Empirical Estimation Issues

Econometric Methodology

7.5 Empirical Estimation Issues

159

moment superfluous, (Arellano and Bover, 1995). So, additional conditions of moment for level regression are:

𝐸𝐸[�𝑌𝑌𝑖𝑖,𝑖𝑖−𝑠𝑠− 𝑌𝑌𝑖𝑖,𝑖𝑖−𝑠𝑠−1�(𝛽𝛽_0𝑖𝑖+𝜀𝜀𝑖𝑖𝑖𝑖] = 0 𝑓𝑓𝐶𝐶𝑓𝑓 𝑠𝑠 = 1 (7.16) 𝐸𝐸[�𝑋𝑋𝑖𝑖,𝑖𝑖−𝑠𝑠− 𝑋𝑋𝑖𝑖,𝑖𝑖−𝑠𝑠−1�(𝛽𝛽_0𝑖𝑖+𝜀𝜀𝑖𝑖𝑖𝑖] = 0 𝑓𝑓𝐶𝐶𝑓𝑓 𝑠𝑠 = 1 (7.17) Hence, we use the moment conditions presented in equations (7.16) to (7.17) and employ the system GMM method to generate consistent and efficient parameter estimates.

160

Working within the context of remittance inflows, current country remittance realizations affects future economic performance and this may, in turn, affect future country remittance realizations. Thus, this gives rise to the problem what may be termed as

“dynamic endogeneity”. The argument here centers on the fact that cross-sectional variation in observed country economic structures is driven by both unobservable heterogeneity and the country’s history. As such, any attempt to explain the role of remittance flows or its effect on economic performances of selected countries that does not recognize these sources of endogeneity may be biased.

The emphasis on unobservable heterogeneity in the literature as the major source of endogeneity often accounts for the widespread use of panel data and fixed-effects estimator. However, traditional fixed-effects (or “within”) estimates that eliminate unobservable heterogeneity are only consistent under the assumption that country characteristics or structures are strictly exogenous. That is, they are purely random observations through time and are unrelated to the country’s history. This is a strong assumption that is unlikely to hold in practice. So, while pooled OLS method may give biased estimate because it ignores unobservable heterogeneity, FEM may also give biased estimates since it ignores dynamic endogeneity.

The problem of endogeneity that is often associated with the use panel data analysis is thus resolved in this study by the choice of the System GMM method to estimate the relation between remittance flows and country economic performance in the Dynamic Panel Data Model framework. This methodology not only eliminates any bias that may arise from ignoring dynamic endogeneity, but also provides theoretically sound and powerful instruments that account for simultaneity while eliminating any unobservable heterogeneity. Dynamic panel estimation is most useful in situations where some unobservable factor affects both the dependent variable and the explanatory variables, and some explanatory variables are strongly related to past values of the dependent variable.

This is likely to be the case in regressions of remittance flows on economic performance.

This is because remittance flows tend to exert a strong, immediate and persistent effect on economic performance.

The dynamic panel data regression model is in fact characterized by another source of persistence over time. That is the problem of autocorrelation which is due to the presence

161

of a lagged dependent variable among the regressors. There are also two major and important complications arising from efforts to estimate the models using macroeconomic panel data: first, the presence of endogenous and/or predetermined covariates, and second, the small time-series and cross-sectional dimensions of the typical panel data set. These identified complications may be addressed applying the Arellano and Bond (1991) generalized method of moments (GMM) method (usually called standard first-differenced GMM method) or the augmented version proposed by Arellano and Bover (1995) and Blundell and Bond (1998), known as (system GMM method).

The dynamic structure of a panel data model suggests that the OLS estimator is upward biased and inconsistent, this is because the lagged level of income is correlated with the error term. The problem is not solvable even if the within transformation is applied owing to a downward bias (Nickell, 1981) and inconsistency. The Generalized Method of Moments (GMM) technique turns out to be the possible solution. Blundell and Bond (1998) show that when α (the coefficient of the lagged dependent variable in the dynamic model) approaches one, so that the dependent variable follows a path close to a random walk, the differenced GMM (Arellano and Bond, 1991) has poor finite sample properties and it is downwards biased, especially when T is small. Therefore, the Blundell and Bond (1998) system GMM derived from the estimation of a system of two simultaneous equations, one in levels (with lagged first differences as instruments) and the other in first differences (with lagged levels as instruments) becomes a more viable method.

The extended GMM (system GMM) method incorporates additional moment conditions for the untransformed equations in levels, and it relies on instrumental variables that are orthogonal to the individual-specific effects. Blundell and Bond (1998) show that an additional mild stationarity restriction on the initial conditions process allows the use of an extended system GMM method that uses lagged differences of the dependent variable as instruments for equations in levels, in addition to lagged levels of dependent variable as instruments for equations in first differences (Baltagi, 2005).

Bond, Hoeffler and Temple (2001) opine that in estimating the dynamic panel economic model applying the system GMM (Blundell-Bond method) estimation techniques, the pooled OLS and the FEM estimators should be considered respectively as the upper and lower bound. As a result, whether the differenced GMM coefficient is close to or lower

162

than the within group one; this is likely a sign that the estimates are biased downward (may be because of a weak instrument problem). Thus, if this is the case, the use of System– GMM is highly recommended and its estimates should lie between OLS and FEM. Moreover, Presbitero (2006) provides the evidence that the System GMM produces results that: (1) lies between the upper and lower bound represented by OLS and FEM, (2) shows an efficiency gain, and (3) has valid instrument set. Therefore, we produce the empirical results of system GMM along with the results obtained from pooled OLS regression and FEM.