Analysis Technique Random Effects Approach

The study employed a random effects framework to analyse the relationship between liquidity and deposit insurance of the LISSA DTMFIs. According to Brooks (2008), the general panel data model is shown as:

𝑌_𝑖𝑡 = 𝛼 + 𝛽𝑋_𝑖𝑡+ 𝜇_𝑖𝑡

(4.8) where: Yitis the regressand factor; α is the intercept term, β is a K x 1 vector of parameters to be estimated on the regressors; Xit is a 1 x K vector of regressors, for i =1, … N and t = 1, … T.

µit is decomposed into սi the error term that represents the unobserved effects or individual DTMFI effects and vit which represents the idiosyncratic error term.

𝜇𝑖𝑡 = 𝑢𝑖 + 𝜈𝑖𝑡 (4.9)

The idiosyncratic error term is assumed to be identically and independently distributed with a zero mean and constant variance, 𝜈𝑖𝑡⁓ 𝐼𝐷𝐷(0, 𝜎𝜈2). Panel data models pool data on the individual DTMFI dimensions which are represented by subscript i collected over time which is represented by subscript t. According to Gujarati (2004) supported by Greene (2012), panel data econometrics method has the advantage of pooling both the time series and cross-sectional components of datasets than pure time series and pure cross-section data econometrics. In a similar vein, Brooks (2008, p. 488) added that with panel data econometrics, more complex problems can be addressed “than would be possible with pure time series or cross-sectional data” econometrics. Hence, Pillai (2016) added that panel data methods can exert controls on heterogeneity across individuals and over time. Amongst other benefits of panel data econometrics, (Baltagi, 2005; Hsiao, 2014) noted the following: highly informative datasets, reduction in multicollinearity, increased degrees of freedom and increased efficiency.

Specifically, the study considered two main panel data econometric methods; the fixed effects and the random effects after noticing that panel data methods facilitate accounting for the heterogeneity of the DTMFIs under study. Reputable microfinance works that used the same econometric methods, inter alia, include; (Bogan, 2012; Vanroose and D’Espallier, 2013; Bayai and Ikhide, 2016b; Abdulai and Tewari, 2017a; da Costa, 2017). Park (2011) distinguished the fixed effects approach from the random effects approach based on the treatment of dummy variables.

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The fixed effects model combines the dummy variable with the intercept as shown in Equation 4.10:

𝑌_𝑖𝑡 = (𝛼 + 𝑢_𝑖) + 𝑋′_𝑖𝑡𝛽 + 𝜈_𝑖𝑡

(4.10) The random effects model combines the dummy variable with the error component as shown in Equation 4.11:

𝑌_𝑖𝑡 = 𝛼 + 𝑋′_𝑖𝑡𝛽 + (𝑢_𝑖 + 𝜈_𝑖𝑡) (4.11) Deciding on adopting either the FE approach or the RE approach is mainly based upon answering the question; is the unobserved effect սi correlated with the regressors Xʹit? While assuming that the explanatory variables Xʹit, are not correlated with the error term սi, the random effects method accommodates time-variant features but does not allow for the characteristic differences in the selected DTMFIs. The random effects approach uses a common mean value for the intercept for the selected DTMFIs. In marked contrast, the fixed effects method assumes that the error term սi is correlated with the regressors Xʹit and allows for time-invariant characteristics of the sampled DTMFIs in the estimation process. Also, the fixed effects method allows the intercept to differ across the DTMFIs and not to vary over time. The Hausman Specification Test (refer Table 4.5) was an aid in choosing between the random effects and the fixed effects models. According to this test, the null hypothesis is that the random effects model is appropriate while the alternative hypothesis is that the fixed effects model is appropriate. The random effects model is chosen when the p-value is insignificant (Gujarati, 2004).

Table 4.5: Hausman Specification Test Results (b) Fixed (B) Random (b - B) differences sqrt(diag(V_b - V_B)) S.E. lnCAR -0.0214812 0.2202193 -0.2417005 0.1860379 lnDTL -0.0431605 0.0196915 -0.062852 0.0739182 lnGLP -0.2503368 -0.094004 -0.1563328 0.097578 lnYoGP -0.1911913 -0.0289048 -0.1622866 0.1809482 lnLLR 0.1278093 0.0753728 0.0524364 0.0371197 lnTETA -0.3839253 -0.1667738 -0.2171514 0.2063509 lnCPI -0.0119737 0.0130675 -0.0250412 0.0374875 chi2(7) = (b – B)'[(V_b – V_B)^(-1)] (b – B) = 8.71 Prob > chi2 = 0.2739

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After running the Hausman test, we failed to reject the null hypothesis as the p-value of 0.2739 was more than the significance level of 0.05 indicating that the random effects model was the most appropriate model for estimating the results. Equation 4.12 shows the linear functional model for estimation:

𝑙𝑛𝑁𝐸𝐿𝐴𝑇𝐴_𝑖𝑡 = 𝛽₀+ 𝛽₁𝐷_𝑖𝑡𝐷𝐸𝑃𝐼𝑁𝑆𝑈+ 𝛽₂𝑙𝑛𝐶𝐴𝑅_𝑖𝑡+ 𝛽₃𝐷_𝑖𝑡𝐵𝐴𝑆𝐸𝐿+ 𝛽₄𝑙𝑛𝐷𝑇𝐿_𝑖𝑡 + 𝛽₅𝑙𝑛𝐺𝐿𝑃_𝑖𝑡+

𝛽₆𝑙𝑛𝑌𝑜𝐺𝑃_𝑖𝑡+ 𝛽₇𝑙𝑛𝐿𝐿𝑅_𝑖𝑡+ 𝛽₈𝑙𝑛𝑇𝐸𝑇𝐴_𝑖𝑡 + 𝛽₉𝑙𝑛𝐶𝑃𝐼_𝑖𝑡+ 𝜇_𝑖𝑡 (4.12)

Before estimating the random effects model, some diagnostic tests were conducted27_.

The multicollinearity test results shown in Table 4.6 were based on the VIF analysis.

Table 4.6: Multicollinearity Test Results using the VIF analysis for the independent variables used for assessing Liquidity and Deposit Insurance

Variable VIF 1/VIF

YoGP 2.60 0.384960 TETA 2.40 0.416663 BASEL 1.42 0.703610 CAR 1.35 0.740528 CPI 1.26 0.793888 DEPINSU 1.25 0.801619 DTL 1.24 0.808876 GLP 1.15 0.870722 LLR 1.10 0.912033 Mean VIF 1.53

Source: Compiled by the author based on estimation results

As Table 4.6 shows, the VIF scores for the variables used for analysing the relationship between liquidity and deposit insurance ranged from 1.10 to 2.60 indicating that multicollinearity levels were very low. The mean VIF for all the explanatory variables was also very low at 1.53 and the tolerance levels ranged between 0.3684960 to 0.912033 and were within the acceptable level.

To test for heteroscedasticity, the Breusch-Pagan test was used again and the p-value obtained was 0.0000 indicating that the null hypothesis was rejected as the errors exhibited heteroscedasticity. To correct this problem, all the variables used in the estimation model were

27_{This section also utilised the same diagnostic tests that were used in Section 4.2.3 for multicollinearity and}

heteroscedasticity, except for the White’s robust standard errors, another technique for solving the problem of heteroscedasticity. Endogeniety in this section was tested using a different technique as explained below.

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transformed into logarithm format except for the dummies (DEPINSU and BASEL). Furthermore, the estimated model was corrected for White’s robust standard errors.

Since the random effects model was adopted as the baseline model, this means that the unobserved individual effects captured in the error term are not correlated with any of the explanatory variables suggesting that there is no problem of endogeniety. Thus, this exogeneity assumption must hold if the random effects model is a consistent and efficient estimator. According to Qian (2014), the random effects model can be consistently estimated using the Ordinary Least Squares (OLS) or Generalised Least Squares (GLS) methods. The GLS method is more efficient than the OLS method. However, in the presence of endogeneity, these methods are biased and inconsistent due to their assumption that the explanatory variables are exogenous. Therefore, to ensure that endogeniety was not a problem in the estimation process, the study employed the Two-Stage Least Squares (2SLS) technique as a testing technique using the ivregress command in Stata.

The results of the ivregress command also enabled the study to identify the correct model (2SLS or the OLS method) for checking the robustness of the random effects model results. In the presence of endogeniety, the 2SLS method is preferred to the OLS method and in the absence of the endogeneity, the OLS method is superior to the 2SLS method. The present study treated size (lnGLP) as an endogenous variable as this variable was suspected to be influenced by financing revenue (lnYoGP) and risk proxied by the loan loss rate (lnLLR). The later variables were treated as instrumental variables. The results of the 2SLS method shown in Table 4.7 indicated that endogeniety was not a problem suggesting that the OLS method was more appropriate than the 2SLS method.

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Table 4.7: Endogeniety Tests using the 2SLS method Test of endogeniety

(estat endog command)

H0: Variables are exogenous

H1: Variables are endogenous

p-values

Durbin test: 0.8216 Wu-Hausman test: 0.8265

The insignificant p-values of the Durbin and Wu-Hausman tests support that the null hypothesis could not be rejected. This led to the conclusion that the suspicion that size (lnGLP) is an

endogenous variable influenced by financial revenue (lnYoGP) and risk (lnLLR) was not supported.

Instruments’ strength (estat firststage command)

H0: Instruments are weak

H1: Instruments are strong

p-value: 0.0045

Minimum eigenvalue statistic: 5.58086

Though the minimum eigenvalue statistic value was low indicating that the instruments were weak, their p-value was significant hence the instrumental variables were appropriate for testing the endogenous variable.

Over-identifying restrictions (estat overid command)

H0: Instruments are valid and

the model is correctly specified.

H1: Instruments are not valid

and the model is not correctly specified.

p-values:

Sargan test: 0.8326 Basmann test: 0.8370

The insignificant values of the Sargan and Basmann tests

supported the null hypothesis that instruments set for testing for endogeneity was valid and that the model was correctly specified.

Source: Compiled by the author based on estimation results

As stated above, the GLS method is more efficient than the OLS estimator in checking the consistency of the baseline random effects model (Greene, 2012), therefore the study

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adopted the GLS method for robustness purposes. Using the xtgls command in Stata, the GLS method allows estimation in the presence of AR(1) autocorrelation within panels, correlation amongst the cross sections and heteroscedasticity across the panels. The robustness check results of the GLS method are presented in Table 5.8 under section 5.3.3 and the estimated regression output showed that the panels were homoscedastic and there was no autocorrelation. Since the present study utilised an unbalanced panel dataset, cross sectional correlation across the panels was not tested because the panels must be balanced for this test to be carried out.

In the next section, the data, variables and the statistical method that were used for answering the third objective of the study are discussed.

4.5 Investigating the Outreach and Financial Sustainability Nexus in depository

In document Financial sustainability, liquidity and outreach of deposit-taking microfinance institutions: evidence from low income Sub-Saharan Africa. (Page 132-137)