Abstract
This paper introduces shrinkage estimators (Ridge DOLS) for the dynamic ordinary least squares (DOLS) cointegration estimator, which extends the model for use in the presence of multicollinearity between the explanatory variables in the cointegration vector. Both analytically and by using simulation techniques, we conclude that our new Ridge DOLS approach exhibits lower mean square errors (MSE) than the traditional DOLS method. Therefore, based on the MSE performance criteria, our Monte Carlo simulations demonstrate that our new method outperforms the DOLS under empirically relevant magnitudes of multicollinearity. Moreover, we show the advantages of this new method by more accurately estimating the environmental Kuznets curve (EKC), where the income and squared income are related to carbon dioxide emissions. Furthermore, we also illustrate the practical use of the method when augmenting the EKC curve with energy consumption. In summary, regardless of whether we use analytical, simulation-based, or empirical approaches, we can consistently conclude that it is possible to estimate these types of relationships in a considerably more accurate manner using our newly suggested method.
Highlights
This paper introduces a new Ridge regression estimator for the dynamic ordinary least squares (DOLS) model
A unique contribution of this paper consists of proposing ridge estimators for the standard DOLS model
It is especially evident that combining DOLS with the Ridge regression estimator suggested by Kibria [11] results in the best performance in terms of mean square errors (MSE)
Summary
This paper introduces a new Ridge regression estimator for the dynamic ordinary least squares (DOLS) model. The remedy of DOLS consist of attaching leads and lags of the first difference of the integrated regressor on the right-hand-side of the equation; the small-sample bias is diminished as these independent variables collect a part of the correlation between the independent variables and the error term (Caballero, [2]). In this way, a second-order bias is denoted, due to the fact that the consistency of the estimator is unaffected by the endogeneity of the regressors. This method is often used in environmental and energy economics, when for example, estimating the energy consumption and economic growth nexus in Belke et al [3], Ouedraogo [4] and Damette and Seghir [5], among others, the environmental Kuznets curve (EKC) by Nasr et al [6] and Aspergis [7], among others, or the effect of oil prices on real exchange rates by Chen and Chen [8]
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