4.2 Main Model with Instrumental Variable (IV) Estimation
The existing studies concerning remittances, IQ, and FI nexus have uncovered the presence of endogeneity issues (Kim, 2021). The endogeneity in econometric analysis denotes the situation where a variable in a model correlated with the error term or other predictors violating the assumption of exogeneity potentially resulting in biased and inconsistent estimates (Nakamura & Nakamura, 1998). These issues can arise in empirical estimations through three channels: reverse causality, measurement errors, and omitted factors (Roberts & Whited, 2013).
In our estimates, this issue can arise from measurement error and omitted factors. Firstly, due to the absence of direct measures for IQ and FI, we are compelled to utilize diverse proxies to gauge these variables. The complex and diverse nature of IQ and FI makes direct measurement infeasible, and a comprehensive assessment that adequately captures the full range of these concepts is currently unavailable. Moreover, the unavailability of a perfect proxy capable of entirely encapsulating these constructs adds to the likelihood of measurement error. Secondly, several influential factors affecting FI, such as social capital, financial development, and information asymmetry, are known to be correlated with our explanatory variable based on various scholarly sources (Kpodar & Andrianaivo, 2011; Lapukeni, 2015; Liang et al., 2019; Nkoa & Song, 2020). Unfortunately, due to the unavailability of data on these factors for the sampled BRI countries, we were unable to include them in our explanatory variables. This omission may result in omitted variables bias, potentially leading to endogeneity issues in our model. Consequently, these limitations might introduce biases and inconsistencies in our inference.
Bun and Sarafidis (2015) contend that conventional inference methods, such as random effect regression and fixed effects regression, which rely on least squares estimation, are unsuitable for producing unbiased and consistent estimates in the presence of endogeneity. While various estimation techniques have been proposed in the econometric literature to tackle endogeneity, a review of empirical studies indicate that the two-stage least squares (2SLS) method is the most commonly used (Issabayev et al., 2020b; Khan et al., 2022; Khan et al., 2019; Liaqat et al., 2022b).To mitigate the endogeneity and obtain reliable and unbiased estimates, 2SLS requires a valid instrument that provides exogenous variation in the endogenous regressors. The validity of an instrument is based on two crucial conditions: relevance and exclusion. Relevance refers to the strong correlation between the instrument and the endogenous regressor, while exclusion requires that the instrument is not correlated with the dependent variable except through the included regressors. In other words, the instrument must not be correlated with the error term, which would result in biased estimates. Hence, selecting a valid instrument is a crucial step in implementing the 2SLS method and obtaining accurate results.
Aggarwal et al. (2011) and Fromentin (2018) resolved the endogeneity challenge in remittance studies by implementing instrumental variables, specifically lagged values of the explanatory variables. This approach helps to mitigate the impact of measurement error, reverse causality, and omitted variables. However, the use of lagged values of explanatory variables as instruments to address endogeneity has limitations. Firstly, it assumes exogeneity of the lagged values, which may not be true if unobserved shocks impact both the current and lagged variables. This can lead to biased estimates (Wang & Bellemare, 2019). Secondly, the lagged values may not capture all relevant variation, resulting in biased estimates (Eckert & Hohberger, 2022). This made us cautious in using this approach and we consider alternative method to address endogeneity by employing external instrument of crop production index and live-stock production index (Amuedo-Dorantes & Pozo, 2004). More recently, these instruments have also employed by Kim (2021) while examining remittances association with financial development (FD).
The issue of endogeneity in IQ estimation has been widely recognized in the literature, and several potential instruments have been proposed to address this problem. In this study, we identified settler mortality rate (SMR) of European settler and legal origin (LO) as appropriate instruments based on their strong theoretical foundation and empirical support in the literature. Fortunately, the use of these instruments has been shown to satisfy the relevant statistical assumptions and provide valid and efficient estimates of IQ. Therefore, we believe that our choice of instruments will help to overcome the endogeneity issue and lead to robust and reliable results in our analysis.
LO and SMR are exogenous and significant predictors of IQ, although their link with IQ is not directly correlated with the country's FI. Therefore, LO and SMR are valid instruments for establishing the moderating effects of IQ on remittances-FI nexus by providing an exogenous source of variation in IQ. There is a stream of empirical evidence supporting the hypothesis that historical differences in legal traditions or origins have a significant impact on the institutional environment, which in turn affects financial system (Ang, 2019; Khan et al., 2022; Khan et al., 2020b). In particular, research has shown that countries with a British common law origin exhibit a significantly positive association with higher IQ, as compared to those with a civil law origin (Khan et al., 2022). This provides strong support for the role of legal traditions in shaping the institutional environment and influencing the development of financial systems and improving access and usage of financial services. Building on existing literature, this study employs British common law origin as an instrument for IQ. This takes the form of a dummy variable equal to “1” for countries whose legal system is based on British common law, and “2” for all others. By utilizing this instrument, we can address endogeneity concerns and establish the causal effects of remittances on FI through IQ.
Acemoglu et al. (2001) propose the settler mortality hypothesis, which posits a negative relationship between settler mortality and current IQ. This hypothesis is supported by several studies in literature. To test this theory, we adopt the use of log mortality rate of European settlers and British common law legal origin (LO) dummy as instruments for IQ, in line with previous studies (Acemoglu et al., 2001; Khan et al., 2022; Rodrik et al., 2004). However, SMR rate data is not available for our sample countries, resulting in a limited sample size. Therefore, we primarily rely on the British common law LO dummy as an instrument, and subsequently verify the robustness of our findings by using SMR as an instrument on a smaller sample. The econometric equation used to estimate the 2SLS analysis are specified as follows. The first-stage equation is expressed as:
$${\text{ X}}_{\text{it}}\text{ }\text{=}{\text{δ}}_{\text{0}}\text{ }\text{ }\text{+}{\text{γ}}_{\text{1}}{\text{Z}}_{\text{it}}\text{+}{\text{γ}}_{\text{2}}{\text{K}}_{\text{it}}\text{+}{\text{ ε}}_{\text{it}}$$
2
Where, \({ X}_{it}\)depicts remittances and IQ for a country i at time t, which are endogenous variables, \({Z}_{it}\) are instrumental variables for remittances and IQ (i.e., crop production index and legal origin), \({K}_{it}\)it is the vector of controlling factors, \({\delta }_{0}\) is constant, while \({\gamma }_{1}\), and \({\gamma }_{2}\) are the coefficients of instrumental variables and controls respectively, and εit represents error term.
In the second stage equation.
$${\text{ Y}}_{\text{it}}\text{ =}{\text{δ}}_{\text{0}}\text{ +}{\text{γ}}_{\text{1}}{\text{X}}_{\text{it}}\text{+}{\text{γ}}_{\text{2}}{\text{K}}_{\text{it}}\text{+}{\text{ ε}}_{\text{it}}$$
3
Where, \({ Y}_{it}\)depict the dependent variables FI, FI_A, FI_U, FI_P for a country i at time t, \({X}_{it}\) denotes remittance and IQ (instrumented remittance with crop production index and IQ with legal origin) for a country i at time t which are independent variables, \({K}_{it}\) it is the vector of controlling factors, \({\delta }_{0}\) is constant, while\({\gamma }_{1}\), and \({\gamma }_{2}\) are the coefficients of explanatory and controlling factors respectively, and finally, εit represents stuff in error term.