Estimation method

Of the three standard panel data estimation methods (pooled OLS, random-effects, and fixed-effects estimators), the fixed effect estimator is not appropriate for estimating the model because it contains a number of time-invariant explanatory variables. I therefore started with the pooled OLS estimator and the random-effects estimator (REE).Also, the Breusch and Pagan Lagrange Multiplier test favoured the use of REE over the OLS counterpart (Breusch & Pagan 1980).

REE is a particular case of the generalized least squares estimator, and it assumes that the time invariant fixed effects are uncorrelated with all explanatory variables. It is generally more efficient compared to the pooled OLS estimator (Wooldridge 2009). However, the REE estimator can yield biased and inconsistent coefficient estimates if one or more explanatory variables are endogenous, that is, if they are jointly determined with the dependent variable. There are two such potential sources of endogeneity. The first is the possible reverse causation from economic growth to remittance inflows. Poor growth performance can act as a push factor in

labour migration, resulting in an increase of remittances. Second, there can be some omitted variables in the model which are correlated with both remittance and growth.

To address the potential endogeneity, system generalized method of moments (GMM) method is used (Anderson & Hsiao 1982; Blundell & Bond 1998). Moreover, due to the presence of a lagged dependent variable, the fixed effect coefficients will produce a ‘dynamic panel bias’ or ‘Nickell bias’, as the lagged dependent variable would be correlated with the error term (Arellano & Bond 1991; Baltagi 2005; Nickell 1981). The bias would be small if the time periods in the estimation is large (Roodman 2009a). However, in our estimation, we have only seven non-overlapping five-year periods, and therefore, the bias may be large.

Tackling the potential endogeneity bias is not easy. Several studies use instrumental variables for remittances. The different instrumental variables used for workers’ remittances are: 1) ratio of country’s income to US income; the country’s real interest rate to the US real interest rate, and lagged per capita growth (right hand variable) (Barajas et al. 2009); 2) distance between the migrants’ home country to their major destination country including the dummy variable if the countries shared a common border or not using the cross section data (Faini 2006; International Monetary Fund 2005);3) inverse of the distance between the migrants’ home country and the destination country multiplied by the GDP per capita; or GDP growth rate or the unemployment rate of the destination country (The World Bank 2006);4) lagged explanatory variables and system Generalized Method of Moments (GMM) techniques (Catrinescu et al. 2009; Giuliano & Ruiz-Arranz 2009).

Barajas et al. (2009) argue that the endogeneity problem associated with remittances has not been adequately addressed and contend that the robust external instrument for remittances has not been found. Thus, my empirical approach is to (1) employ a five-year panel to mitigate the business cycle effects; (2) examine the quadratic relationship between remittances and growth; (3) include a detailed set of conditioning variables; and (4) use internal instruments to tackle the endogeneity problem. As argued forcefully by Clemens et al. (2012) in their discussion on empirical relationship between foreign aid and economic growth, I use the more transparent method of lagging and differencing as an identification strategy in the

It is well known that the quality and magnitude of the coefficients depend on the types of instruments used, and the results are quite sensitive to the choice of instrument. It is difficult to defend the exclusion restriction of the instruments which cannot be tested. In the absence of a strong instrument of remittance, I use the dynamic panel data method which utilizes the internal instruments from the lags of the explanatory variables.

I then estimate Equation 2.1 using the system GMM regression technique developed by Arellano and Bover (1995) and Blundell and Bond (1998). This involves differencing equation the equation by either subtracting the previous observations of the variables, or alternatively subtracting the variables from their means of all future available observations of the variables. The second method of differencing, known as ‘forward orthogonal deviations’ is preferable when dealing with an unbalanced panel (Roodman 2009a). Then the differenced GDP per capita ( 𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔_{𝑖𝑖,𝑡𝑡−1} ) can be instrumented by 𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔_{𝑖𝑖,𝑡𝑡−2} (and previous lags), as these are uncorrelated with the differences error terms. The difference GMM technique only utilizes this set of instruments. However, lagged levels of the variables are weak instruments for the first differences if the variable is persistent (Bond et al. 2001). The system GMM technique derives additional moment conditions by instrumenting 𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔_{𝑖𝑖,𝑡𝑡−1} in the original level equation by its contemporaneous and lagged first differences, as these are uncorrelated with the level of the error term.

The system GMM estimation has another important advantage in addition to allowing consistent estimation of an equation that controls for the lagged dependent variable. It allows the explanatory variables to be either endogenous, or weakly exogenous (predetermined), and deals with the problem of likely reverse causality from GDP per capita growth to remittances. In order to estimate the model, I impose the restriction that the remaining explanatory variables are exogenous. Thus, the system GMM technique provides us with the set of internal instruments, rather than the external instruments.

The turning point implied by the remittance-growth equation is estimated and its significance is calculated based on the Wald test for confidence interval for a scalar non-linear combination of the parameters using the delta method (Cameron & Trivedi 2010). Due to the presence of lagged and squared remittances term, the main effect or

the marginal effect of remittances and its significance is also reported in the regression estimations.

To check the robustness of the results, I first re-estimate the model after removing the outliers and influential observations using the leverage ratio method and Cook’s distance measure. Second, the data for the time invariant institutional quality was not available for 24 developing countries, resulting in the loss of observations. I estimate the models using the fixed effects estimations including the extended sample of 98 developing countries. Third, some studies have shown that the impact of remittances depend on the level of financial development (Giuliano & Ruiz-Arranz 2009). I also interact the financial development variable with the remittance variable and the years of schooling to test if the impact of remittances depends on the levels of financial deepening and education. Fourth, I use the annual panel and re-estimate the model. Finally, a simple non-parametric graph is used to see if the functional form of remittances in the model impacts the estimation results.