Learning about what observed variables you need for selection on observed variables to be a reasonable assumption

I like this paper a lot, both in the narrow sense that it presents interesting and useful results that I have already been citing, but also more generally because it follows the path that I think the literature should follow but rarely does. That path takes claims about the important of selection on unobserved variables in particular contexts and puts them to an empirical test.
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Marco Caliendo, Robert Mahlstedt, Oscar A. Mitnik:

Unobservable, but Unimportant? The Influence of Personality Traits (and Other Usually Unobserved Variables) for the Evaluation of Labor Market Policies

Abstract:
Many commonly used treatment effects estimators rely on the unconfoundedness assumption ("selection on observables") which is fundamentally non-testable. When evaluating the effects of labor market policies, researchers need to observe variables that affect both treatment participation and labor market outcomes. Even though in many countries it is possible to access (very) informative administrative data, concerns about the validity of the unconfoundedness assumption remain. The main concern is that the observed characteristics of the individuals may not be enough to properly address potential selection bias. This is especially relevant in light of the research on the influence of personality traits and attitudes on economic outcomes. We exploit a unique dataset that contains a rich set of administrative information on individuals entering unemployment in Germany, as well as several usually unobserved characteristics like personality traits, attitudes, expectations, and job search behavior. This allows us to empirically assess how estimators based on the unconfoundedness assumption perform when alternatively including or not these usually unobserved variables. Our findings indicate that these variables play a significant role for selection into treatment and labor market outcomes, but do not make for the most part a significant difference in the estimation of treatment effects, compared to specifications that include detailed labor market histories. This suggests that rich administrative data may be good enough to draw policy conclusions on the effectiveness of active labor market policies.

http://ftp.iza.org/dp8337.pdf