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Article • BBR, Braz. Bus. Rev. 21 (1) • 2024 • https://doi.org/10.15728/bbr.2021.1165.en copy

Diversification and Performance in Credit Unions: A Non-Linear Approach

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

This study verified the existence of a non-linear relationship between diversification and the performance of Brazilian credit unions by analyzing panel data from 455 credit unions from June 2012 to December 2019. Through three regression models, estimated by the Systemic Generalized Method of Moments, it was identified that diversification has a non-linear U-shaped relationship with performance. This result demonstrates the existence of a minimum point for diversification, from which increases in diversification of financial products would provide positive effects on performance. This study stands out for bringing a curvilinear model for diversification in credit unions. This finding facilitates the understanding of which level of diversification is beneficial for the performance of credit unions, in addition to favoring the formation of strategies and analysis of the implementation of new financial products in credit unions.

Keywords:
Inverted U; curvilinear relationship; Systemic GMM

Acronyms	Definition of dependent variables	References
ROE_it	Return on Equity. Credit union profitability measure and proxy for financial performance. $ROE = \frac{Surplus}{Equity}$	DeYoung and Rice (2004DeYoung, R., & Rice, T. (2004). Noninterest income and financial performance at US commercial banks. Financial Review, 39(1), 101‒127. https://doi.org/10.1111/j.0732-8516.2004.00069.x https://doi.org/10.1111/j.0732-8516.2004... ); Goddard et al. (2004Goddard, J., Molyneux, P., & Wilson, J. O. (2004). The profitability of European banks: A cross‐sectional and dynamic panel analysis. The Manchester School, 72(3), 363‒381. https://doi.org/10.1111/j.1467-9957.2004.00397.x https://doi.org/10.1111/j.1467-9957.2004... ); Stiroh and Rumble (2006Stiroh, K. J., & Rumble, A. (2006). The dark side of diversification: The case of US financial holding companies. Journal of Banking & Finance, 30(8), 2131‒2161. https://doi.org/10.1016/j.jbankfin.2005.04.030 https://doi.org/10.1016/j.jbankfin.2005.... ); Mercieca et al. (2007Mercieca, S., Schaeck, K., & Wolfe, S. (2007). Small European banks: Benefits from diversification? Journal of Banking & Finance, 31(7), 1975‒1998. https://doi.org/10.1016/j.jbankfin.2007.01.004 https://doi.org/10.1016/j.jbankfin.2007.... ); Goddard et al. (2008Goddard, J., McKillop, D., & Wilson, J. O. (2008). The diversification and financial performance of US credit unions. Journal of Banking & Finance, 32(9), 1836‒1849. https://doi.org/10.1016/j.jbankfin.2007.12.015 https://doi.org/10.1016/j.jbankfin.2007.... ); Bressan et al. (2011Bressan, V. G. F., Braga, M. J., Bressan, A. A., & Resende Filho, M. A. (2011). Uma aplicação do sistema PEARLS às cooperativas de crédito brasileiras. Revista de Administração, 46(3), 258‒274. https://doi.org/10.1590/S0080-21072011000300005 https://doi.org/10.1590/S0080-2107201100... ); Lee et al. (2014Lee, C.-C., Yang, S.-J., & Chang, C.-H. (2014). Non-interest income, profitability, and risk in banking industry: A cross-country analysis. The North American Journal of Economics and Finance, 27, 48‒67. https://doi.org/10.1016/j.najef.2013.11.002 https://doi.org/10.1016/j.najef.2013.11.... ).
CPLA_it	Growth in Adjusted Shareholders' Equity (PLA). Equity evolution measure and proxy for the financial performance of the credit union. $CPLA = (\frac{PLA of the current semester}{PLA of the previous semester}) -1$	Bressan et al. (2011Bressan, V. G. F., Braga, M. J., Bressan, A. A., & Resende Filho, M. A. (2011). Uma aplicação do sistema PEARLS às cooperativas de crédito brasileiras. Revista de Administração, 46(3), 258‒274. https://doi.org/10.1590/S0080-21072011000300005 https://doi.org/10.1590/S0080-2107201100... ); Gollo and Silva (2015Gollo, V., & da Silva, T. P. (2015). Eficiência no desempenho econômico-financeiro de cooperativas de crédito brasileiras. Revista de Contabilidade e Organizações, 9(25), 43‒55. https://doi.org/10.11606/rco.v9i25.88099 https://doi.org/10.11606/rco.v9i25.88099... ).
LnNCoop_it	Natural logarithm of the number of members with debts of at least R$ 200.00, according to IF.Data. Proxy used to measure the social function of the credit union through its body of members (active members).	Adapted from Bialoskorski Neto et al. (2006BialoskorskiNeto, S., Nagano, M. S., & da Costa Moraes, M. B. (2006). Utilização de redes neurais artificiais para avaliação socioeconômica: Uma aplicação em cooperativas. Revista de Administração-RAUSP, 41(1), 59‒68. https://doi.org/10.1590/S0080-21072006000100005 https://doi.org/10.1590/S0080-2107200600... ).

Acronyms	Definition	Expected sign	References
DIV_it	Diversification: one minus the Herfindahl-Hirschman Index (1-HHI). Measures the indirect effect of income diversification. $DIV =1- (\begin{matrix} {(\frac{OCRED}{RO})}^{2} + {(\frac{AIL}{RO})}^{2} + {(\frac{TVMIFD}{RO})}^{2} \\ + {(\frac{PSERV}{RO})}^{2} + {(\frac{OUTRAS}{RO})}^{2} \end{matrix})$	Positive	Esho et al. (2005Esho, N., Kofman, P., & Sharpe, I. G. (2005). Diversification, fee income, and credit union risk. Journal of Financial Services Research, 27(3), 259‒281. https://doi.org/10.1007/s10693-005-1804-0 https://doi.org/10.1007/s10693-005-1804-... ); Stiroh and Rumble (2006Stiroh, K. J., & Rumble, A. (2006). The dark side of diversification: The case of US financial holding companies. Journal of Banking & Finance, 30(8), 2131‒2161. https://doi.org/10.1016/j.jbankfin.2005.04.030 https://doi.org/10.1016/j.jbankfin.2005.... ); Mercieca et al. (2007Mercieca, S., Schaeck, K., & Wolfe, S. (2007). Small European banks: Benefits from diversification? Journal of Banking & Finance, 31(7), 1975‒1998. https://doi.org/10.1016/j.jbankfin.2007.01.004 https://doi.org/10.1016/j.jbankfin.2007.... ); Goddard et al. (2008Goddard, J., McKillop, D., & Wilson, J. O. (2008). The diversification and financial performance of US credit unions. Journal of Banking & Finance, 32(9), 1836‒1849. https://doi.org/10.1016/j.jbankfin.2007.12.015 https://doi.org/10.1016/j.jbankfin.2007.... ); Elsas et al. (2010Elsas, R., Hackethal, A., & Holzhäuser, M. (2010). The anatomy of bank diversification. Journal of Banking & Finance, 34(6), 1274‒1287. https://doi.org/10.1016/j.jbankfin.2009.11.024 https://doi.org/10.1016/j.jbankfin.2009.... ); Kang et al. (2011Kang, K. H., Lee, S., & Yang, H. (2011). The effects of product diversification on firm performance and complementarities between products: A study of US casinos. International Journal of Hospitality Management, 30(2), 409‒421. https://doi.org/10.1016/j.ijhm.2010.06.008 https://doi.org/10.1016/j.ijhm.2010.06.0... ); Ali et al. (2016Ali, S., Hashmi, S. H., & Mehmood, T. (2016). Corporate diversification and firm performance: An inverted U-shaped hypothesis. International Journal of Organizational Leadership, 5, 381‒398. https://ijol.cikd.ca/article_60389_4f9d4f185908b18ab20c749d2bc5a6fd.pdf https://ijol.cikd.ca/article_60389_4f9d4... ).
DIV_it	Quadratic transformation of diversification. The quadratic variable of diversification is included to test the nonlinear relationship between diversification and performance, seeking to identify an optimal degree of diversification.	Negative	Rogers et al. (2008Rogers, P., Mendes-da-Silva, W., & Paula, G. M. D. (2008). Diversificação e desempenho em empresas industriais brasileiras: Um estudo empírico no período de 1997 a 2001. Revista de Adinistração Contemporânea, 12(2), 313‒338. https://doi.org/10.1590/S1415-65552008000200003 https://doi.org/10.1590/S1415-6555200800... ); Elsas et al. (2010Elsas, R., Hackethal, A., & Holzhäuser, M. (2010). The anatomy of bank diversification. Journal of Banking & Finance, 34(6), 1274‒1287. https://doi.org/10.1016/j.jbankfin.2009.11.024 https://doi.org/10.1016/j.jbankfin.2009.... ); Kang et al. (2011Kang, K. H., Lee, S., & Yang, H. (2011). The effects of product diversification on firm performance and complementarities between products: A study of US casinos. International Journal of Hospitality Management, 30(2), 409‒421. https://doi.org/10.1016/j.ijhm.2010.06.008 https://doi.org/10.1016/j.ijhm.2010.06.0... ); Ali et al. (2016Ali, S., Hashmi, S. H., & Mehmood, T. (2016). Corporate diversification and firm performance: An inverted U-shaped hypothesis. International Journal of Organizational Leadership, 5, 381‒398. https://ijol.cikd.ca/article_60389_4f9d4f185908b18ab20c749d2bc5a6fd.pdf https://ijol.cikd.ca/article_60389_4f9d4... ).

Acronym	Definition	Expected sign	References
Y_i,t-1	Lagged dependent variable (ROE, CPL and LnNCoop). They are the dynamic variables of the model; seek to capture the persistence of performance and the number of members of credit unions with loans.	Positive	Goddard et al. (2004Goddard, J., Molyneux, P., & Wilson, J. O. (2004). The profitability of European banks: A cross‐sectional and dynamic panel analysis. The Manchester School, 72(3), 363‒381. https://doi.org/10.1111/j.1467-9957.2004.00397.x https://doi.org/10.1111/j.1467-9957.2004... ); Athanasoglou et al. (2008Athanasoglou, P. P., Brissimis, S. N., & Delis, M. D. (2008). Bank-specific, industry-specific and macroeconomic determinants of bank profitability. Journal of International Financial Markets, Institutions and Mone y , 18(2), 121‒136. https://doi.org/10.1016/j.intfin.2006.07.001 https://doi.org/10.1016/j.intfin.2006.07... ); Carvalho et al. (2010Carvalho, F. D. M., Kayo, E. K., & Martin, D. M. L. (2010). Tangibilidade e intangibilidade na determinação do desempenho persistente de firmas brasileiras. Revista de Administração Contemporânea, 14(5), 871‒889. https://doi.org/10.1590/S1415-65552010000500007 https://doi.org/10.1590/S1415-6555201000... ); Migliardo and Forgione (2015Migliardo, C., & Forgione, A. (2015). Extra profits in the healthcare factoring industry: Evidence from panel data analysis. Economics Bulletin, 35(1), 322‒337.); Barros et al. (2020Barros, L. A., Bergmann, D. R., Castro, F. H., & da Silveira, A. D. M. (2020). Endogeneity in panel data regressions: Methodological guidance for corporate finance researchers. Revista Brasileira de Gestão de Negócios, 22, 437‒461. https://doi.org/10.7819/rbgn.v22i0.4059 https://doi.org/10.7819/rbgn.v22i0.4059... ).
LnAT_it	Natural logarithm of total assets. Proxy to control the size of the credit union and its effect on performance.	Positive	Stiroh and Rumble (2006Stiroh, K. J., & Rumble, A. (2006). The dark side of diversification: The case of US financial holding companies. Journal of Banking & Finance, 30(8), 2131‒2161. https://doi.org/10.1016/j.jbankfin.2005.04.030 https://doi.org/10.1016/j.jbankfin.2005.... ); Goddard et al. (2008Goddard, J., McKillop, D., & Wilson, J. O. (2008). The diversification and financial performance of US credit unions. Journal of Banking & Finance, 32(9), 1836‒1849. https://doi.org/10.1016/j.jbankfin.2007.12.015 https://doi.org/10.1016/j.jbankfin.2007.... ); Lee et al. (2014Lee, C.-C., Yang, S.-J., & Chang, C.-H. (2014). Non-interest income, profitability, and risk in banking industry: A cross-country analysis. The North American Journal of Economics and Finance, 27, 48‒67. https://doi.org/10.1016/j.najef.2013.11.002 https://doi.org/10.1016/j.najef.2013.11.... ); Ali et al. (2016Ali, S., Hashmi, S. H., & Mehmood, T. (2016). Corporate diversification and firm performance: An inverted U-shaped hypothesis. International Journal of Organizational Leadership, 5, 381‒398. https://ijol.cikd.ca/article_60389_4f9d4f185908b18ab20c749d2bc5a6fd.pdf https://ijol.cikd.ca/article_60389_4f9d4... ).
ΔlnAT_it	Variation in the natural logarithm of total assets. Proxy to control the effects of the growth of credit unions.	Positive	Stiroh and Rumble (2006Stiroh, K. J., & Rumble, A. (2006). The dark side of diversification: The case of US financial holding companies. Journal of Banking & Finance, 30(8), 2131‒2161. https://doi.org/10.1016/j.jbankfin.2005.04.030 https://doi.org/10.1016/j.jbankfin.2005.... ); Mercieca et al. (2007Mercieca, S., Schaeck, K., & Wolfe, S. (2007). Small European banks: Benefits from diversification? Journal of Banking & Finance, 31(7), 1975‒1998. https://doi.org/10.1016/j.jbankfin.2007.01.004 https://doi.org/10.1016/j.jbankfin.2007.... ); Goddard et al. (2008Goddard, J., McKillop, D., & Wilson, J. O. (2008). The diversification and financial performance of US credit unions. Journal of Banking & Finance, 32(9), 1836‒1849. https://doi.org/10.1016/j.jbankfin.2007.12.015 https://doi.org/10.1016/j.jbankfin.2007.... ); Lee et al. (2014Lee, C.-C., Yang, S.-J., & Chang, C.-H. (2014). Non-interest income, profitability, and risk in banking industry: A cross-country analysis. The North American Journal of Economics and Finance, 27, 48‒67. https://doi.org/10.1016/j.najef.2013.11.002 https://doi.org/10.1016/j.najef.2013.11.... ).
(ΔlnAT)²_it	Quadratic transformation of the variation of the asset's natural logarithm. Included to verify the non-linear relationship between asset growth and performance.	Negative	Stiroh and Rumble (2006Stiroh, K. J., & Rumble, A. (2006). The dark side of diversification: The case of US financial holding companies. Journal of Banking & Finance, 30(8), 2131‒2161. https://doi.org/10.1016/j.jbankfin.2005.04.030 https://doi.org/10.1016/j.jbankfin.2005.... ); Mercieca et al. (2007Mercieca, S., Schaeck, K., & Wolfe, S. (2007). Small European banks: Benefits from diversification? Journal of Banking & Finance, 31(7), 1975‒1998. https://doi.org/10.1016/j.jbankfin.2007.01.004 https://doi.org/10.1016/j.jbankfin.2007.... ); Goddard et al. (2008Goddard, J., McKillop, D., & Wilson, J. O. (2008). The diversification and financial performance of US credit unions. Journal of Banking & Finance, 32(9), 1836‒1849. https://doi.org/10.1016/j.jbankfin.2007.12.015 https://doi.org/10.1016/j.jbankfin.2007.... ).
EA_it	Ratio between loans and total assets. Interpreted as a measure of loan specialization that can provide benefits from valuable information. $EA= \frac{Loans}{Total assets}$	Uncertain	Kimball (1997Kimball, R. C. (1997). Specialization, risk, and capital in banking. New England Economic Review, 51‒73. https://www.bostonfed.org/publications/new-england-economic-review/1997-issues/issue-november-december-1997/specialization-risk-and-capital-in-banking.aspx https://www.bostonfed.org/publications/n... ); Stiroh and Rumble (2006Stiroh, K. J., & Rumble, A. (2006). The dark side of diversification: The case of US financial holding companies. Journal of Banking & Finance, 30(8), 2131‒2161. https://doi.org/10.1016/j.jbankfin.2005.04.030 https://doi.org/10.1016/j.jbankfin.2005.... ); Mercieca et al. (2007Mercieca, S., Schaeck, K., & Wolfe, S. (2007). Small European banks: Benefits from diversification? Journal of Banking & Finance, 31(7), 1975‒1998. https://doi.org/10.1016/j.jbankfin.2007.01.004 https://doi.org/10.1016/j.jbankfin.2007.... ); Goddard et al. (2008Goddard, J., McKillop, D., & Wilson, J. O. (2008). The diversification and financial performance of US credit unions. Journal of Banking & Finance, 32(9), 1836‒1849. https://doi.org/10.1016/j.jbankfin.2007.12.015 https://doi.org/10.1016/j.jbankfin.2007.... ); Lee et al. (2014Lee, C.-C., Yang, S.-J., & Chang, C.-H. (2014). Non-interest income, profitability, and risk in banking industry: A cross-country analysis. The North American Journal of Economics and Finance, 27, 48‒67. https://doi.org/10.1016/j.najef.2013.11.002 https://doi.org/10.1016/j.najef.2013.11.... ).
PA_it	Ratio between equity and total assets. Proxy interpreted as a security measure for credit unions. $PA= \frac{Equity}{Total Assets}$	Uncertain	Berger (1995Berger, P. G., & Ofek, E. (1995). Diversification's effect on firm value. Journal of Financial Economics, 37(1), 39‒65. https://doi.org/10.1016/0304-405X(94)00798-6 https://doi.org/10.1016/0304-405X(94)007... ); Goddard et al. (2004Goddard, J., Molyneux, P., & Wilson, J. O. (2004). The profitability of European banks: A cross‐sectional and dynamic panel analysis. The Manchester School, 72(3), 363‒381. https://doi.org/10.1111/j.1467-9957.2004.00397.x https://doi.org/10.1111/j.1467-9957.2004... ); Stiroh and Rumble (2006Stiroh, K. J., & Rumble, A. (2006). The dark side of diversification: The case of US financial holding companies. Journal of Banking & Finance, 30(8), 2131‒2161. https://doi.org/10.1016/j.jbankfin.2005.04.030 https://doi.org/10.1016/j.jbankfin.2005.... ); Mercieca et al. (2007Mercieca, S., Schaeck, K., & Wolfe, S. (2007). Small European banks: Benefits from diversification? Journal of Banking & Finance, 31(7), 1975‒1998. https://doi.org/10.1016/j.jbankfin.2007.01.004 https://doi.org/10.1016/j.jbankfin.2007.... ); Goddard et al. (2008Goddard, J., McKillop, D., & Wilson, J. O. (2008). The diversification and financial performance of US credit unions. Journal of Banking & Finance, 32(9), 1836‒1849. https://doi.org/10.1016/j.jbankfin.2007.12.015 https://doi.org/10.1016/j.jbankfin.2007.... ); Lee et al. (2014Lee, C.-C., Yang, S.-J., & Chang, C.-H. (2014). Non-interest income, profitability, and risk in banking industry: A cross-country analysis. The North American Journal of Economics and Finance, 27, 48‒67. https://doi.org/10.1016/j.najef.2013.11.002 https://doi.org/10.1016/j.najef.2013.11.... ).
ΔlnPIB_it	Variation in the natural logarithm of the semi-annual national GDP (Gross Domestic Product). It verifies the impact of economic growth on the performance of credit unions.	Positive	Goddard et al. (2008Goddard, J., McKillop, D., & Wilson, J. O. (2008). The diversification and financial performance of US credit unions. Journal of Banking & Finance, 32(9), 1836‒1849. https://doi.org/10.1016/j.jbankfin.2007.12.015 https://doi.org/10.1016/j.jbankfin.2007.... ).
Incorp_it	Incorporation. Dummy variable that assumes a value equal to 1 when total and/or partial incorporation occurs, and 0 otherwise. Included to consider the effect of mergers (by the developer) on credit union performance.	Uncertain	Goddard et al. (2009Goddard, J., McKillop, D., & Wilson, J. O. (2009). Which credit unions are acquired? Journal of Financial Services Research, 36(2‒3), 231‒252. https://doi.org/10.1007/s10693-009-0055-x https://doi.org/10.1007/s10693-009-0055-... ); Mckillop and Wilson (2011McKillop, D., & Wilson, J. O. (2011). Credit unions: A theoretical and empirical overview. Financial Markets, Institutions & Instruments, 20(3), 79‒123. https://doi.org/10.1111/j.1468-0416.2011.00166.x https://doi.org/10.1111/j.1468-0416.2011... ); Pessanha et al. (2012Pessanha, G. R. G., Calegario, C. L. L., Safadi, T., & Ázara, L. N. D. (2012). Impactos de las estrategias de fusión y adquisición en la rentabilidad de los bancos adquirentes: Una aplicación de modelos de intervención en el sector bancario brasileño. RAM: Revista de Administração Mackenzie, 13(5), 101‒134. https://doi.org/10.1590/S1678-69712012000500005 https://doi.org/10.1590/S1678-6971201200... ).

	N	Minimum	Maximum	Median	Mean	Std-Dev	Coef. Of Variation
ROE	7280	-0.5452	0.6900	0.0678	0.0677	0.0590	0.8716
CPLA	7280	-0.5526	5.8072	0.0850	0.0951	0.1278	1.3436
LnNCoop	7280	0.0000	11.8173	7.5642	7.6435	1.3012	0.1702
(N Coop.)	7280	0.00	135,580	1,928	4,684.83	7,754.63	1.6553
DIV	7280	0.0544	0.7438	0.5517	0.5292	0.0948	0.1791
(DIV)²	7280	0.0030	0.5533	0.3044	0.2890	0.0890	0.3078
LnAT	7280	14.2898	22.5104	18.5124	18.4956	1.3609	0.0736
ΔlnAT	7280	-0.3876	1.6115	0.0858	0.0934	0.0979	1.0480
(ΔlnAT)²	7280	0.0000	2.5971	0.0078	0.0183	0.0560	3.0602
EA	7280	0.0708	0.9429	0.5452	0.5389	0.1426	0.2645
PA	7280	0.0537	0.9805	0.1915	0.2413	0.1562	0.6475
ΔlnPIB	7280	-0.0114	0.0788	0.0326	0.0311	0.0281	0.9034

	DIV	DIV ²	LnAT	ΔlnAT	ΔlnAT ²	EA	PA	ΔlnPIB
DIV	1
DIV ²	0.9865***	1
LnAT	0.3352***	0.3221***	1
ΔlnAT	0.0203*	0.0155	0.0184	1
ΔlnAT²	0.0101	0.0067	-0.0408***	0.6965	1
EA	-0.5768***	-0.5842***	-0.1194***	0.0528***	0.0296**	1
PA	-0.5192***	-0.4909***	-0.4603***	-0.1589***	-0.0451***	0.3515***	1
ΔlnPIB	0.0062	0.0122	-0.063***	0.0245**	0.0205*	0.0995***	0.0387***	1

	Dependent Variable (Y)
	ROE	CPLA	LnNCoop
Y_i,t-1	-0.1853***	-0.0745***	0.3998***
Y_i,t-1	(0.0511)	(0.0273)	(0.0501)
DIV	-1.5621***	-1.1941***	-4.7161***
DIV	(0.3085)	(0.3074)	(1.3096)
DIV²	1.7299***	1.4599***	5.8568***
DIV²	(0.3041)	(0.3283)	(1.2799)
LnAT	-0.0224***	-0.0151**	0.4800***
LnAT	(0.0031)	(0.0062)	(0.0448)
ΔlnAT	0.0115	-0.1808**	-0.0070
ΔlnAT	(0.0173)	(0.0823)	(0.1044)
(ΔlnAT)²	-0.0589	2.0758***	0.7866*
(ΔlnAT)²	(0.0395)	(0.4521)	(0.4099)
EA	0.2433***	0.2561***	1.2259***
EA	(0.0241)	(0.0415)	(0.1823)
PA	-0.6623***	-0.4045***	0.4626
PA	(0.0732)	(0.1283)	(0.2993)
ΔlnPIB	-0.2929***	0.5483***	1.9532***
ΔlnPIB	(0.0342)	(0.0435)	(0.1853)
Incorp	-0.0096	-0.0132	0.0499
Incorp	(0.0062)	(0.0345)	(0.0830)
Intercept	0.8597***	0.5138***	-4.3074***
Intercept	(0.1171)	(0.1462)	(0.6926)
AR(1)	-6.3970***	-3.9432***	-4.2539***
AR(2)	1.8344*	0.8029	0.8498
Sargan test	4979.4622***	5288.5137***	2580.5291***
Hansen test	442.1111	453.2491	454.9849
Dif-Hansen (iv) test	0.49	0.99	0.00
N. of observations	6825	6825	6825
N. of groups	455	455	455
N. of instruments	423	483	528

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