The participatory and partisan impacts of mandatory vote-by-mail

This paper shows that mandatory vote-by-mail increases voter turnout but does not advantage one political party over the other.


Menger et al. study the adoption of vote-by-mail in Colorado
. They find that "VBM elections lead to greater ballot completion, but that this effect is only substantial in presidential elections" (pp. 1039). As a part of their study on the effects of voting technology on voter turnout in California, Alvarez et al. explore the relationship between optional vote-by-mail and the residual vote rate in the state (15) (for another study of California's system, see (66)).
They find that "regardless of the election, increased use of the mail to cast ballots is robustly associated with a significant rise in the residual vote rate" (pp. 658). Holbein and Hillygus use difference-in-differences models look at the effects of optional vote-by-mail on youth turnout, finding that it has small effects on this subgroup (36). Kousser and Mullin use matching-onobservables with data from Oregon and California and find that "voting by mail does not deliver on the promise of greater participation in general elections (pp. 428)" (3). Recent work has shown that vote-by-mail may also increase political discussion and information acquisition (65,67).
Finally, political scientists have considered how campaigns and various get-out-the-vote (GOTV) organizations would interface with a VBM system. In a series of GOTV experiments, Arceneaux, Kousser, and Mullin show that "door-to-door mobilization campaigns have a larger effect on the participation of those who vote at polling places than on registrants assigned to cast mail ballots, but only among individuals whose voting behavior is most likely to be shaped by extrinsic social rewards (pp. 882)" (50). Other GOTV experiments in a vote-by-mail context have tested the efficacy of various voter contact strategies see (51)(52)(53), generally finding the standard set of get-out-the-vote interventions can still operate reasonably well in a vote-by-mail system.
In short, our work takes an important step in this literature in that it is the largest and most comprehensive study of mandatory vote-by-mail to date and takes the important step of honing in on differential effects by political party (in large-scale individual-level voter files) and on the effects on party vote shares. While research in political science has studied vote-by-mail for decades, our work builds on the previous literature in important ways. Most previous studies take a 'conditional-on-observables' approach rather than approaches that utilize exogenous variation in VBM. Moreover, many previous works take a single state approach, with many focusing on Oregon or California or Colorado, but not pooling these together. And only a few exceptions use rich, large-scale, individual-level voter files in the analysis of vote-by-mail; many rely on self-reported surveys which may have issues with social desirability in the outcome measure and sampling framework, with many surveys not being designed and simply being under-powered to drill down into the dynamics at a sub-state level (68). They also tend to focus on overall turnout rates, usually only look by demographic characteristics other than political party. Furthermore, many studies only explore optional vote-by-mail (i.e. no excuse absentee voting) rather than all mail/mandatory vote-by mail. Our work takes an important step forward going beyond a conditional-on-observables designs and leveraging exogenous variation in vote-by-mail over time, pooling across multiple states to improve our levels of external validity, leveraging rich individual-level voter file data to increases our statistical precision and ability to draw causal inferences, focusing on turnout rates across political parties, bringing party vote shares into the analysis, and by drawing attention to the (currently actively debated) role of mandatory/all mail voting instead of optional vote-by-mail.

Are the Results With Voter Files Confounded by Differential Registration Bias? Effects of Mandatory Vote-by-Mail on Rates of Voter Registration
One potential concern with looking only among those registered to vote-as we have to do in the voter registration lists-is that it may bias our conclusions, particularly in the regression models we run given the potential for differential registration bias (69). Exploring this possibility is not possible using voter files alone. However, we can test for this possibility by using data from one of the most-commonly used sources in political science-the Cooperative Congressional Election Study (CCES). Here, we look at whether the presence of mandatory vote-by-mail in one's county is related to voter registration as measured by the CCES (which matches participants to voter file data from another voter file vendor Catalist). If mandatory vote-by-mail is unrelated to registration patterns, we are unlikely to have an issue with differential registration bias. Figure S4 shows this test. It plots effects across a number of specifications listed in the note of the figure. As can be seen in the Figure, mandatory vote-by-mail in one's community has little effect on whether an individual chooses to register or not. Despite being well-powered, the estimate is not close to being significant and equivalence testing allows us to rule out effects that are very small (23,24). This suggests that our approach in the Utah and Washington analyses is appropriate.

Model Number Effect of VBM on Registration
Note: Regression results from the Cooperative Congressional Election Study (CCES) 2006-2008 samples. The models estimate the effect of mandatory vote-by-mail in one's county (the lowest geographic level available in the CCES) and individual-level registration (from the CCES). Model 1 includes state and year fixed effects and a linear state-specific time trend. Model 2 includes county and year fixed effects. Model 3 includes county and year fixed effects plus a a linear state-specific time trend. The models all include controls for age, race, education, income, ideology, and political interest. The takeaway point from this figure is the presence of mandatory vote-by-mail does not affect the chances an individual registers to vote, hence differential registration bias is unlikely in our Utah-specific analysis. Figure S5 presents results using a variety of modelling strategies indicated on the x-axis. The first type of model includes only county and year fixed effects, the most common approach of implementing a difference-in-differences design in the study election laws (17). This approach is outlined in Equation (1) of the main paper. Importantly, this model does not account for factors that vary across units over time, and Section 7 below shows that this model is subject to endogeneity bias. The second type of model includes county and state-by-year fixed effects, which partially address the endogeneity concerns but still requires the parallel trends assumption to hold. The third type of model in Figure S5 includes county and state-by-year fixed effects as well as state-specific time trends. This modelling approach relaxes the parallel trends assumption, but only at the state level. As discussed in the main paper, our preferred model includes county-specific time trends to allow for differential temporal trends by county, particularly since individual counties within states adopted VBM at different times in four of the six states.  Are the results being driven by a particular state? Figure S6 reruns the county-level analysis omitting one state at a time (labeled on the x-axis if the figure). Here we use our preferred model specification that includes county and state-by-year fixed effects as well as linear county time trends. As can be seen, the results are robust to iteratively holding out one state at a time.

Additional Robustness Checks
The results are quite stable-with all not statistically significant and able to rule out very precise estimates.  Figure S7 does something similar to Figure S6, but here we hold out states where the entire state adopted at the same time (OR, CO), as opposed to a county-by-county rollout (CA, UT, WA, NE). As the right panel shows, our results become even more precise and remain not significant. This should not be surprising as these are the counties providing identification for the nationwide models that all include county-level fixed effects.
An alternate approach that we can take is to focus exclusively on states that adopt VBM all at once and compare the change in voter turnout in these states to places that did not adopt.
Unfortunately, this approach is inherently noisy given that we have only two treated units. The left panel in Figure S7 shows that, unsurprisingly, in this setup the estimates are highly sen- Note: Coefficient plot testing for whether the type of adoption (be it county-by-county or statewide) influences our results. Points are coefficient estimates and bars are 95% confidence intervals. Figure S8 differentiates between mandatory vote-by-mail in states that also maintain vote centers (CA, CO) and those that do not (UT, WA, OR, NE). To do so, we code the treatment variable in two ways. First, we include an indicator variable for both kinds of VBM (right side of the panel) and second we construct a continuous measure of ease in using the vote-by-mail system: 0 (no VBM), 1 (VBM with vote centers), and 2 (only VBM). These values allow us to account for various types of VBM exposure. As can be seen, either way we code this variable the results are the same-VBM does not affect democratic vote share. fi   Note: Coefficient plot testing different elections separately rather than averaged together (as is shown in the main paper).

Testing the Parallel Trends Assumption
Figure S10 tests whether current-year VBM adoption predicts previous-year turnout and vote share. If this is the case, this suggests a violation fo the parallel trends assumption that is key to the validity of the difference-in-difference design. The two-way fixed effects models show signs of imbalance. However, adding county time trends improves balance considerably, making models with these trends preferential to a two-way fixed effects model without county time trends.    Note: Points are coefficient estimates and bars are 95% confidence intervals. Models include state-by-year and county fixed effects and individual county time trends. Standard errors are clustered at the county level. Figure S13 tests for the possibility that adoption of VBM in a county might have an impact on voting patterns in adjacent counties. Given that changes in the voting system may also lead to changes in how information regarding the election is distributed, discussed in the media, or impacts the strategies of campaigns and candidates, it might be that these changes spill over to adjacent counties. To test for this, we not only code each county for whether or not it has adopted VBM in a particular election, we also code a separate dichotomous variable for any county that is geographically adjacent to a VBM county. We then include both the VBM and VBM-adjacent variables in the original models used in Figure 2 of the main paper. While we still find effects of VBM on turnout, we find no effects for being a VBM-adjacent county. Note: Points are coefficient estimates and bars are 95% confidence intervals. Models include state-by-year and county fixed effects and individual county time trends with heteroskedasticity robust standard errors.