Abstract
We extend a recently developed generalized local polynomial estimator into a semiparametric smooth coefficient framework to estimate a generalized cost function. The advantage of the generalized local polynomial approach is that we can simultaneously choose the degree of polynomial for each continuous nonparametric regressor and the bandwidths via data-driven methods. We provide estimates of scope economies from the joint production of microloans and microdeposits for a dataset of Microfinance Institutions from over 50 countries. Our approach allows analysis on all Microfinance Institutions rather than only those offering just microloans. Moreover, the smooth coefficient estimator provides a general interface in which to account for both direct and indirect environmental factors. We find substantial scope economies in general, of about 10 % at the median, as well as evidence that economies of scope vary across the type of services and country in which the MFIs operate, suggesting key insights into policy prescriptions.
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Notes
Throughout the paper, we use microdeposits (microsavings) to mean voluntary microdeposits since mandatory savings that MFIs require are a part of some of the lending technology associated with solidarity groups and village banks.
See Du et al. (2013) for an approach to impose linear homogeneity in this setting.
Note that this generalized formulation nests the familiar local constant least squares problem when \(p_s = 0, \,\forall s\)
$$\begin{aligned} \frac{1}{nh} \sum _{i=1}^n \left[ Y_i - \sum _{\ell =0}^L a_\ell X_{\ell i} \right] ^2 {\mathcal {K}}\left( \frac{Z_i-z}{h} \right) \end{aligned}$$or the local linear least-squares problem when \(p_s = 1, \,\forall s\)
$$\begin{aligned} \frac{1}{nh} \sum _{i=1}^n \left[ Y_i - \sum _{\ell =0}^L a_\ell X_{\ell i} - \sum _{\ell =0}^L \sum _{s=1}^{S} b_{\ell s}(Z_{si}-z_s)X_{\ell i} \right] ^2 {\mathcal {K}}\left( \frac{Z_i-z}{h} \right) . \end{aligned}$$We also explore the robustness of our primary results by selecting bandwidths that are optimal for estimation of economies of scale. We find that, in general, our empirical results are qualitatively consistent when we smooth over scale.
For a detailed comparison of this with other available datasets see Mersland (2009).
Distribution of MFIs by country is presented in the “Appendix”. Comparison with other publicly available data shows that these data have more observations from Latin America.
Differences in funding costs may also stem from differences in inflation across countries and different risk premiums. Inflation is, however, to a large extent taken care of in the dataset since all amounts are converted into US dollars.
Since the cost function is homothetic in input prices, we can always normalize by one of the input prices. Thus, while we have three inputs, only two of them enter into our analysis.
Multistarts are the number of different trials used to calculated the minimum of the least-squares cross-validation function. Given the nonlinearity of this function with respect to multiple bandwidths, it is good practice to use numerous multistarts to avoid obtaining bandwidths indicative of a local minimum as opposed to the global minimum.
We note that with the use of flexible estimation methods that theoretical consistency may be sacrificed. In our case, this entails the estimated cost function satisfying given axioms of producer theory, notably monotonicity of the cost function in both outputs, loans and deposits. The percentage of observations where our estimated cost function is non-monotonic for loans is 6.7 % when we include controls and roughly 3 % with no controls. However, for deposits, across both models roughly 50 % of the estimated cost function derivatives are negative. What drives this behavior is a single, smooth coefficient term which dominates the expression—the interaction between loans and deposits. The coefficient on this term is largely negative, and when multiplied by the amount of loans in the derivative of cost w.r.t. deposits, we have a largely negative term. This matters because many other terms in this derivative are zero, since deposits is mostly zero for almost 75 % of the observations. While this is certainly an important issue to explore, we leave it for future research to combine the approach detailed here with constrained nonparametric methods.
We also considered augmented variants of the 45\(^{\circ }\) plots presented in Fig. 1 that differentiate between institutions in our sample that offer only loans and those that jointly offer savings and loans, to assess whether there are large distributional differences between scope estimates across these groups. We omit these plots since we were not able to identify distinct differences across the scope estimate distributions across these two groups. Note that this merely indicates that the heterogeneity we identify in our estimates of scope economies affects scope economies across these two groups similarly.
As a comparison, we consider our standard scope measure for only this subset of 178 countries and find that, while there is a wider interquartile range of our estimates, the qualitative conclusion from our main results is unchanged.
It is also worth noting that most of these studies measure output by the number of active borrowers (or clients), while we use the volume of loans and deposits.
References
Abramson M, Audet C, Couture G, Dennis J, Le Digabel S (2011) The NOMAD project. Technical Report
Ahlin C, Lin J, Maio M (2011) Where does microfinance flourish? Microfinance institution performance in macroeconomic context. J Dev Econ 95(2):105–120
Ariff M, Can L (2008) Cost and profit efficiency of Chinese banks: a non-parametric analysis. China Econ Rev 19(2):260–273
Armedráriz B, Szafarz A (2010) On mission drift in microfinance institutions. In: Armendáriz B, Labie M (eds) Handbook of microfinance. World Scientific Publishing Co., Singapore
Balkenhol B (2009) Microfinance and public policy. Outreach, performance and efficiency. Palgrave, New York
Baumol WJ, Panzer J, Willig R (1982) Contestable markets and the theory of market structure. Harcourt, New York
Beck T, Demirguc-Kunt A, Martinez P, Soledad M (2008) Symposium on access to finance: banking services for everyone? Barriers to bank access and use around the world. World Bank Econ Rev 22(3):397–430
Berger A, Humphrey D (1991) The dominance of inefficiences over scale and product mix economies in banking. J Monet Econ 28:117–148
Berger AN, Hasan I, Zhou M (2009) Bank ownership and efficiency in China: what will happen in the worlds largest nation? J Bank Financ 33:113–130
Caudill SB, Gropper DM, Hartarska V (2009) Which microfinance institutions are becoming more cost effective with time? Evidence from a mixture model. J Money Credit Bank 41:651–672
Christiansen LR, Jorgensen DW, Lau LJ (1971) Conjugate duality and the transcendental logarithmic production function. Econometrica 39:255–256
Collins D, Morduch J, Rutherford S, Ruthven O (2009) Portfolios of the poor: how the world’s poor live on $2 a day. Princeton University Press, New Jersey
Cull R, Demirguc-Kunt A, Morduch J (2007) Financial performance and outreach a global analysis of leading MFIs. Econ J 117:F107–F133
Cull R, Demirguc-Kunt A, Morduch J (2009) Microfinance meets the market. J Econ Perspect 23:167–192
Cull R, Demirguc-Kunt A, Morduch J (2011) Does regulatory supervision curtail microfinance profitability and outreach? World Dev 39:949–965
Diamond D (1984) Financial intermediation and delegated monitoring. Rev Econ Stud 51:393–414
Du P, Parmeter CF, Racine JS (2013) Nonparametric kernel regression with multiple predictors and multiple shape constraints. Stat Sin 23:1343–1372
Freixas X, Rochet J (1997) Microeconomics of banking. MIT Press, Cambridge
Garmaise MJ, Natividad G (2010) Information, the cost of credit, and operational efficiency: an empirical study of microfinance. Rev Financ Stud 23:2560–2590
Gutierres-Nieto B, Serrano-Cinca C, Mar M (2007) Microfinance institutions and efficiency. Omega Int J Manag Sci 35:131–142
Hall PG, Racine JS (2013) Infinite order cross-validated local polynomial regression. Working paper
Hartarska V, Mersland R (2012) What governance mechanisms promote efficiency in reaching poor clients? Evidence from rated microfinance institutions. Eur Financ Manag 18:218–239
Hartarska V, Mersland R, Nadolnyak D, Parmeter CF (2013) Governance and scope economies in microfinance institutions. Int J Corp Gov 4(1):74–96
Hartarska V, Nadolnyak D (2007) Do regulated microfinance institutions achieve better sustainability and outreach? Cross-country evidence. Appl Econ 39(10–12):1207–1222
Hartarska V, Parmeter CF, Nadolnyak D (2011) Economies of scope of lending and mobilizing deposits in microfinance institutions: a semiparametric analysis. Am J Agric Econ 93(2):389–398
Hartarska V, Parmeter CF, Nadolnyak D, Zhou B (2010) Economics of scope for microfinance: differences across output measures. Pac Econ Rev 15(4):464–481
Hartarska V, Shen X, Mersland R (2013) Scale economies and elasticities of substitution in microfinance instituitions. J Bank Financ 37:118–131
Henderson DJ, Kumbhakar SC, Parmeter CF (2012) A simple method to visualize results in nonlinear regression models. Econ Lett 117:578–581
Henderson DJ, List JA, Millimet DL, Parmeter CF, Price MK (2012) Empirical implementation of nonparametric first-price auction models. J Econom 168:17–28
Hermes N, Lensink B, Meesters A (2011) Outreach and efficiency of microfinance institutions. World Dev 39:938–948
Hughes JP, Mester L (2009) Efficiency in banking: theory, practice, and evidence, Chapter 19. In: Berger AN, Molyneux P, Wilson J (eds) The Oxford handbook of banking. Oxford University Press, Oxford
Humphrey DB (1985) Costs and scale economies in bank intermediation. In: Aspinwail RC, Eisenbeis RA (eds) Handbook for banking strategy. Wiley, New York
Li Q, Racine J (2007) Nonparametric econometrics: theory and practice. Princeton University Press, Princeton
Mersland R (2009) Corporate governance and ownership in microfinance organizations. PhD thesis, University of Agder
Mersland R, D’Espallier B, Supphellen M (2013) The effect of religion on development efforts: evidence from the microfinance industry and a research agenda. World Dev 41(1):145–156
Mersland R, Randøy T, Strøm RØ (2011) The impact of international influence on microbanks performance: a global survey. Int Bus Rev 20(2):163–176
Mersland R, Strøm RØ (2009) Performance and governance in microfinance institutions. J Bank Financ 33(4):662–669
Mitchell K, Onvural NM (1996) Economies of scale and scope at large commercial banks: evidence from the Fourier flexible functional form. J Money Credit Bank 28:178–199
Nie Z, Racine JS (2012) The crs package: nonparametric regression splines for continuous and categorical predictors. R Journal 4:48–56
Paxton J (2007) Technical efficiency in a semi-formal financial sector: the case of Mexico. Oxf Bull Econ Stat 69(1):57–74
Pulley LB, Braunstein YM (1992) A composite cost function for multiproduct firms with an application to economies of scope in banking. Rev Econ Stat 74:213–230
Pulley LB, Humphrey D (1993) The role of fixed costs and cost complementarities in determining scope economies and the cost of narrow banking proposals. J Bus 66:437–462
R Development Core Team (2008) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0
Racine JS, Li Q (2004) Nonparametric estimation of regression functions with both categorical and continuous data. J Econom 119(1):99–130
van Cayseele P, Wuyts C (2007) Cost efficiency in the European securities settlement and depository industry. J Bank Financ 31(10):3058–3079
Varian H (1984) The nonparametric approach to production analysis. Econometrica 52(3):579–597
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We thank Daniel Henderson, participants at the 2013 Western Economic Association International conference, and seminar participants at Hebei Finance University for helpful feedback.
Appendix
Appendix
Distribution of MFIs by country is presented in Table 10. Comparison with other publicly available data shows that these data have more observations from Latin America, perhaps because they needed external funds.
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Delgado, M.S., Parmeter, C.F., Hartarska, V. et al. Should all microfinance institutions mobilize microsavings? Evidence from economies of scope. Empir Econ 48, 193–225 (2015). https://doi.org/10.1007/s00181-014-0861-3
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DOI: https://doi.org/10.1007/s00181-014-0861-3