7
Israel
Financial Education 2014

Australia
0.6
United States
Austria
0.5 Spain
Greece
South Africa Chile Mongolia
0.4
Kenya
Brazil
Colombia South Korea
0.3
Iraq Peru
Turkey

0.2 El Salvador
Bangladesh

0.1

0
0 10 20 30 40 50 60 70 80 90 100

Financial Inclusion 2014

6. Geography and Financial Inclusion

• Hypothesis: There is spatial autocorrelation between the level of

financial inclusion in the country i and its neighbors

• We find evidence in favor of our hypothesis of spatial dependence

• We introduce a weighting mechanism based on geo-position to

control for spatial dependence when calculating the financial
inclusion index
 6. Geography and Financial Inclusion
Spatial autocorrelation

Morans’I: 0.481399 Morans’I: 0.42409

Lagged FI Index 2011

Lagged FI Index 2014

FI Index 2011 FI Index 2014

6. Geography and Financial Inclusion
2011 2014
6. Geographical Proximity and Financial
Inclusion
• A weighted method of principal component analysis (GWPCA) is
computed to account for the proximity between countries

𝑢𝑢 𝑎𝑎 𝑏𝑏
𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑖𝑖 = 𝝎𝝎𝟏𝟏 𝑌𝑌𝑖𝑖𝑖𝑖 + 𝝎𝝎𝟐𝟐 𝑌𝑌𝑖𝑖𝑖𝑖 + 𝝎𝝎𝟑𝟑 𝑌𝑌𝑖𝑖𝑖𝑖 + 𝝐𝝐𝒊𝒊

• We use the Euclidean distance between the centroid of the countries

and their geographic location. We obtain a value for each pair of
coordinates

• Spatial weights are calibrated by introducing a specification of the

distance that consider adjacent countries (located at 2,500 km)
6. Financial inclusion growth with spatial effects:
2011 - 2014
6. Financial inclusion growth with spatial effects:
2011 - 2014
5. PCA vs. GWPCA
 7. Conclusions
• We propose a parametric index to measure the degree of financial systems’
inclusiveness. It is comparable across countries and over time. It is easy to
interpret

• Demand and supply information is considered

• Our index has desirable properties: It comprises information from all the
indicators but it is not strongly biased towards one or more indicators

• It accounts for the dependence between countries’ geo-position and financial

inclusion

• This financial inclusion index may help in advising policy makers though the
financial inclusion diagnosis and potential market failures
 Thank you!

noelia.camara@bbva.com
Appendices