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Happy New Year! After running out of easy, off-the-top-of-my-head topics for this series, I have decided to go with a friend’s suggestion of blogging econometrics papers whose results are useful for applied work.

Given that I am working on a paper in which I am dealing with an instrumental variable that is only plausibly exogenous–that is, the exclusion restriction is likely to hold, but there is a small chance that it does not–I thought I should begin the year with two posts on how to deal with imperfect instruments.

This does not mean that these posts will discuss what to do with plain-old bad instrumental variables (IVs), i.e., instruments for which the exclusion restriction clearly does not hold. Again, this post and the next will discuss situations where your IV most likely meets the exclusion restriction, but wherein there is a small chance that it does not.

If you are interested in the use of randomized controlled trials (RCTs) in economics–particularly in development economics–Timothy Ogden has a new book out titled Experimental Conversations: Perspectives on Randomized Trials in Development Economics.

I am preparing a longer review that should see the light of day in the near future, but in the meantime, the book features a series of conversations with prominent economists–from Abhijit Banerjee and Esther Duflo to Angust Deaton, and from Jonathan Morduch to David McKenzie–not only about the advantages and disadvantages of RCTs, but also about the past, present, and future of RCTs.

If you are not already familiar with his work, Timothy Ogden is the managing director of the Financial Access Initiative at NYU, and he is the editor in chief of Philanthropy Action.

A few weeks ago, one of my doctoral advisees wrote to me asking me how she could test for a specific mechanism behind the causal effect she is trying to estimate in her job-market paper.

Letting [math]y[/math] be her outcome of interest, [math]D[/math] her treatment of interest, [math]x[/math] be a vector of control variables, and [math]\epsilon[/math] be an error term with mean zero, my student was estimating

(1) [math]y = \alpha_{0} + \beta_{0}{x} + \gamma_{0}{D}+\epsilon[/math],

in which she was interested in [math]\gamma[/math], or the causal impact of [math]D[/math] on [math]y[/math].

But more importantly for the purposes of this post, she was also interested in whether [math]M[/math] is a mechanism through which [math]D[/math] causes [math]y[/math]. I suggested the usual thing I often see done, which is to estimate

(1′) [math]y = \alpha_{1} + \beta_{1}{x} + \phi_{1}{M} + \gamma_{1}{D}+\nu[/math],

in which case if [math]\gamma[/math] dropped out of significance and [math]\phi[/math] was significant (and had the “right”) sign, then she could say that [math]M[/math] was a mechanism through which [math]D[/math] cause [math]y[/math]. I also suggested maybe conducting a Davidson-MacKinnon J-test for non-nested hypotheses to assess the robustness of her mechanism finding.