Hi everyone, assume the Stata command is as follows:

xtpmg d.Y d.X, lr(l.Y X) ec(ec) replace pmg

The purpose is to estimate an ARDL model for panel data with error correction reparameterization . The dependent variable is Y and the independent variable is X. However, I have doubts about the corresponding equation. I think that the aforesaid command corresponds to:

\Delta \Y_{i,t}= \theta_{0} + \mu_{i}+ \phi_i(Y_{i,t-1} - \theta_{1} X_{i,t-1})+ \lambda_{i} \Delta X_{i,t} + \epsilon_{it} where \mu_{i} is a fixed-effect associated with panel i.

In particular, as pool mean group regression (PMG) is used, long-run relationships are homogenous across panels, so I think \theta_{1} can be written without panel indexing (i.e. \theta_{1} instead of \theta_{1i}), but I would be glad if someone confirms that point.

Besides, I am not sure if \mu_{i} is part of the model, or if instead it should be a panel-specific constant.

Thank you in advance for your help!