La evolución de la UNRWA: contribuciones desde los estudios sobre

4.3.1 Financial inclusion determinants

To answer the first three research questions, individual country‘s composite index of financial inclusion (henceforth CIFI) is modelled as a function of several financial

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inclusion determinants including the types of financial system. Specifically, the following linear model is estimated on CIFI measures:

(4.1)

where:

= the logit function of country‘s CIFI,

= vector of all explanatory variables affecting financial inclusion, = constant term,

= disturbance term, = individual countries,

= time period of variables‘ measurements, and

k = quantity of explanatory variables.

4.3.2 Testing procedures

Principally, the testing procedures are divided into two parts. The objective of the first part is to answer the first three research questions, while the second part provides answer to the fourth research question. Univariate and multivariate statistical analyses are used to analyze the data. Detail discussions on the analyses are presented in the subsequent sub-sections.

4.3.2.1 Pooled cross-sectional regressions

Initially, the first and the second parts of the analysis are estimated using the pooled ordinary least squares (OLS) method which yields the best linear unbiased estimated (BLUE). The OLS estimation is common in financial inclusion literature. With regard to the results of OLS, it has been identified that heteroskedasticity has some

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potentially serious implications for inferences. This problem can be solved using the White's (1980) correction for heteroskedasticity procedure when the heteroskedasticity problem is reported (i.e., when the Breusch-Pagan/Cook-Weisberg test is significant at 1%, 5% or 10% level). In this regard, the robust t-statistic is reported using the OLS regressions with robust option.

4.3.2.2 Analysis of panel data method

Since there are some arguments that OLS results may be biased due to the failure to control for country-specific, time-invariant heterogeneity [see, for example, Bevan & Danbolt (2004)], the panel data analysis is also conducted in the present study. In this regard, Eq. (4.1) is re-estimated using the analysis of panel data method. The method employs a one-way error component model for the disturbance, , with

(4.2)

where:

= countries fixed effects, and = remainder disturbance.

Intuitively, Eq. (4.2) expands the disturbance term in Eq. (4.1) into two components and the countries‘ fixed effects become one of the parameter to be estimated. For the purpose of estimating the panel equation, the assumption of the can be in two forms, namely fixed effects and random effects. Nonetheless, it ―is not as easy as a choice as it might seem‖ (Baltagi, 2005, p.19) to select between the fixed effects and the random effects. Hence, a formal Hausman specification test for fixed versus random effects panel estimation is performed to identify the suitable estimation

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results with regard to the underlying assumption of . The test‘s null hypothesis is that the difference in coefficient is not systematic (or random).

A number of separate regressions are estimated as additional checks for robustness of the main results.

4.3.2.3 Quantile regression

Apart from the pooled OLS, quantile regression is used to examine the last research question (i.e., are the financial inclusion determinants heterogeneous across the whole distribution of countries?). Introduced by Koenker & Bassett (1978) and Koenker & Hallock (2001), the conditional quantile regression estimator can be employed to examine the entire distribution of a response variable, conditional on a set of covariates (i.e., explanatory variables). Particularly, this regression method estimates the coefficients of the inclusion barriers depending on the location (i.e., th quantile) of the conditional distribution of CIFI.

Instead of running separate regressions, the quantile regression approach is used to segment the dependent variables into different subsets according to its conditional distribution. With regard to running separate regressions, Heckman (1979) argues that they have the tendency to produce inconsistent and biased estimates because of the sample selection bias. Furthermore, Gallant & Fuller (1973) and Ramsay (1988) also point out that running separate regressions are least-squares based and can be sensitive to the Gaussian assumption or to the presence of outliers. Montenegro (2001) also added that the quantile regression method could deal with the following issues:

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i. frequently the error terms are not necessarily constant across a distribution thereby violating the axiom of homoscedasticity,

ii. by focusing on the mean as a measure of location, information about the tails of a distribution are lost,

iii. OLS is sensitive to extreme outliers that can distort the results significantly.

These are all the advantages that make the quantile regression approach robust especially to departures from normality and skewed tails (Mata & Machado, 1996). In accordance with Eq. (4.1), the regression specification of the th conditional quantile can be presented as follows:

(4.3)

| { | } (4.4)

where:

| = th conditional quantile of on the regressor variable ,

= unknown parameters to be estimated for different values of in (0,1),

| = conditional distribution function of , and

= disturbance term where it requires that | = 0.

From the regression, the entire distribution of , condition on , can be traced by placing the value of from 0 to 1. Regression for dependent variable is run simultaneously using the seven setting quantiles being examined in this study, namely 5th, 10th, 25th, 50th, 75th, 90th and 95th, which largely considers the whole distribution of the sample. As suggested by Efron (1980) and Buchinsky (1995, 1998), bootstrap

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method is used to estimate the coefficients of the parameters. Particularly, 1,000 bootstrap replications27 are employed and it is argued that the bootstrap estimate is evidence to be fairly robust (Buchinsky, 1995).

The robustness of the quantiles regression results is examined by conducting inter- quantile regression, where the disparity of the estimated coefficient between different quantiles is examined. The disparity is checked between the two extreme tails (95th and 5th), the right tail and the median (95th and 50th), the median and the left tail (50th and 5th) and the two quartiles (75th and 25th) respectively. The inter-quantile regression is modelled as higher quantile minus lower quantile, and the positive sign represents an ascending pattern of coefficients between the two quantiles while a negative sign indicates a descending pattern (Dzolkarnaini, 2009).