The theoretical literature on the relationship between market structure and performance is based on two contradictory approaches: the structure-behaviour-performance (SBP) paradigm, the efficient structure (ES) hypothesis and the contestable market theory.

The first, developed by Mason (1939) and Bain (1956) , implies that behaviour and performance in a market are determined by the structures of that market. This results in rates that are higher than those in the competitive market. This situation reduces the incentive for financial institutions to make their activities more efficient, as any increase in costs can easily be covered by an increase in lending rates and/or a decrease in deposit rates ( Lapteacru & Nys, 2011 ). According to ( Dietsch 1992 ), the SCP model focuses on two essential elements that determine the degree of competition: entry conditions and prices. With the presence of high barriers to entry, the market power induced by concentration in favour of large firms leads to excessive profits, despite the low level of efficiency (“quiet life hypotheses” of Hicks (1935) . SCP theory postulates that the more concentrated the market, the lower the degree of competition ( Tregenna, 2009 ) and the higher the economic rent ( Samad, 2008 ).

In addition to the structuralist current, a second paradigm of the SCP model is known as the “efficient structure theory”. According to the authors, it is the performance of companies that explains market structure. Demsetz (1973) and Peltzman (1977) attempted to propose new tools for theoretical analysis in which competition was no longer seen as a static mechanism, but as a process of dynamic selection of the most efficient firms. This is why Hien & Hanch (2013) argue that firms with a high market share are the most efficient because of the advantages of economies of scale. They argue that a high-performing firm tends to improve its performance and increase its market share. Berger & Hannan (1989) , Hannan (1991) and Cyrnak & Hannan (1999) emphasise that market concentration can act as a catalyst in increasing the performance of MFIs. By dominating the market, large financial institutions benefit from significant economies of scale. This enables them to reduce their production costs, which in turn enables them to offer more competitive rates to their customers. This in turn attracts more customers, who are price-sensitive and seek to minimise their expenditure when choosing a financial institution.

The second theory, known as “contestable markets”, was developed by Baumol, Panzar, & Willig (1982) . It emerged in the context of a revival of economic and political liberalism. The fundamental idea of this theory is that competition is governed by the conditions of entry and exit from the industry, not by the number of firms, as is the case in the Structure-Behaviour-Performance model. Baumol et al. (1982) pointed out that firms with few competitors are competitive when they operate in markets with low barriers to entry. In markets with low barriers to entry, new MFIs can easily enter the market and compete with existing MFIs. This means that MFIs must continually improve their performance in order to remain competitive. They also need to develop innovative solutions to reach the unbanked and rural areas. Liberto (2022) argues that low-level businesses become competitive when they operate in markets with low barriers to entry. The theory posits that even in a monopoly or oligopoly, incumbents will act competitively in the absence of barriers such as government regulation and high entry costs, will do whatever it takes to deter new entrants and eventually put them out of business.

Numerous studies conducted throughout the world have supported the validity of the theory (SCP). Wondirad (2020) , applying generalised methods of moments (GMM) on a sample of 183 Indian MFIs between 2005 and 2014, finds that competition positively moderates the relationship between the social and financial performance of MFIs. Deb & Sinha (2022) in a study devoted to analysing the effect of competition on the efficiency of MFIs in India and Bangladesh, on 75 MFIs, from 2009 to 2016 shows that the increase in the level of competition is more pronounced in India than in Bangladesh, and that competition has a positive influence on the financial and social efficiency of MFIs.

Kar & Swain (2014) use a dynamic panel model to show that competition improves the performance and quality of the loan portfolio. Baquero et al. (2012) use the concentration indicator (HHI) and the DEA method to analyse the effect of concentration on the efficiency of 379 MFIs in 69 countries between 2002 and 2008. They conclude that increased concentration has a positive influence on the efficiency of MFIs. In contrast, Kar & Bali (2018) using the Boone indicator as a measure of competition and the Generalized Method of Moments (GMM) estimation technique show that increased competition leads to higher performance.

Hossain & Shahadat (2020) study how competition affects the efficiency of MFIs. Using the DEA method, and on a sample of 4576 observations of MFIs in 59 countries, between 2005-2014 show that competition has a negative effect on the economic sustainability of MFIs, however, it improves the depth of outreach of MFIs. According to Dannon et al. (2019) , competition negatively affects the level of efficiency of MFIs, thus confirming Demsetz (1973)’s theory of efficient structures.

Hermès et al. (2013) examine the relationship between competition and the efficiency of Microfinance Institutions (MFIs). They measure competition by constructing a Lerner index. Using the DEA method for 362 MFIs in 73 countries over the period 1995-2008, they conclude that competition between MFIs is negatively associated with their efficiency. Finally, Faye & Ratsimalahelo (2022) conducted an in-depth study of 798 MFIs over a 12-year period, from 2003 to 2015. The study used the method of generalised moments in a system (GMM-SYSTEME). The study was limited to selected developing countries in five geographical regions: Africa, the Middle East, Latin America and the Caribbean, Eastern Europe and Central and South Asia. The results indicate that the performance of MFIs is negatively affected by competition.

This empirical review shows divergent opinions on the question. Some researchers support the theory (SCP), while others advocate the theory (ES). Using an adopted methodology, we will attempt to examine the effect of market structure on the performance of MFIs in the WAEMU zone.

The data used in this study comes from the database of BCEAO (2023) . The analysis covers a sample of 49 MFIs from 07 WAEMU countries (Benin, Burkina Faso, Côte d’Ivoire, Mali, Niger, Senegal and Togo) over the period from 2016 to 2022.

The variables used are of two types: Dependent variable Return on assets (ROA)

Independent variables: Herfindahl-Hirschman Index (HHI), capitalisation ratio (CAR), liquidity ratio (ratio_liq); credit ratio (ratio_cred); portfolio deterioration rate (taux_degrad); geographical penetration rate (penetr_geo)

Developed by Aitken (1926) , the generalised least squares (GLS) method or Aitken estimator is an extension of the ordinary least squares method. It estimates the parameters of a mathematicalp model by minimising the sum of the squares of the differences between the observed values and the predicted values. This method offers a robust statistical approach for analysing non-linear data or data with measurement errors. Moreover, autocorrelation and heteroscedasticity are a frequent problem in economic studies, where the variables of interest are often influenced by other unobserved factors. This can lead to biases in the estimates of causal relationships and distort the results. To solve this problem, our study proposes to use the GCM (Generalised Method of Moments) test to correct for autocorrelation and heteroscedasticity errors.

The empirical form of the generalized least squares method is as follows:

$\begin{array}{c}per{f}_{it}={\alpha }_{it}+{\beta }_{1}ih{h}_{it}+{\beta }_{2}ca{r}_{it}+{\beta }_{3}ratio\_li{q}_{it}+{\beta }_{4}ratio\_cre{d}_{it}\\ +{\beta }_{5}penetr\_ge{o}_{it}+{\beta }_{6}T\_degr{a}_{it}+{\epsilon }_{it}\end{array}$ (1)

In this equation,

Quantile regression was first proposed by Koenker & Bassett (1978) and is defined as the continuity of linear regression used when linear regression conditions are not taken into account. Unlike ordinary least squares (OLS), which estimates the conditional mean of the response variable at the values of the predictor variables, quantile regression is the conditional median of the response variable. In other words, it can provide a more accurate description than traditional linear regression, because it focuses on the entire distribution of the dependent variable, not just its mean. However, quantile regression offers the possibility of obtaining precise estimates of the coefficients in different levels of the distribution. By analysing the data across several quantile points, it captures the variations specific to each segment of the distribution, providing a more complete and nuanced view of the relationships between the variables. It contributes to a better understanding of the causal relationships between variables ( D’Haultfoeuille & Givord, 2014 ).

Quantile regression is a useful statistical method for tackling some common problems in econometrics, notably extreme values, endogeneity, autocorrelation and heteroscedasticity. It reduces the impact of extreme values on the results by focusing on a certain quantile of the dependent variable. This results in more robust estimates. However, it does not completely eliminate endogeneity, but in some cases, by focusing on different points in the distribution of the dependent variable, it makes it possible to obtain less biased estimates than ordinary regression. With regard to autocorrelation, quantile regression is not specifically designed to handle autocorrelation, but some versions of the method (such as panel quantile regression) can help to alleviate this problem. Heteroscedasticity can also bias estimates and lead to inappropriate standard errors. Quantile regression can provide more robust estimates in the face of heteroscedasticity because it does not rely on the assumption of a constant variance of the residuals. The empirical form of the quantile regression model can be formulated as follows:

$\begin{array}{c}q\left(per{f}_{it}\right)={\alpha }_{it}+{\beta }_{1}ih{h}_{it}+{\beta }_{2}ca{r}_{it}+{\beta }_{3}ratio\_li{q}_{it}+{\beta }_{4}ratio\_cre{d}_{it}\\ +{\beta }_{5}penetr\_ge{o}_{it}+{\beta }_{6}taux\_degra{d}_{it}+{\epsilon }_{it}\end{array}$ (2)

Where

$q\left(Per{f}_{it}\right)$ is the conditional quantile of the performance of the MFI sector.

Table 1 presents the descriptive statistics of data and analysis of correlation between variables.

Source: Authors, based on data of BCEAO (2023) .

Source: Authors, based on data of BCEAO (2023) . Note: (*) represents levels of significance at the 1% threshold.

On analysis, the variables in the sample are correlated with each other.

The results of the homogeneity test are shown in Table 2 below.

Source: Authors, based on data of BCEAO (2023) . Note: (**) represents the significance level of 5%.

The results of this test reject the null hypothesis at the 5% threshold. The panel is heterogeneous, so there is a specific individual effect. To check whether this specific effect is random or fixed, we performed the fixed-effect, random-effect and Hausman tests. The results are shown in Table 3 .

Table 3. Hausman test results

Source: Authors, based on data of BCEAO (2023) . Note: (***) denotes the 10% significance level.

In the Hausman test we note the presence of a random effect, as the associated p-value is greater than the 10% threshold. Since there is a random effect, we will use the between estimator because it allows us to control for random effects and focus on systematic differences. However, given that the between estimator is ineffective in the presence of autocorrelation and heteroscedasticity, it is important to test for their presence in the sample in order to confirm the choice of estimator.

In order to verify the presence of autocorrelation or heteroscedasticity, we present the results of the tests in Table 4 below.

Source: Author, based on data of BCEAO (2023) . Note: (**) represents the significance level of 5%.

The results show that the null hypothesis of no autocorrelation is rejected at the 5% threshold. Since the probabilities are below the 5% threshold, we conclude that the errors are autocorrelated. The p-value associated with the heteroskedasticity test is also below the 5% threshold, so the null hypothesis of no heteroskedasticity is rejected. Heteroscedasticity is therefore present.

This test of the model’s validity indicates the presence of autocorrelation and heteroscedasticity errors. The between estimator is no longer valid because it does not correct for these errors. On the other hand, the GCM estimator is more appropriate for our study because it corrects for autocorrelation and heteroscedasticity errors.

Table 5. Estimation results using the GCM method.

Source: Authors, based on data of BCEAO (2023) . Note: the coefficient is significant at the 5% (*) and 10% (**) thresholds.

The results in Table 5 show that market concentration has a positive and statistically significant effect on MFI performance at the 10% threshold. The variables “liquidity”, “credit” and “geographical penetration” have a positive and statistically significant effect on performance at the 5% threshold. On the other hand, the portfolio “deterioration rate” has a negative and statistically significant effect on MFI performance at the 5% threshold.

These results show that increased concentration improves performance. Our results corroborate those of ( Deb & Sinha, 2022 ). They show that MFIs with greater market power are more effective at reducing costs. Indeed, lower costs allow MFIs to provide financial services to their customers at more affordable prices. As a result, this can attract more potential clients and promote access to financial services among the unbanked. Where the microfinance market is concentrated, MFIs can benefit from economies of scale by streamlining their operations and sharing fixed costs such as IT systems, infrastructure and staff. This can reduce costs and improve operational efficiency, leading to stronger financial performance. In addition to lower costs, where MFIs have market power, they may be motivated to develop long-term relationships with customers, which can improve performance through customer loyalty ( Rajan & Petersen, 1994 ).

The results of the quantile regression (see Table 6 )

Source: Author, based on data of BCEAO (2023) . Note: (*), (**) represent significance levels of 1% and 5% respectively (P-value).

The quantile regression results indicate that market concentration has a positive and significant effect on MFIs that are already performing at the 1% and 5% thresholds. These results are identical to those of ( Faye & Ratsimalahelo, 2022 ). This indicates that market concentration can be beneficial for successful MFIs. It allows them to attract investors and lenders by enabling them to access additional financial resources, finance their activities and meet the needs of their customers. It also helps them to position themselves in specific market segments, enabling them to maximise their revenues and improve their performance. In addition, market concentration encourages the sharing of best practice between already successful MFIs. This enables them to collaborate and exchange knowledge on risk management, governance, innovation, etc., which can translate into improved performance.

The liquidity ratio “ratio_liq” has a positive influence on performance at the 5% threshold. This means that an increase in the liquidity ratio improves performance. This result is similar to that of ( Trad et al., 2017 ) who show that institutions with high liquidity ratios efficiently meet their financial obligations. Our results also corroborate with those of ( Elouali & Oubdi, 2020 ) who argue that financial institutions with high liquidity are better able to obtain additional funding if needed. Lenders prefer to extend credit to institutions that are better equipped to meet customers’ needs.

The “ratio_cred” credit ratio has a significant and positive influence on performance at the 5% threshold. This means that a high credit ratio contributes to improving MFI performance. Our results are identical to those of ( Berger & Udell, 2002 ) who find that a high credit ratio broadens their client base and increases their activities. Brickley et al. (2003) find similar results. According to them, when MFIs have higher credit ratios, they are able to diversify their loan portfolio by making loans to different types of clients or in different economic sectors. This reduces credit risk and makes them more resilient to potential defaults by a single borrower or a specific sector ( Honlonkou, 2006 ).

The geographical penetration “penetr_geo” has a positive and significant influence on the performance of MFIs at the 5% threshold. A high penetration rate leads to an increase in deposits and loans granted, which contributes to the growth of the institutions’ assets. It can also lead to a greater number of customers ( Jégourel, 2008 ). An increase in the number of customers means an increase in the income generated by the interest on the loans granted by the MFI. This can help to improve the MFI's profit margins and profitability. In addition, the risk of default is reduced, as the risks are spread over a larger number of borrowers. In this way, a higher penetration rate can improve asset quality and reduce losses linked to non-performing loans. It also helps to reduce the operating costs of microfinance institutions. This result is similar to those of Creusot & Poursat (2009) .

The portfolio degradation rate has a negative impact on MFI performance at the 5% threshold. This implies that an increase in the degradation rate reduces MFI performance. According to Abebaw (2014) and Solhi & Mohamed (2014) , when borrowers fail to repay interest and late fees to microfinance institutions (MFIs), this creates a domino effect that negatively affects their income. MFIs operate by lending money to low-income borrowers, often without collateral. Abdula & Devi (2016) arrive at the same result. They show that a high degradation rate is the result of poor risk management on the part of the MFI. Clients and investors may be deterred from doing a bad deal with the MFI because of these high risks. As a result, deposit levels will fall and have a negative impact on the MFI’s performance.

Two hypotheses were put forward in this study. The first was that market concentration has a positive influence on MFI performance. This hypothesis was verified as the results showed a positive effect of concentration on performance. The second hypothesis was that market concentration had a greater influence on the performance of fairly efficient MFIs than on that of less efficient MFIs. It was also verified because when MFIs have a high level of performance, the effect of market concentration on their performance is significant.