SU+ @ Strathmore University Library Electronic Theses and Dissertations This work is availed for free and open access by Strathmore University Library. It has been accepted for digital distribution by an authorized administrator of SU+ @Strathmore University. For more information, please contact library@strathmore.edu 2021 Construction of a Financial Inclusion Index for Kenya. Wafula, Kelly Akuku Strathmore Institute of Mathematical Sciences Strathmore University Recommended Citation Wafula, K. A. (2021). Construction of a Financial Inclusion Index for Kenya [Thesis, Strathmore University]. http://hdl.handle.net/11071/12901 Follow this and additional works at: http://hdl.handle.net/11071/12901 https://su-plus.strathmore.edu/ https://su-plus.strathmore.edu/ http://hdl.handle.net/11071/2474 mailto:library@strathmore.edu http://hdl.handle.net/11071/12901 http://hdl.handle.net/11071/12901 Construction of a Financial Inclusion Index for Kenya Kelly Akuku Wafula Submitted in partial fulfillment for the Degree of Master of Science in Mathematical Finance at Strathmore University Institute of Mathematical Sciences Strathmore University Nairobi, Kenya November 2021 This thesis is available for Library use on the understanding that it is copyright material and that no quotation from the thesis may be published without proper acknowledgment. 1 Declaration I confirm that this thesis is my original work and has not been submitted or presented for assessment for the award of a degree by Strathmore or in any institution. To the best of my knowledge, the thesis contains no material previously published or written by another person except where due reference is made. Signature Date Kelly Akuku Wafula This thesis has been submitted for assessment with our approval as supervisors according to Strathmore University regulations. Signature Date Dr. Samuel Tiriongo Strathmore Institute of Mathematical Sciences Strathmore University Signature Date Mr. Meleah Oleche Strathmore Institute of Mathematical Sciences Strathmore University i Abstract This study constructed a Financial Inclusion Index (FII) to measure access to, availability of and usage of financial services in Kenya using data collected from IMF reports for the period 2013 – 2019. A two-stage principal component analysis (PCA) method was applied in constructing the FII that was found to satisfy the Kaiser-Meyer-Olkin (KMO) measure to both the indicators and the dimensions. The research offers ideas for policy-making by highlighting the contributions of the variables to the dimensions, subsequently, the contributions of the dimensions to the index. Therefore, the FII can act as an analytical tool for surveillance of the variables for a more inclusive financial system. ii Contents Declaration i Abstract ii List of Figures v List of Tables vi Acknowledgment vii Dedication viii Abbreviations ix 1 Introduction 1 1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Background to the study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Statement of the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.5 Justification of Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 Literature review 6 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Financial Inclusion Research Models . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2.1 Non-Parametric Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2.2 Parametric Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 Financial Inclusion Dimensions and Indicators . . . . . . . . . . . . . . . . . . . 8 2.4 Research Gaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3 Research Methodology 10 3.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.2 Financial Inclusion Indicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.3 Principal Component Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.4 Development of the FI Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 iii 3.4.1 Estimation of the Dimensions (First Stage of the PCA) . . . . . . . . . . 12 3.4.2 Estimation of the Weights of the three dimensions (Second Stage of the PCA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 4 Results and Discussion 14 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 4.2 Bartlett’s Sphericity Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 4.3 KMO Measure of Sampling Adequacy (MSA) . . . . . . . . . . . . . . . . . . . 15 4.4 Financial Inclusion Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.5 Overall Financial Inclusion Index . . . . . . . . . . . . . . . . . . . . . . . . . . 16 5 Conclusions and Recommendations 17 5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 5.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 5.3 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 iv List of Figures List of Figures 1 Dimension’s Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2 Correlation Matrix for the variables . . . . . . . . . . . . . . . . . . . . . . . . . 14 3 Weights for the variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 v List of Tables List of Tables A1 Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 A2 Eigenvalues for the corresponding Principal Components . . . . . . . . . . . . . 23 A3 Changes in Financial inclusion measurement . . . . . . . . . . . . . . . . . . . . 25 vi Acknowledgment I wish to recognize and sincerely appreciate all those who assisted me to complete this thesis. It would have been very difficult without your support. I would especially like to thank my supervisors Dr. Samuel Tiriongo and Mr. Meleah Oleche for their time, support and great intellect throughout this research process. I would also like to acknowledge my other lecturers: Dr. Lucy Muthoni, Dr. Ferdinand Othieno, Dr. Livingstone Luboobi, Dr. Samuel Chege, Dr. Ivivi Mwaniki, Dr. Collins Odhiambo and Dr. Caroline Kariuki. You all made learning a great experience. To my family, thank you for your assistance and constant encouragement, Dad, for your unend- ing prayers, push and appreciating my efforts. To my partner Jackson Kisaro, for his unending support. Finally, I would like to acknowledge my classmates, thank you for the support, helpful discussions and comic relief. vii Dedication This research work is dedicated to my daughter (Maya Kaptuya) for her undying love and support throughout the study, and above all the Almighty God for His provisions that were in abundance throughout my studies. viii Abbreviations CBK Central Bank of Kenya CFA Common Factor Analysis DTR Distance to Reference FI Financial Inclusion FII Financial Inclusion Index FSD Financial Sector Deepening GDI Gender-Related Development Index HDI Human Development Index HPI Human Poverty Index IRA Insurance Regulations Authority KBA Kenya Bankers Association NGOs Non-governmental organizations PC Principal Component PCA Principal Component Analysis PWD Persons with Disabilities SME Small and Medium-sized Enterprises UNDP United Nations Development Program ix Chapter One 1 Introduction 1.1 Overview Financial Inclusion is defined as access to affordable and useful financial services and prod- ucts that cater for daily needs and are delivered in a responsible sustainable way, World Bank (2020). This paper defines an inclusive financial system as one that maximizes access, us- age and availability of affordable and formal financial services. Financial Inclusion facilitates day-to-day activities and assists families to plan for random events as well as long-term achieve- ments. According to World Bank (2020), Financial inclusion is fundamental to understanding poverty and it is a building block to boosting prosperity while eradicating poverty. Access to and utilization of formal financial services is a key enabler for financial inclusivity, Findex (2017). Africa’s financial system’s limited outreach and its underdevelopment are well documented. Low and volatile high illiteracy rates, income levels, governance challenges, inflationary envi- ronments, inadequate infrastructure, the limited competition within the banking industry and high cost of banking in Africa are some of the factors used in explaining the limited outreach and less development of the financial sector, ABD (2013). Overall progress in financial inclusion has been achieved in Africa between 2011 and 2017, the share of adults with financial accounts in the region grew by 20%, driven largely by growth in mobile money. Although East Africa has seen the most dramatic increase, Central and West Africa have also seen a rapid gain in recent years, bolstered by enabling regulatory poli- cies. Most of these countries also experienced a sharp uptick in financial inclusion rates among women. Within the same period, the number of women with their accounts doubled in Ghana and Kenya while in Senegal it increased by almost seven times the previous rate, Gates Foun- dation (2019). Findex (2017) highlights that the state of financial inclusion across the world has improved tremendously over the past years. Adults with accounts have increased by 94% in North Amer- ica, which was the highest compared to the rest of the continents, while Africa increased by 1 less than 50%. Adults with accounts in Sub-Saharan Africa between 2011 and 2017 had an increment of 48%. It is noted that unbanked adults are more likely to have low educational attainment. Nigeria was found to have the highest number of non-account holders at 64.5 million and a gender gap of approximately 25% in account ownership. Lesotho and South Africa were the only Sub-Saharan countries in Africa that exhibited a gender gap in favor of women. The gender gaps have implications for women’s labor force participation, in particular, entrepreneurship as they restrict women’s economic opportunities, Gonzales et al. (2015). Indeed, the literature on banking and entrepreneurship also provides evidence of gender dis- crimination in entrepreneurs’ ability to obtain a loan, Klapper et al. (2010). 1.2 Background to the study The Kenyan Government has set up new initiatives for financial inclusion through the Financial Sector Deepening (FSD) Kenya. FSD Kenya is an independent trust which works together with the Kenyan Government and the financial service industry to achieve an inclusive financial sys- tem by developing financial solutions that address challenges faced by low-income households and under-served groups such as the youth and women. FSD Kenya has set up a series of household surveys that measure both the demand and supply dimensions of financial inclusion and the impact of financial services for the country. The surveys assist identify barriers to fi- nancial inclusion as well as assisting the private sector in identifying new market opportunities, FSD (2020). In Kenya’s history, people had to come up with financial solutions. The informal approaches are often effective due to their flexibility and low cost. However, as the economy modernizes most informal lenders tend to reach limits of informal finance. As a result, there has been much emphasis on the expansion of the reach of formal finance. Unfortunately, the impact has been lower than expected. First, many formal services are not relevant to the needs of many Kenyans especially the less fortunate households which find informal solutions better, FinAccess (2019). Second, market conduct is an increasing challenge mainly due to a lack of fair treatment and transparency. Formal financial inclusion has grown from 29% to 83% in Kenya in 2019 while exclusion has gone down to 11% of the population who use no financial services. Meanwhile, over half the population is still using informal financial solutions. Most regions in Kenya have seen a modest 2 increment in financial inclusion since 2016. FinAccess (2019), shows major cities reaching almost full financial inclusion with 96% being in Nairobi and 94% in Mombasa. North-Eastern region has seen a jump of close to 60% mainly through the introduction of mobile money. This is also the case for the gaps in inclusion by wealth and gender. Digital revolution has narrowed the gap, which is evident from 6% difference between women and men and the increase in for- mal access for the less fortunate which has risen from 10% in 2006 to 70% in 2019, FSD (2020). In 2009 and 2012, the banking industry received a boost with the launch of agency banking and MShwari respectively which opened a new era of banking. Recently, however, the banks are un- able to maintain the pace due to inadequate innovation which is now a standard mobile banking offer, FinAccess (2019). This has led to a decline of 4% in the usage of banks by the wealthy. Nevertheless, cost remains the main barrier to the usage of banks, mobile money and insurance. In 2014 regulation and supervision of payment service providers and payment systems were brought within the jurisdiction of the CBK. This fostered codependence, improved the stability of the systems, acted as a measure to reduce systemic risk and also increased competition (thus consumer protection). To improve on price transparency, commercial banks began disclosing the repayment schedule for loans and the total cost of credit, FSD (2020). The Kenyan Govern- ment has overcome policy constraints by committing to increase access to financial providers’ capacity to better meet the need of SMEs and expansion of credit information sharing system. Kenya has experienced a steady increase in borrowing and saving from 2013 to 2019. Over 50% of the population have a loan while 70% of the population are saving either formally or informally. The savings rates have almost remained the same through the years with peri- odic fluctuations due to liquidation of deposits in times of stress and the change in economic conditions, FSD (2020). 1.3 Statement of the Problem It has been argued that financial inclusion may effect financial development growth and poverty reduction, Hanning and Jansen (2010). Sayi et al. (2016) documented that a financial In- clusion Index is a measurement tool that provides detailed insight into how adults in a given economy manage risk, make payments, save, borrow and access accounts. The development of a comprehensive Financial inclusion index for Kenya would therefore assist in measuring 3 progress and identification of priorities. It would also deepen the understanding of an inclusive financial system by testing relationships between financial inclusion and other variables and measuring the impact of policies put in place. Recent studies show that there have been some efforts to develop a multidimensional index to measure FI level. However, this also opens the debate that these indices are necessary but not sufficient for an all-inclusive idea. Therefore, it can be seen that the measurement of the degree of FI has not yet reached a formal consensus, Park and Mercado (2018). The measure- ments of FI through studies are not only different in approach, but the indicators selected to calculate the FI index are also different. In addition, the absence of “mobile money” factor in measuring FI is also one of the key points filled in the study and the addition of other services besides banking-related services to the FI index when calculating this index. Therefore, this study aimed to investigate the contributions of the financial inclusion vari- ables to the overall financial inclusion index and subsequently, the construction of a financial inclusion index for Kenya. The study would also add to the existing research base as well as pro- vide information to policy makers to improve on the areas of weaknesses, thereby encouraging a more inclusive financial system. 1.4 Objectives Main Objective To construct a financial inclusion index for Kenya. Specific Objective 1. To estimate the dimensions (access, availability and usage) using a two-stage PCAmethod- ology. 2. To compute the FI index for the period 2013 to 2019. 1.5 Justification of Study The study aims to create a robust indicator of the depth of financial inclusion based on a sound methodology. The index improves existing financial inclusion indices, for example, by Camara et al. (2014) in three different ways. This is achieved by the inclusion of both the population 4 and geometric variables, the study expands the scope of variables captured in the dimensions for the construction of the index. The study also uses a parametric method which avoids the problem of weighting assignment, Nguyen (2015). Unlike other studies, the research seeks to compare the depth of financial inclusion in Kenya throughout the years, instead of ranking it with other countries. This is a microscopic level study that shows which variables need to be emphasized. The selected dimensions have been proven in the literature to be of importance in the con- struction of financial indices. However, there is an absence of a standard measure that includes multiple dimensions and information to define financial inclusion. The research incorporates a multidimensional measurement of financial inclusion which is important in several aspects. First, it is a measure that allows a linkage between other macroeconomic variables such as economic growth and financial inclusion. Second, an index that aggregates several indicators into a single measure assists to monitor its evolution and aids in summarizing the complex nature of financial inclusion. Therefore, this study harmonizes the different dimensions utilized by previous studies. 5 Chapter Two 2 Literature review 2.1 Introduction This Chapter focuses on three areas: Section 2.2 explains the ideology of the methodologies utilized in building Indices, section 2.3 describes the rationale for the chosen sub-indices and the indicators that measure financial inclusion dimensions as supported by empirical evidence and finally section 2.4 gives the research gaps. 2.2 Financial Inclusion Research Models Recent studies have been carried out in the building of FI indices. They have applied both parametric and non-parametric methods. 2.2.1 Non-Parametric Methods Non-parametric methods that have been utilized to build financial inclusion indices include the Simple arithmetic method (Sarma (2016), Nabard (2009), Mynard et al. (2015) and Sayi et al. (2016)), Geometric mean method as utilized by Nguyen (2015) and Modified Distance to Reference (DTR) method, Mynard et al. (2015). Sarma (2016) used the arithmetic mean as utilized by UNDP in the development of indices such as the Human Development Index (HDI), Gender-Related Development Index (GDI) and Human Poverty Index (HPI). This is also similar to Sayi et al. (2016), the study calculates a measurement for each dimension then the index for the ith city is then expressed as the normalized Euclidean distance of the sub-indices from the ideal point. The ideal point is equal to one. The dimensions utilized are banking penetration, availability and usage. Sethy (2016) utilized the same methodology introducing a different weighting element in com- puting both the dimensions and the index. The dimensions were grouped into two: the demand- side and the supply-side where the demand-side covered access, availability and usage of the banking services. The supply-side captured access to savings, insurance accounts and bank risk. Following the methodology proposed by UNDP in computing its indices, a financial inclu- sion index was constructed for India as a geometric mean for the dimensions, Gupte et al. 6 (2012). The methodology adopted by UNDP to calculate HDI before 2010 attracted a lot of criticism which led to the introduction of the geometric mean in the construction of indices. The introduction of the geometric mean embodies the uneven substitutability across all dimen- sions, thus addressing serious criticisms of the linear aggregation formula which allowed for perfect substitution in all dimensions, Gupte et al. (2012). The study covered two dimensions: penetration of banks and usage. In Mynard et al. (2015), the Philippines Financial Inclusion index was constructed based on a modified DTR which focused on two dimensions: access and usage. FII index is con- structed for banking outreach, where FII lies between zero which depicts no inclusion and one which represents full inclusion. The actual value for each dimension is divided by the overall mean of that indicator, and subsequently, the mean of all the dimensions provides the proposed demand-side or supply-side composite index. Separate composite FIIs using both the data sets are then calculated for the different years. The financial inclusion index built from the above-mentioned non-parametric methods failed to capture the percentage contribution of individual components to the index. This makes the proposed indices unsuitable for identifying the strengths of the specific dimensions in the index. The weighting method utilized in non-parametric methods has received criticism since they rely on a researcher’s intuition. Recent research has therefore relied on parametric methods to construct indices. 2.2.2 Parametric Methods Parametric methods used in the construction of the indices include Principal Component Anal- ysis and Common Factor Analysis (CFA). Massara et al. (2014) and Amidzic et al. (2014) attempted to build a composite financial inclusion index using CFA. Empirical evidence sup- ports that PCA is preferred over Common Factor Analysis as an indexing strategy because it does not necessitate making assumptions on the raw data, for example, the selection of the underlying number of common factors. Pineiro (2013) attempted to construct a financial inclusion index for Mexico using dimen- sions such as access, usage, financial education, consumer protection and social development. The paper highlights that Principal Components are linear combinations of original indicators, 7 which are uncorrelated and have a maximum variance. In the paper, PCA is used to reduce the number of clusters. Wards method is then applied for hierarchical cluster analysis. Finally, the study distinguishes the differences between states and geographical regions through explana- tory data analysis. Camara et al. (2014) measured the Financial Inclusion of several countries using a two- stage PCA method. The study utilized three dimensions: access, usage and barriers. In the study, the methodology was found to be statistically sound for index construction and highly recommended for high-dimensional data. The study, however, did not utilize the availability of financial products to capture the financial inclusion indices. Nguyen (2015) focused on measuring financial inclusion for developing countries using the PCA methodology. In the study, the dimensions were grouped into two: demand-side and supply-side. The supply-side dimensions were access and availability while the demand-side dimension was usage. The study then verified the strength of the Financial Inclusion Index. This was achieved by examining the correlation between the household-based indicator from the Global Findex database and the financial inclusion index generated by PCA methodology. The strength was found to be 51%, thus concluding that PCA is a recommendable methodology. 2.3 Financial Inclusion Dimensions and Indicators Sarma (2016) categorized countries depending on the value of FII where an index of above 0.6 was for high financial inclusion, medium financial inclusion was between 0.4 to 0.6 and low fi- nancial inclusion was less than 0.4. She finally ranked 45 countries that had all three sub-indices available and a further 81 countries that had only two sub-indices available in chronological order of the FII to indicate their relative positions among other countries. Following Sarma (2016), several researchers, have calculated the FII for specific states (Nguyen (2015), Camara et al. (2014), Sayi et al. (2016)) and some like Nabard (2009) estimated values of the Financial Inclusion Index at the district level in India. In (Sarma (2016), Chattopadhyay et al. (2011), Charkravarty et al. (2010) and Kuri et al. (2011)), the accessibility dimension focused on one demographic indicator (Number of Bank accounts per 1000 adults), availability dimension focused on two demographic indicators (Number of Branches per 1000 adults and Number of ATMs per 1000 adults) and the usage 8 dimension utilized one proxy indicator (Volume of Deposits + Loans as a percentage of GDP). Similarly, Gupte et al. (2012), considers the demographic indicators in each dimension and in addition to the demographic indicators she also considers the geographic indicators. However, under penetration, she does not include the number of bank accounts per 1000 adults. Arora (2010) on the other hand utilizes only two dimensions accessibility and availability and fails to capture the number of bank accounts per 1000 adults in the accessibility dimension. Following Yadav et al. (2020), Velan et al. (2021) used five supply-side and three demand-side indicators for measuring financial inclusion across the Indian states. The supply-side financial inclusion indicators used in the study were one measuring penetration and three measuring availability. Usage was captured using the percentage of total credit and deposit as the pro- portion of the state’s GDP. 2.4 Research Gaps In each of the previous attempts, the index was computed using select dimensions. An attempt to measure financial inclusion should consider as many FI dimensions and FI indicators as possible. Therefore, the present paper attempts to include all dimensions and indicators within the dimensions that have been considered so far by various authors. Therefore, this index will be more representative of the extent of financial inclusion in Kenya. Further, the existing indices covered a period up to 2017 (Sarma (2016), Gupte et al. (2012), Charkravarty et al. (2010), Kuri et al. (2011), Nabard (2009)). The current study has constructed the index using the recently available databases from the IMF. The database gives access to additional information on the variables in the various dimensions. This makes the study more current and reflective of the initiatives adopted by the Government, Banks and NGOs throughout the years. Further, since the index is computed identically over 7 years the result is comparable and highlights the impact of financial inclusion in Kenya during this period. 9 Chapter Three 3 Research Methodology 3.1 Data The study uses data on access from the International Monetary Fund’s Website. It is a source of data that offers raw information on a panel of 189 countries. The study will focus on the annual data for the period 2013 to 2019. 3.2 Financial Inclusion Indicators The study will focus on accessibility, availability and usage as indicators of financial inclusion. 1. Accessibility: A good financial system should have many users Nguyen (2015), the study, therefore, utilizes: the number of registered mobile money accounts, institutions of commercial banks, number of insurance corporations and Number of deposit-taking microfinance institutions. 2. Availability: According to Sarma (2016) and Nguyen (2015) the bank transaction points should be readily available for the users. The study, therefore, employs the use of commer- cial bank branches per 1,000 km2, commercial bank branches per 100,000 adults, ATMs per 1,000 km2, ATMs per 100,000 adults, Number of registered mobile money agents out- lets per 100,000 adults and Number of registered mobile money agents outlets per 1,000 km2. 3. Usage: Outstanding deposits with commercial banks as a% of GDP, Outstanding loans from commercial banks as a % of GDP, Number of mobile money transactions (during the reference year) per 1,000 adults, Value of mobile money transactions (during the reference year) (% of GDP), credit cards per 1,000 adults and debit cards per 1,000 adults. 10 Figure 1: Dimension’s Variables 3.3 Principal Component Analysis Early literature on PCA dates Pearson in 1901 and Hotelling in 1933. Pearson, in his attempt to explain PCA Methodology, concluded that the best fitting straight line is the one that captures maximum variance. Both attempt to preserve as much variability as possible while translating into finding new variables. It was not until electronic computers became available widely that it became feasible to use data-sets that were not trivially small Everitt (2001). The selection of relevant variables is a key element in indexing financial inclusion. Standard reduction methods of variable selection, such as elimination of less informative variables, result in loss of information. Weight assignment to variables is essential to capture maximum infor- mation in the index. A reliable financial index should capture relevant information from all the variables Camara et al. (2014) while avoiding strong biasedness towards one of the indicators. Thus, the study seeks to determine the best weighted combination of indicators by use of a two-stage PCA method to estimate a financial inclusion index. The data set is divided into three sub-indices to get undistorted information as well as for methodological purposes. After 11 estimation of the sub-indices, the weights assigned to the variables are estimated. Finally the financial inclusion index is estimated using the dimensions. 3.4 Development of the FI Index FIi = w1Y a i c + w2Y a i v + w3Y u i + ϵi (1) Where i is the year Y a i c, Y a i v and Y u i is the accessibility, availability and usage dimension respectively. Y a i c = β1banksi + β2insurancei + β3mobilei + ...+ ui (2) Y a i v = ϑ1branchesi + ϑ2ATMSi + ϑ3outletsi + ...+ ei (3) Y u i = γ1depositsi + γ2loansi + γ3mtransactionsi + ...+ vi (4) 3.4.1 Estimation of the Dimensions (First Stage of the PCA) These are the three endogenous variables Y a i c, Y a i v and Y u i together with the parameters in the following equations. Since the dimensions are unobserved they will be estimated together with the parameters β, ϑ and γ . Let Rp is a pxp correlation matrix of the p standardized variables for each dimension and λj is the jth eigenvalue. Where j is equal to the number of Principal Components(PC) and j = 1, ..., p. The eigenvector of the correlation matrix is presented as p and the assumption λ1 > λ2 > ... > λp and denote Pk(k = 1, ...p) as the kth PC. The respective estimator for each dimension to the weighted averages: Y a i c = ∑p k,j=1 λ ac jp ac ki∑p j=1 λ ac j (5) Y a i v = ∑p k,j=1 λ av jp av ki∑p j=1 λ av j (6) Y u i = ∑p k,j=1 λ u j p u ki∑p j=1 λ u j (7) Where Pk = Xλjλj is the variance of the k th principal component (weights) and X is the matrix of the explanatory variables. 3.4.2 Estimation of the Weights of the three dimensions (Second Stage of the PCA) Here the overall financial inclusion index is computed by replacing Y a i c, Y a i v and Y u i and ap- plying a similar procedure to the one in the first stage. FIi = ∑p k,j=1 λjp u ki∑p j=1 λj (8) 12 The largest weight λ1 is assigned to the first principle component and the subsequent in a chronological manner. A linear combination of the three dimensions and the eigenvectors of the respective correlation matrices ϕ is formed: P1i = ϕ11Y a i c + ϕ12Y a i v + ϕ13Y u i (9) P2i = ϕ21Y a i c + ϕ22Y a i v + ϕ23Y u i (10) P3i = ϕ31Y a i c + ϕ32Y a i v + ϕ33Y u i (11) Thus FI is computed as, FIi = ∑3 j=1 λj(ϕj1Y a i c + ϕj2Y a i v + ϕj3Y u i )∑3 j=1 λj (12) The weights: wk = ∑3 j=1 λj(ϕjk)∑3 j=1 λj (13) where k = 1, 2, 3 13 Chapter Four 4 Results and Discussion 4.1 Introduction This chapter focuses on the results and the discussions of the analysis carried out. Section 4.2 focuses on correlation within the dataset, section 4.3 measures the sampling adequacy, section 4.4 explains the computation of the sub-indices while section 4.5 shows how the FII was built. 4.2 Bartlett’s Sphericity Test The correlation matrix for the independent variables used to measure financial inclusion is reported in figure 2. By visualization of the correlation matrix, the values outside the main diagonal are high in absolute value, therefore PCA is appropriate for the chosen variables. Figure 2: Correlation Matrix for the variables Bartlett’s Sphericity was carried out to check if the observed correlation matrix drifts sig- nificantly from the identity matrix. The null hypothesis states that the variables for the matrix are orthogonal. Therefore, PCA cannot perform compression of the available information if the null hypothesis is true. For measurement of the relationship between variables the absolute value of the correlation matrix is computed, Camara et al. (2014). If the variables are highly 14 correlated, the absolute value will be equal to zero, thus the null hypothesis is rejected. In this study, the null hypothesis is rejected at the 5% level since the p− value = 0.004528 < 0.05. Thus, the correlations between the data-set are significantly large which implies that PCA can be performed on the data-set efficiently. 4.3 KMO Measure of Sampling Adequacy (MSA) The study utilized the KMO measurement to check if the original variables can be factorized efficiently to build the sub-indices. The overall KMO measure for the accessibility dimension is 0.66, availability dimension 0.62 and usage dimension 0.79. This is sufficient for factorization of the indicators as it satisfies KM0 > 0.5, Nguyen (2015). 4.4 Financial Inclusion Dimensions In the attempt to find the weights, eigenvalues were calculated as displayed by table A2. The principal components analysis is based on the rule that eigenvalues greater than 1 are considered for analysis, Pineiro (2013). Therefore, the first principal components (PCs) are considered for analysis. This is also supported by figures 4a, 5a and 6a which show the contribution of each variable to the different PCs. Figures 4b, 5b and 6b show the contributions of the variables in each dimension to PC1. Figure 3 shows that the weights assigned to each variable are derived from the information in the first PCs. Registered mobile money outlets have the highest assigned weight in compari- son with the other variables for the accessibility dimension. Similarly, the number of registered mobile money outlets per 1000km2 is the highest for the availability dimension. For the usage dimension, the number of credit cards per 1000 adults has the highest assigned weight followed by the value of mobile transactions as a percentage of GDP. 15 Figure 3: Weights for the variables 4.5 Overall Financial Inclusion Index In the second stage, PCA Method is applied as in the first stage on the dimensions to estimate their weights in the overall FI Index. The eigenvalues for the three PCs are 1.724, 0.99 and 0.286 respectively for PC1, PC2 and PC3, figure 7a. The first PC is retained for the study since it is the only eigenvalue greater than one. It is then utilized to estimate the weights assigned to the dimensions. Further KMO measure is applied to the correlations data of the dimensions, KMOMeasure = 0.64, satisfies KMO > 0.5, Camara et al. (2014). PCA assigns the highest weight to availability; 0.923, followed by usage;0.921 and finally access; 0.155, figure 7b. This is used to estimate the overall FI Index for Kenya. FIi = 0.155Y a i c + 0.923Y a i v + 0.921Y u i + ϵi (14) Where i is the year. Table A3 shows the changes in the financial inclusion index for the period 2013 to 2019. 16 Chapter Five 5 Conclusions and Recommendations 5.1 Conclusions Financial inclusion is an important tool in economic development and the eradication of poverty. It also prevents social exclusion. The right to access formal financial services should be priori- tized as a way of risk mitigation and for advancement in recurrent duties. Financial inclusion is a multidimensional concept that cannot be captured by a single indicator, instead, it is cap- tured using a large set of indicators to get all aspects that affect the measurement. The study established that availability is the most important dimension for determining the level of financial inclusion in Kenya. The variables that have the highest contributions to availability are the number of registered mobile money outlets both per 1000km2 and per 100, 000adults. The study also established that mobile money outlets had the most impact on the accessibility dimension. This can be used to further test the impact of mobile money on Financial Inclusion. In the usage dimension, the number of credit cards per 1000adults had the most impact which implied that there was an increase in credit card acquisition in Kenya. Outstanding deposits as a percentage of the GDP were found to be higher than the outstanding loans as a percentage of the GDP which implies that most Kenyans are saving more and borrowing less. The methodology used in this study was found to be sufficient by applying the KMO mea- sure to both the indicators and the dimensions. 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. 5.2 Recommendations Improvements and technical innovations in constructing the FII are possible, therefore, this paper could further stimulate interest to conduct more studies related to financial inclusion in Kenya by looking into its research gaps and addressing them accordingly. The FII can be used in econometric models requiring a measure of financial inclusiveness. It can serve as a dependent variable in regression models to identify the key drivers of financial inclusion. Al- 17 ternatively, the FII can be used as an explanatory variable to test whether financial inclusion significantly contributes to specific outcomes. The study highlights that the addition of new indicators into the construction process can extend the measures of the financial inclusion index. This should help in understanding Finan- cial Inclusion in Kenya better, hence, aiding in creating the right policies. 5.3 Limitations The study is restricted to the period 2013 to 2019. This is due to the introduction of MShwari in November 2012 which increased the uptake in mobile banking services. The study used mobile banking variables to measure financial inclusion across all the dimensions. It is also because of the Covid period which saw an economic downfall in many economies. Therefore, a similar study carried out in the future for 15 to 20 years would produce more accurate results. More refined information on the different dimensions, in the form of dis-aggregated data by geo-location (county-wise), usage frequency and product information on access points, would be useful for a more accurate assessment of financial inclusion that leads to policy recommen- dations. 18 References ADB (2013). Financial Inclusion in Africa. Amidzic, G., Massara, M.A. and Mialou, A. (2014), Assessing countries financial inclusion standing-A new composite index (No. 14-36)”, International Monetary Fund, available at: https://www.elibrary.imf.org/view/. Arora, R. (2010). Measuring Financial Access, Griffith University, Discussion Paper Economics 7, ISSN1837-7750 Camara. N and Tuesta. D (2014). Measuring finacial inclusion: a multidimensional Index, 2014. CBK (2018). Summary of the study on interest caps, https://www.centralbank.go.ke/wp- content/uploads/2018/03/. CBK Annual Report (2020), https://www.centralbank.go.ke/ Charkravarty, S. R. Pal, R. (2010). Measuring financial inclusion: An Axiomatic Approach. (IGIDR Working Paper), Mumbai. Chattopadhyay, S. K. (2011). Financial Inclusion in India: A Case Study of West Bengal. (RBI Working Paper), Mumbai. Everitt. B and Dunn G. (2001), Applied Multivariate Data Analysis (PCA). Finaccess (2019). Inclusive Finance, Headline findings from FinAccess. FSD (2020). The prevalence and drivers of Financial resilience among adults evidence from the Global Findex. Gates Foundation(2019). Women’s Digital Financial Inclusion in Africa. Global Findex Report 2017, globalfindex.worldbank.org. Gonzales, C., S. Jain-Chandra, K. Kochhar, and M. Newiak (2015). “Catalyst for Change: Empowering Women and Tackling Income Inequality,” IMF Staff Discussion Note 15/20, (Washington: International Monetary Fund). Gupte, R., Venkataramani, B. and Gupta, D. (2012), “Computation of financial inclusion index for India”, Procedia-Social and Behavioral Sciences, Vol. 37, pp. 133-149 19 Hannig, A. and Jansen, S. (2010), “Financial Inclusion and Financial Stability: Current Policy Issues”, ADBI Working Paper No. 259. Huang, Y. and Zhang, Y. (2020), “Financial inclusion and urban–rural income inequality: long- run and short-run relationships”, Emerging Markets Finance and Trade, Vol. 56 No. 2, pp. 457-471 IMF (2016). Financial Inclusion: Bridging Economic Opportunities and Outcomes. https://www.imf.org/en/News/Articles/2016/09/20/sp092016/ IRA Quarter 4 Release (2020), https://www.ira.go.ke/ KBA (2020). State of the Banking Industry Report - 2020. https://www.kba.co.ke/. Klapper, L. and Simon P. (2010). “Gender and the Business Environment for New Firm Cre- ation”, World Bank Research Observer, Vol. 26, No. 2, pp. 237–257. Kuri, P. K. Laha, A. (2011). Financial inclusion and human development in India: An inter- state analysis. Indian Journal of Human Development, 5(1), 61–78. Massara. H, Goran . N and Mialou. A (2014). Accessing Countries’ Financial Inclusion Standing - A New Composite Index. Mynard, Bryan R. Mojica and Claire Dennis S. An Index of financial inclusion in the phillip- pines: Construction and Analysis. NAFINDEX: Measure of financial inclusion based on NABARD, All India Rural Financial Inclusion Survey (NAFIS) Data. Nguyen ,T. T. H (2015). Measuring financial inclusion:a composite FI index for the developing countries. Park, C.Y. and Mercado, R. (2018), “Financial inclusion: new measurement and cross-country impact assessment”, ADB Economics Working Paper Series (No. 539 - March 2018), Asian Development Bank, Manila, pp. 1-27. Pineiro (2013). Financial Inclusion Index: Proposal of a multidimensional measure for Mexico. Revista Mexicana de Econom´ıa y Finanzas, Vol. 8, No. 2, (2013), pp. 157-180 Sarma, M. (2016), “Measuring financial inclusion for Asian economies”, Financial Inclusion in Asia,Palgrave Macmillan UK, London, pp. 3-34. 20 Sayi. D, T (2016).Construction of a Financial inclusion index for Member and Candidate Coun- tries of the European Union. Sethi, S.K. and D. (2019). “Financial inclusion matters for economic growth in India: some evidence from cointegration analysis”, International Journal of Social Economics, Vol. 46 No. 1,pp. 132-151. Sethy. K (2016). Developing a financial inclusion index and inclusive growth in India. Tuesta, D. and Camara, N. (2014), “Measuring financial inclusion: a multidimen- sional index (No.1426)”, BBVA Bank, Economic Research Department, available at: https://www.bbvaresearch.com/. UFA (2020). Universal Financial Access Overview. World Bank (2020). Financial Inclusion Overview. Yadav, V., Singh, B.P., Velan, N. (2020). Multidimensional financial inclusion index for Indian states. Journal of Public Affairs. https://doi.org/10.1002/pa.2238. Yadav, V. Velan, N. (2021). Computing a Composite Financial Inclusion Index for the Indian States: A Principal Component Analysis. 21 Appendix I: Descriptive Statistics Table A1: Descriptive Statistics 22 Appendix II: PCA Stage 1 Table A2: Eigenvalues for the corresponding Principal Components Accessibility Dimension Figure 4a Figure 4b 23 Availability Dimension Figure 5a Figure 5b Usage Dimension Figure 6a Figure 6b Appendix III: PCA Stage 2 Financial Inclusion Index Figure 7a Figure 7b 24 Year Accessibility Availability Usage FII 2013 0.97 0.211 0.963 0.855 2014 0.967 0.642 0.099 0.455 2015 0.63 0.413 0.248 0.005 2016 0.717 0.095 0.475 0.754 2017 0.941 0.439 0.053 0.134 2018 0.317 0.639 0.282 0.134 2019 0.89 0.838 0.02 0.804 Table A3: Changes in Financial inclusion measurement 25 Declaration Abstract List of Figures List of Tables Acknowledgment Dedication Abbreviations Introduction Overview Background to the study Statement of the Problem Objectives Justification of Study Literature review Introduction Financial Inclusion Research Models Non-Parametric Methods Parametric Methods Financial Inclusion Dimensions and Indicators Research Gaps Research Methodology Data Financial Inclusion Indicators Principal Component Analysis Development of the FI Index Estimation of the Dimensions (First Stage of the PCA) Estimation of the Weights of the three dimensions (Second Stage of the PCA) Results and Discussion Introduction Bartlett's Sphericity Test KMO Measure of Sampling Adequacy (MSA) Financial Inclusion Dimensions Overall Financial Inclusion Index Conclusions and Recommendations Conclusions Recommendations Limitations