Addressing the distributed lag models with heteroscedastic errors

The use of Almon technique is very common for the estimation of distributed lag model (DLM) to encounter the problems stemming due to direct application of the ordinary least squares (OLS) method to this model. However, the Almon estimator may suffer from the problem of multicollinearity as the constructed regressors in the Almon technique may be plagued with considerable degree of multicollinearity. To address this issue, the use of Almon-ridge estimator (ARE) has been considered as an alternative method for the estimation of DLM by many authors. In addition, the DLM may also face the problem of heteroscedasticity that may result in inconsistent covariance matrix estimator of ARE, leading to invalid testing inference about parameters of the DLM. In the present article, we propose to use the robust covariance matrix estimators of ARE for providing valid inference about parameters of the DLM taking multicollinearity and heteroscedasticity into account. These covariance estimators are used to construct confidence intervals, t- and F-tests. The performance of these confidence intervals and tests is evaluated empirically through the Monte Carlo simulations. The simulation results reveal an attractive performance of the proposed covariance matrix estimators.