Internal functions for the Pooled Mean Group (PMG) estimator of Pesaran, Shin & Smith (1999). PMG imposes common long-run coefficients across units while letting the speed of adjustment and short-run dynamics remain heterogeneous.
The model is the same ARDL\((p_y, p_x)\) as CS-ARDL, but the long-run coefficient vector \(\theta\) is pooled. This implementation uses a two-step inverse-variance weighted pooling of the unit-level long-run coefficients obtained from the CS-ARDL fit, a simplification of the concentrated maximum-likelihood estimator of Pesaran, Shin & Smith (1999) that is fast, consistent, and requires no numerical optimisation.