Model specification

To measure the role of labour regulation on the contribution of trade to growth, we have used a new endogenous trade model, which assumes that openness of trade is an endogenous rather than an exogenous variable. Our endogenous growth model specification can be shown as follows

(1) $Y_{i,t}=function\left(K_{i,t},L_{i,t},O_{i,t},X_{i,t}\right)+{\epsilon }_{i,t}$

where $Y_{i,t}$ represents the GDP per capita growth rate in country i in year t and ${\epsilon }_{i,t}$ indicates the error component. The production function consists of the standard production components of capital ( $K_{i,t}$ ) and labour ( $L_{i,t}$ ) while including trade openness ( $O_{i,t}$ ) as an endogenous variable in the aggregate. Our main variables of interest and additional control variables are represented by $X_{i,t}$ , including the three labour protection indices, GDP, CR indices and financial risk as a component of CR.

Once the assumption of openness as an endogenous variable is acknowledged in the new trade model, this calls for a dynamic structure. Thus, we estimate equation (1) using a dynamic panel data estimator. In this context, we employ a GMM method that is simply an ordinary least squares (OLS) procedure applied to a suitably transformed version of the model whose parameters we are trying to estimate. The transformation involved is an instrumental variables transformation. All instrumental variable estimators can be interpreted as a GMM estimator. Whenever autocorrelation or heteroskedasticity arises in the error terms, a GMM approach is more efficient than using a two-Stage least squares (2SLS) approach. Whenever we use a system of equations, the benefits of the GMM approach become more apparent.

There are several reasons to employ the GMM approach. First, the estimation procedure is a plausible fit because growth is persistent over time. In essence, the correlation between the economic growth and their corresponding first lagged values is higher than the threshold level of 0.800 for persistence in a dependent variable. Second, the number of years (T) should be lower than the number of cross-sectional units – in this case, countries (N), a condition that applies here. For a large T, the Arellano–Bond method generates many instruments, leading potentially to a poor performance of asymptotic results. Furthermore, if T is bigger than the cross-sectional N, panel data may incorporate time series for several cross sections so that the unit-root tests can also be of interest. Moreover, as N increases, one may need to control for unobserved cross-sectional heterogeneity. Thus, the GMM estimation method is mostly appropriate for short panel data where T is less than N (cross section) (see Reference Cameron and TrivediCameron and Trivedi, 2010). Third, the GMM approach also controls for potential endogeneity among the explanatory variables.

First, the one-step difference GMM estimation (GMM-dif), deriving from Arellano Bond (1978), has been estimated but not chosen as the best GMM estimation technique since this estimation technique may perform poorly if the autoregressive parameters are too large or if the independent variables are persistent. As a result, the instruments may become weak in the sense noted by Reference Staiger and StockStaiger and Stock (1997). The usage of additional instruments by using lagged first differences (LFD) leads to what is described as GMM system estimation (GMM-sys). Although the inclusion of extra instruments will inevitably create additional moment conditions (associated with both first differenced and level form), we are nevertheless able to incorporate additional information by this method, reducing bias and imprecision. Many disappointing features of the standard GMM-dif approach can be overcome by GMM-sys, although this may also come at a cost as the time dimension grows, since with the resulting increase in the number of instruments, the power of the tests may weaken. However, the costs of this trade-off between efficiency and power may be alleviated by adopting Reference RoodmanRoodman’s (2009) instrument reduction technique, imposing lag limits and collapsing the instrument matrix. Consequently, we have adopted the system approach and performed it as our main estimation method to ensure the robustness of our estimates. Both the Hansen and the AR(2) test results reveal no evidence of misspecification associated with over-identification or serial correlation for GMM system specification. Thus, using Roodman’s instrument reduction technique and collapsing instruments does not come at the expense of lost information, so in our analysis we rely on system GMM rather than GMM-dif.