I want to suggest reading an interview with Angus Deaton, the most recent Nobel Laureate in economics, for a frank assessment of the issues raised by the OPs "channel" question regarding their "test and comparison"...here's the link:
And here's a quote:
People turned to RCTs (random control trials) because they got tired
of all the arguments over observational studies about exogeneity and
instruments and sample selectivity and all the rest of it. But all of
those problems come back in somewhat different forms in RCTs. So I
don’t see a difference in terms of quality of evidence or usefulness.
There are bad studies of all sorts.
Deaton's point is an honest assessment of the difficulties of untangling ("testing and comparing") confounded information. It is also a point that has been made by many others in other contexts. For instance, the excellent Cosima Shalizi, in a paper critiquing the social network analyses of James Fowler and Nicholas Christakis (http://smr.sagepub.com/content/40/2/211.abstract), notes that several processes analyzed by social theorists are generically confounded:
Homophily, or the formation of social ties due to matching individual
traits; social contagion, also known as social influence; and the
causal effect of an individual’s covariates on his or her behavior or
other measurable responses.
Similarly in studies of aging, it has been noted that the challenges associated with untangling the confounding effects of age, cohort, and temporal period effects are virtually insuperable.
Econometrics is no different in this regard. The metrics or "channels" may have changed, but the difficulties of reliably and accurately decomposing confounding effects related to education, health, poverty, status, wealth, income, etc., remain. The irony of Deaton's point throughout the interview is that RCTs -- the naively imagined "magic bullet" and gold standard for many -- are not able to resolve the problems. As one poster to this thread noted, at that point, "theory" becomes your best guide. Of course, multiple, widely differing theories can all provide an adequate fit to the same data.