Penalized leads-and-lags cointegrating regression: a simulation study and two empirical applications

When leads and lags are added to a cointegrating regression to eliminate endogeneity bias, overfitting and multicollinearity problems can arise. For this purpose, we propose a regularized extension of the conventional dynamic ordinary least squares (DOLS) estimator which facilitates lead–lag selection and improves estimate accuracy. Simulation experiments show that the proposed approach outperforms traditional selection procedures, in terms of precision and accuracy. We propose two empirical applications to illustrate the outlined methodology. The first one revisits the effect of media attention on Bitcoin trading volume, which is highly exposed to endogeneity bias due to a two-way causal effect. Our results show that the proposed procedure leads to a lower mean absolute error than when one uses conventional procedures. In a second empirical illustration, we apply the methodology to carbon dioxide emissions forecasting. The case of France is examined. Our estimates show that the penalized leads-and-lags cointegrating regression outperforms DOLS for long horizons.