We want to focus on the state-specific turnout gap, i.e., what remains of the gap after we account for the "demographic" part, coming from national-level turnout among different types of voters combined with the demographic makeup of the state. To do this we compute four post-stratifications– VOC and WHNV turnout with and without state/race interaction (SRI)– then take the appropriate differences. If we do this in the same Monte-Carlo model fit we can also estimate a confidence interval for that difference. When we estimate the with-SRI and without-SRI models separately, we lose the ability to estimate a confidence intervals for the difference.
But adding the SRI term shifts the other parameters some, so we it’s worth checking that estimating the "demographic" turnout with the full model is similar to estimating without the SRI term. The estimates and confidence intervals for both models are shown below. Results from the full model are in blue and the no-SRI model in orange. NB: the x-axis here is different from the charts in the main post in order to emphasize the differences between the models.
The results are fairly close, most differences are between 0.5 and 1 point of turnout. The turnout gaps in the full model are all slightly smaller in magnitude (less negative) and have larger confidence intervals. For all 50 states (and DC) the confidence interval of the model without SRI is within the confidence interval of the full model1. So we are comfortable using the "demographic" component as calculated via the full model, at least for the sort of broad questions entertained in the post.
The converse is not always true: there a few states (PA, CO, NM), where the full-model estimate is outside the 90% confidence interval of the no-SRI model.↩︎