We used the Rubin causal model framework (36) to provide additional evidence for a causal link between cross-disciplinary collaboration and increasing citation impact. According to the potential outcome notation, let YXD=1 = zi,p,1 represent the outcome, that is, scientific impact proxied by citations, of a publication drawing on cross-disciplinary collaboration, denoted in our data set by the indicator Embedded Image = 1; conversely, the counterfactual Embedded Image represents the potential outcome of the same publication but without cross-disciplinary collaboration (Embedded Image = 0). To obtain counterfactual pairs from our data set (Embedded Image for each XD publication p of each faculty Embedded Image with Embedded Image, we searched through just their profile for the most similar p′ to pair with p. More specifically, for each p with Embedded Image = 1, we collected all publications from the same profile within ± 2 years (|tptp| ≤ 2). From this potential match set, we then selected the p′ with the closest number of coauthors to ap, and if ap was larger or smaller than ap by more than 20% (|apap| ≥ 0.2), then we rejected this match and did not include p in the set of matched pairs. We produced matches without replacement so that each p′ was included only once.

We then combined these matched pairs (p, p′) into an observation subset and ran the same regression model as in Eq. 2 on this set of faculty with Ni,XD ≥ 10 matched data pairs. Table S6 shows the model estimates for the resulting 53 Embedded Image. Using these matched publication pairs, we also estimated the mean cross-disciplinary “treatment effect,” Embedded Image. As such, the average value, Embedded Image, is an estimate of the average treatment effect on the treated (ATET). In addition to comparing the outcome according to normalized citation impact, YXD=1 = zi,p,1, we also report the ATET calculated using the total citation difference, Embedded Image, and the percent citation difference, Y1Yo ≡ 100(ci,pci,p)/ci,p.

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