The methodology of this chapter follows previous studies that have examined the relationship between financial development and poverty (Clarke et al., 2006; Li et al., 1998). These studies measured the size and/or depth of the financial sector using formal financial sector measures to represent financial development. This chapter adopts a similar approach, but it replaces formal sector measures with measures of the size and depth of microfinance. This chapter also follows other recent empirical studies to inform its model (Hermes, 2014; Hisako & Shigeyuki, 2009; Imai et al., 2012). The empirical specification is given as:
𝑦𝑖𝑡 = 𝛽𝑀𝑖𝑡 + 𝛾𝑋𝑖,𝑡+ 𝛼𝑖 + 𝜆𝑡+ 𝜀𝑖𝑡 (2.1) where 𝑦𝑖𝑡 is a vector of dependent variables, which refers to the poverty indicators for country 𝑖 at time 𝑡, and 𝑀𝑖𝑡 is a vector of microfinance variables, which is the main focus of this chapter. The vector, 𝑋𝑖𝑡, contains control variables, while 𝛼𝑖 is a country dummy, 𝜆𝑡 is a time dummy (year fixed effects) that is used to control for omitted shocks that every country suffers (e.g., the Global Financial Crisis) and 𝜀𝑖𝑡 is a normally distributed mean-zero error term.
9 http://www.microcreditsummit.org 10 http://www.mixmarket.org
11 Hisako and Shigeyuki (2009) did not consider the possibility of endogeneity and did not control for
fixed effects in their study. As a result of data availability, Imai et al.’s (2012) analysis is based on data from only 48 countries for 2007 (for cross-sectional estimations) and 2003 and 2007 (for panel data estimations). To address the potential endogeneity problems, they used two types of instrument: cost of enforcing contract and weighted five-year lag of average gross loan portfolios. Based on a five-year average cross-sectional data set using 70 countries, Hermes (2014) also used IV estimation to address possible endogeneity problems. Compared with Imai et al. (2012), two additional instruments have been used: the country’s legal origin and the absolute value of the country’s capital city latitude.
There are potentially two endogeneity problems to be addressed in this model. The first is sample selection bias. In many surveys, non-randomly missing data may occur because of a variety of self-selection rules. According to Baltagi (2008), if the selection rule is ignorable for the parameters of interest, one can use standard panel data methods for consistent estimation. However, if the selection rule is non-ignorable, then one must take into account the mechanism that causes the missing observations to obtain the consistent estimates of the parameters of interest. In the model used in this study, the dependent variable—poverty estimates—is only available for two or three specific years for most countries because the construction of international poverty estimates relies on nationwide household expenditure or income surveys (Imai et al., 2012). As a result of limited resources and a large population, most developing countries only collect data once or twice per decade. Thus, it is improper to apply a standard panel data method. The second problem is reverse causality, which usually results in inconsistent parameter estimates. In this study, the microfinance variables are likely to be endogenous in the poverty equation. Reverse causality from poverty to microfinance indicators may arise, suggesting that microfinance development is driven by poverty reduction.
To control for both sample selection bias and reverse causality, this chapter employs a model developed by Mroz (1987). The model (also called the combined Heckman two- step correction) consists of two stages. Stage one corrects for selection bias by estimating a probit model with the dependent variable, taking the value of 1 if the country has poverty data in a given year. Stage two uses instrumental variables to control for reverse causality (Wooldridge, 2010). The purpose of stage one is to eliminate the problem of sample selection bias, which is usually done by modelling the selection mechanisms explicitly and adjusting the estimation of the parameters in the regression equation for the selection effect (Heckman, 1976, 1977). This is obtained by including the inverse Mills ratio (IMR) in the structural equation. The IMR is calculated from the first stage and reflects how the variables included in this stage are related to the selection of the sample.
When estimating Equation (2.1), a specific selection problem occurs—namely, that of a truncated sample—because poverty estimates are only available for two or three specific years for most countries. Consequently, the sample is not random, and the relationship between poverty and microfinance is not estimated correctly. Thus, in stage
one, this chapter uses a probit estimation to estimate the probability of being in the selected sample. Two variables—gross domestic product (GDP) per capita and total population—are chosen as the selection criteria based on two considerations. First, countries with low GDP per capita are poor; thus, they have limited resources to conduct surveys. Second, it is assumed that it is more difficult to collect household data in very populous economies.
In stage two, the structural equation is estimated. Given the difficulty in finding a sound instrument that correlates with microfinance variables but does not have a direct causal effect on poverty, this chapter uses the lagged value of the endogenous variables (here, three microfinance variables). This technique is based on the idea that the past value of independent variables will affect the present value of dependent variables. Finally, the dependent variable of interest—in this case, two types of poverty measurements—is regressed on the lagged microfinance variables, the IMR and a number of control variables. In doing so, this chapter controls for both sample selection bias and endogeneity at the same time.