I'd like to build a general-to-specific model in econometrics as an
exercises. I am looking for an example where this method was used. By
preference the example is easy to follow and step-by-step.

This method is also called the LSE methodology and is associated with
Sargan and Hendry.

A link pointing me to a worked-out exaple will do the job.

I'll be glad to give any clarifications needed.