internal instruments to address potential endogeneity challenges. The GMM estimation is executed in three steps: (1) specify the regression equation as a dynamic panel data model; (2) take first differences to remove unobserved time-invariant country-specific fixed effects; and (3) instrument the right-hand-side variables in the first-differenced equation using levels of the series, lagged two periods or more, while ensuring that the model is not overidentified (Blundell and Bond 1998). The model is specified as follows: Where ln[Y]i,t is the logarithm of GDP and Xi,th represents growth determinants, including trade and control variables for i countries over time t, and h is the number of growth determinants where h= 1, 2, ... k. The GMM estimates Equation (5) and identifies inherent dynamic panel bias associated with the correlation between explanatory variables and error terms (Anderson and Hsiao 1982; Nickell 1981).<sup>29</sup> Following standard practice for GMM estimation, this study tests for panel stationarity or presence of unit roots using the Levin and Lin (1992) (LL-test) and the Maddala and Wu (1999) (MW-test) tests. The longer the time series dimension of the panel dataset, the greater the need to test for panel stationarity. In addition, the validity of the results of the GMM estimator can be affected by overidentification of instruments and second-order autocorrelation of the residuals. The system GMM estimator performs uses lagged values of endogenous variables as instruments, the number of instruments can easily explode as the time-series dimension of the dataset becomes longer weakening the test for over-identifying restrictions due to instrument proliferation or overidentification (Roodman 2009). According to Windmeijer (2005), GMM becomes more efficient when the lag length is controlled to use fewer instruments in the estimation. The Sargan or Hansen tests are diagnostic tests designed to establish whether additional instruments associated with the system GMM estimator are valid.<sup>30</sup> Practically, when using the system GMM estimator, the instrument count can be reduced creating one instrument per variable instead of different instruments for each variable and for each period (Daumal 2010). The result is a smaller set of instruments without compromising the optimal number of lags required (Roodman 2009). In addition, second-order autocorrelation of the residuals (serially correlated residuals) undermines the results of the GMM estimator by rendering instruments inconsistent. The Arellano–Bond test for first order (AR1) and second order (AR2) serial correlation are used to detect this problem.

3.2.3. Sample, data type and sources

> 29 The validity of the results of the GMM estimator can be affected by overidentification of instruments and second-order autocorrelation of the residuals. The system GMM estimator uses lagged values of endogenous variables as instruments.  The number of instruments can easily explode as the time-series dimension of the dataset becomes longer (Roodman 2009).  This weakens the test due to instrument proliferation or overidentification. According to Windmeijer (2005), GMM becomes more efficient when the lag length is controlled to use fewer instruments in the estimation. The Sargan or Hansen tests are designed to establish whether additional instruments associated with the system GMM estimator are valid. In addition to potential challenges with the number of instrument-based data points, there is the potential for second-order autocorrelation of (serially correlated) residuals. This can undermine the results of the GMM estimator by rendering instruments inconsistent. The Arellano–Bond tests for first order (AR1) and second order (AR2) serial correlation are used to detect this problem, since in the GMM approach, first order autocorrelation is allowed while second order correlation is not.

> 30 There is a tension between the two tests because although, on the one hand, the Hansen test is robust to heteroscedasticity, it is sensitive to instrument proliferation. On the other hand, the Sargan test is not sensitive to instrument proliferation, but it is not robust to heteroscedasticity. Therefore, as a rule of thumb, the Hansen test is used with an eye on instrument proliferation which is curtailed by ensuring that for every specification, the number of instruments is less than the corresponding number of countries.

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