Our reports per 1000 enrolled students for participating institutions over the period of interest is displayed graphically in Fig. 3a. Applying the synthetic control approach to the natural log of reports to Title IX coordinator offices, we found an increase in the reports received by U.S. institutions after the 2017 regulations by slightly over one report per 1000 enrolled students at AAU institutions one year after implementation, slightly over four reports per 1000 enrolled students at AAU institutions after two years of implementation, and slightly over two reports per 1000 enrolled students at AAU institutions in the third year of implementation, as displayed in Fig. 3b. The bias-corrected synthetic control results were very stable relative to the original 2017 Title IX analysis, as indicated by Fig. 3c. This model suggests an additional 1.18, 4.27, and 2.32 reports per 1000 enrolled students at AAU institutions in the 2017–2018, 2018–2019, and 2019–2020 academic years, respectively. All other inference tables and figures derived using the biased-corrected synthetic control approach are available in Supplementary Material Part 2.

Longitudinal trends and synthetic control results | sexual misconduct per 1000 enrolled students at included U.S. and Canadian institutions, academic year 2014–2015 to academic year 2020–2021. a Sexual misconduct reports received per 1000 enrolled students at included U.S. institutions (solid, n = 40) and Canada institutions (dashed, n = 11). b Synthetic control for log-transformed reports of sexual misconduct per 1000 enrolled students, academic year 2014–2015 to academic year 2020–2021 for U.S. AAU institutions (solid) and synthetic U.S. institution (dashed); c bias-corrected synthetic control for log-transformed reports of sexual misconduct for U.S. AAU institutions (solid) and synthetic U.S. institution (dashed)

Table S2 summarizes the weights assigned to donor pool units to reach the synthetic control, suggesting the ‘synthetic US’ with the closest fit to the observed US trajectory in the pre-period was constructed by assigning 2.5% weight to donor institution one, 27.4% to donor institution three, 55.7% to donor institution five, 7.2% to donor institutions eight and nine, and 0% weight to all other institutions, summing to 100%.

Table S3 contrasts the predictor values for each explanatory variable included in the model. Comparable values between the affected unit, or the unit affected by a policy change, and the synthetic unit implies a strong ‘fit’, supporting the notion that it is appropriate to use the synthetic unit as a counterfactual proxy. Pearson tests confirm strong agreement between the affected unit and synthetic unit across most of our controls.

Performing placebo tests in which we pretend each of our unaffected synthetic control donors were actually the affected group, we reach the ratios of pre-period and post-period RMSPE values displayed in Fig. 4. If a policy is impacting the outcome of interest, we would expect none of the pre:post ratios to be as extreme as our affected group, and that most of the placebo ratio values would be near one, which is what we found.

Ratios of pre-period: post-period root mean squared prediction error (RMSPE), 2017 Title IX synthetic control

Ranking our ratio values from greatest to least, we converted this finding into a p-value, as displayed in Table 2. If we assume the Title IX 2017 guidance had no effect on rates of reporting, or a null of 0, we have would expect a result as extreme or more extreme than what we have observed here about 8% of the time. This is marginally significant, near but not reaching the alpha = 0.05 standard for significance.

A graph of the gap between our actual reports and our predicted report values for our affected and placebo units can be found in Fig. 5 (next page). Our treatment group is bolded, hovering near zero in the pre-period, and taking a notable dip in the post-period, whereas the gaps between our actual and predicted reports in both the pre- and post-periods follow much different paths for the unaffected placebo units.

Gap in predicted reports of sexual misconduct per 1000 enrolled students pre- and post-2017 Title IX guidance, academic year 2014–2015 to academic year 2020–2021

Our reports per 1000 enrolled students for participating institutions over the period of interest are displayed graphically in Fig. 6a. Applying the synthetic control approach to the natural log of reports made to Title IX coordinator offices, we found an estimated decrease in the reports received by U.S. AAU institutions after the 2020 regulations of about five reports per 1000 enrolled students at AAU institutions, as displayed in Fig. 6b. The bias-corrected synthetic control results were very stable relative to the original 2020 Title IX analysis, as is indicated by Fig. 6c. This model similarly implies a decrease in reporting to Title IX Coordinator offices by approximately five per 1000 at AAU institutions. Applying the synthetic control approach iteratively to each individual U.S. institution, instead of treating the U.S. average as a single affected unit, we calculated a similar but slightly larger estimate of a 6.19 report decrease per 1000 enrolled students at AAU institutions. All other inference tables and figures derived using the biased-corrected synthetic control approach are available in Supplementary Material Part 3.

Longitudinal Trends and Synthetic Control Results | Sexual Misconduct per 1000 Enrolled Students at included U.S. and Canadian Institutions, academic year 2017–2018 to academic year 2021–2022. a Sexual misconduct reports received per 1000 enrolled students at included U.S. institutions (solid, n = 40) and Canada institutions (dashed, n = 11). b Synthetic control for log-transformed reports of sexual misconduct per 1000 enrolled students, academic year 2017–2018 to academic year 2021–2022 for U.S. AAU institutions (solid) and synthetic U.S. Institution (dashed). c Bias-corrected synthetic control for log-transformed reports of sexual misconduct for U.S. AAU institutions (solid) and synthetic U.S. institution (dashed)

The weights assigned to donor pool units to reach the synthetic control are displayed in Supplementary Material Table S6 and suggest the ‘synthetic US’ with the closest fit to the observed US trajectory in the pre-period was constructed by assigning 16.3% weight to donor institution three, 6.8% to donor institution four, 76.9% to donor institution five, and 0% weight to all other institutions, summing to 100%. Table S7 contrasts the predictor values for each explanatory variable included in the model. Relatively strong agreement is again observed between the affected unit and synthetic unit across most controls.

Figure 7 displays the ratios of pre-period and post-period RMSPE values from performing placebo tests. We again find the pre: post ratios for the affected value are extreme relative to most of the ratios near one held by the donor units.

Ratios of pre-period: post-period root mean squared prediction error (RMSPE), 2020 Title IX synthetic control

Ranking our ratio values from greatest to least, we converted this finding into a p-value, as displayed in Table 3. If we assume the Title IX 2020 regulation had no effect on rates of reporting, or a null of 0, we would expect a result as extreme or more extreme than what we had observed here about 8% of the time. This is marginally significant, near but not reaching the alpha = 0.05 standard for significance.

Graphing the gap between our actual reports and our predicted report values for our affected and placebo units, we have Fig. 8 (next page). Our treatment group is bolded, hovering near zero in the pre-period, and taking a notable dip in the post-period, whereas the gaps between our actual and predicted reports in both the pre- and post-periods followed much different paths for the unaffected placebo units.

Gap in predicted reports of sexual misconduct per 1000 enrolled students pre- and post-2020 Title IX guidance, academic year 2017–2018 to academic year 2021–2022