How to cite information removed from a working paper when it was published

Question

Here's a simplified version of a bibliographic problem I'm facing.

A working paper estimated that Public Policy X caused Social Indicator Y to increase by 25%—practically significant, but not statistically significant at p < .05. So the paper's authors, as they told me by e-mail, omitted the discussion of Indicator Y when the paper was published in a journal.

Other studies of Policy X have found effects of 20%–40% on Indicator Y, so I'd like to cite the 25% estimate to corroborate these other studies. I'm writing for semi-popular consumption, so I'd like to minimize bibliographic clutter in the main text without confusing readers who can't find Indicator Y in the published paper. (The working and published papers have identical titles. The working paper is paywalled on every website that hosts it, and the published paper is unpaywalled on the website of one of its authors, so readers may find the published paper if they chase a citation to the working paper and aren't told that the two differ.)

What's the best solution? My current idea is this, but if there's a standard method, I'd prefer that. My publisher generally follows Chicago format.

In main text:

Kent and Parker found that Policy X increased Indicator Y by approximately 25%.¹ Though not statistically significant,² this estimate corroborates independent studies' estimates, such as [etc.]

In footnotes:

¹ Clark Kent and Peter Parker. "Various Effects of Policy X." NBER Working Paper No. 90210, June 2016. Discussion of Indicator Y is absent from the version ultimately published: Clark Kent and Peter Parker. "Various Effects of Policy X." Los Angeles Journal of Sociology 16, no. 1 (2017): 42–50.

² Peter Parker, e-mail message to author, October 31, 2017.

Answer 1

This is a rare situation, because “interesting enough to cite” and “interesting enough to include in the final draft” tend to be highly correlated. Therefore I wouldn’t expect there to be a “standard” way to do this.

However, there are standard ways to cite working papers. For Chicago style, it’s this:

Author. Year. “Title of Paper.” Title of Series. Sponsoring Organization, Month Day.

Add URL at the end if available online.

Deal, Ashley. 2009. “Collaboration Tools.” Teaching with Technology Whitepaper. Eberly Center for Teaching Excellence and Educational Innovation, Carnegie Mellon University, January 23. http://www.cmu.edu/teaching/technology/whitepapers/CollaborationTools_Jan09.pdf.

Source: CMOS 14.228, as quoted here.

I would switch the first part of your citation to match this format. The additional commentary that the result was excluded from the final paper is, in my mind, extremely important to include. I would do exactly what you’ve done (after correcting the second citation to Chicago style as well).