Online Appendix for Redistricting and the Causal Impact of Race on Voter Turnout

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1 Online Appendix for Redistricting and the Causal Impact of Race on Voter Turnout Bernard L. Fraga Contents Appendix A Details of Estimation Strategy 1 A.1 Hypotheses A.2 Redistricting Design A.3 Matching A.4 Aggregation of Trials Appendix B Covariate Balance between Treatment and Control Groups 9 Appendix C District Demographic Composition as a Continuous Variable 13 Appendix D Accounting for Electoral Competition 17 Appendix E Cross-Group Matching as a Placebo Test 22 Appendix F Matching on State Lower House District 28 References 31

2 Appendix A Details of Estimation Strategy Using the Neyman-Rubin potential outcomes framework (see Rubin 2005; Morgan and Winship 2007), to test the impact of a binary treatment D on an individual (i) for outcome Y, we would like to witness a specific individual s outcome (Y i ) when D i = 1 (or the treatment condition) and compare it to Y i when D i = 0 (the control condition), or estimation of Yi 1 Yi 0. However, since we cannot observe both conditions for a single individual at the same time (or the counterfactual for an individual i), we are only able to estimate the effect of treatment by comparing values of Y for individuals who received the treatment to those who did not, or formally: E[Y i D i = 1] E[Y i D i = 0]. Thus, in the study I seek to estimate the average treatment effect of D on the treated (AT T D ), where AT T D E[Yi 1 Yi 0 D i = 1], and is estimated via comparison of E[Y i D i = 1] to E[Y i D i = 0]. A.1 Hypotheses Recall the hypotheses tested in the study: H1 (D = INC): Individuals are more likely to turn out to vote when assigned to congressional districts with a co-ethnic incumbent, ceteris paribus. H2 (D = CAN): Individuals are more likely to turn out to vote when assigned to congressional districts where a co-ethnic candidate seeks office, ceteris paribus. H3 (D = MAJ): Individuals are more likely to turn out to vote when assigned to congressional districts where their ethnic group comprises a majority of the voting-age population, ceteris paribus. Formalized via the potential outcomes framework, for individual i, D INC i individual is assigned to a district with a co-ethnic incumbent, D CAN i 1 = 1 if the = 1 if the individual

3 is assigned to a district with a co-ethnic candidate, and D MAJ i = 1 if the individual is assigned to a district where their racial/ethnic group is in the majority. The relevant comparison population, or control group, consists of individuals where D i = 0 for the hypothesis being tested. Formalized in terms of each AT T D : AT T INC = E[Yi 1 Yi 0 Di INC = 1] = E[Y i Di INC = 1] E[Y i Di INC = 0] (A.1) AT T CAN = E[Yi 1 Yi 0 Di CAN = 1] = E[Y i Di CAN = 1] E[Y i Di CAN = 0] (A.2) AT T MAJ = E[Yi 1 Yi 0 D MAJ i = 1] = E[Y i D MAJ i = 1] E[Y i D MAJ i = 0] (A.3) Since we are interested in the effect of assignment, ensuring that the individuals did not receive treatment prior to assignment necessitates a time component, t, such that comparisons are only made among those for which D it 1 = 0 (and remains 0 for the control group). Continuing from above: AT T INC = E[Y it D INC it AT T CAN = E[Y it D CAN it AT T MAJ = E[Y it D MAJ it = 1,Dit 1 INC = 0] E[Y it Dit INC = 0,Dit 1 INC = 0] (A.4) = 1,Dit 1 INC = 0] E[Y it Dit CAN = 0,Dit 1 CAN = 0] (A.5) = 1,D MAJ it 1 = 0] E[Y it D MAJ it = 0,D MAJ it 1 = 0] (A.6) A.2 Redistricting Design With random assignment, we can be certain that, on average, there are no observable or unobservable differences between populations based on treatment status, such that (Y 1,Y 0 ) D. As discussed in the main text, the analysis makes use of the redistricting process to approximate random assignment. Comparing individuals who resided in the same district pre-treatment (t 1), but were later placed into differing districts for election t, we can plausibly estimate the effect on Y of a difference in treatment conditions 2

4 (D {0,1}) between the two districts in election t. 1 As discussed in the main text, existing work that leverages redistricting often characterizes the appropriate comparison as voters who are moved to a new district, while others are left in the old district (Sekhon and Titiunik 2013). However, redistricting may induce fundamental shifts to all districts involved; every district may be new in some fashion. The only appropriate solution, therefore, is to compare treated individuals in post-redistricting districts to control individuals assigned all possible postredistricting districts that meet the appropriate control criteria above. Such a method of defining treatment and control groups means that multiple comparisons are available for individuals with the same 2010 district, but whose 2012 districts differ in binary treatment status D. Figure A.1 presents the basic strategy for comparing voters from the same 2010 district, but differing 2012 districts: Figure A.1: District Comparison Strategy (a) 2010 District (t 1) (b) 2012 Districts (t) Co-Ethnic No Co-Ethnic No Co-Ethnic (1) (2) (3) No Co-Ethnic (4) Co-Ethnic Figure A.1(a) represents a district under the 2010 plan. To be included in the study, the 2010 district that a registrant resides in must not have had a co-ethnic incumbent, 1 Sekhon and Titiunik (2013) demonstrates that additional, implausible assumptions are necessary to compare individuals who differ in their pre-treatment district (p ). 3

5 candidate, or a majority of the ethnic group in question, depending on the hypothesis being tested (in other words, D it 1 = 0). For the purposes of this example, the 2010 district in Figure A.1(a) has no co-ethnic incumbent. This districts is split apart into four districts for the 2012 election, as a result of redistricting, and as such there are four distinct groups of registrants who shared the same 2010 district but differ in their assignment post-redistricting. Figure A.1(b) indicates that two of these 2012 districts have a co-ethnic incumbent, while two do not, which produces the variation on D it necessary to estimate AT T INC. Including the darker shaded areas of the new 2012 districts only, which consists of registrants who shared the 2010 district presented in Figure A.1(a), we can compare turnout for registrants in area (1) to area (3), with registrants in (1) as the treatment group (D it = 1) and registrants in (3) as the control group (D it = 0). Yet, we can also create treatment-control pairs of districts by contrasting areas (1) and (2), (4) and (3), or (4) and (2). 2 Each of these treatment-control pairs of 2012 districts serves as a unique trial (k), and by contrasting the rate of turnout for individuals within a trial for the treatment group to those from the control group, we can calculate the AT T for said trial. A.3 Matching However, the non-random nature of redistricting may indicate that there are observable characteristics X that are correlated with treatment status D. 3 To deal with this problem, the study exact matches individuals across treatment and control conditions within each pair of 2012 districts on age group, gender, and previous turnout. Matching assumes that once we condition on a set of observable characteristics X such that 2 Registrants lying outside of the darkly shaded region of Figure A.1(b) are excluded from comparison, and comparison of those in area (1) to area (4) and area (2) to area (3) do not contribute to our estimate of AT T INC, as there is no variation on 2012 treatment status as defined here. 3 See the main text for examples. 4

6 (Y 1,Y 0 ) D X, we may also assume E[Yi 0 D i = 1,X] = E[Yi 0 D i = 0,X], and thus can estimate AT T for any treatment D given matching on X as: AT T D X = E[Y 1 i Y 0 it D i = 1,X] = E[Y i D i = 1,X] E[Y i D i = 0,X] (A.7) Which, after adding a time component and the restriction that comparisons only be made between individuals who shared the same pre-redistricting (t 1) congressional district, yields the following comparison groups to establish AT T X : AT T INC X AT T CAN X AT T MAJ X = E[Y it D INC it = E[Y it D CAN it = E[Y it D MAJ it = 1,Dit 1 INC = 0,X] E[Y it Dit INC = 0,Dit 1 INC = 0,X] = 1,D CAN it 1 = 0,X] E[Y it D CAN it = 0,D CAN it 1 = 1,D MAJ it 1 = 0,X] E[Y it D MAJ it = 0,D MAJ it 1 = 0,X] (A.8) = 0,X] (A.9) (A.10) As detailed in the Data section of the main text, I exact match individuals on age group, gender, turnout in previous elections, and through the design of the study, race and pre-2012 congressional district. 4 A secondary benefit of exact matching on previous turnout is that I have ensured balance on Y it 1, which is likely to share unobservable correlates with Y it and (under the parallel trends assumption) further enhances the internal validity of the analysis (Athey and Imbens 2006). Such a comparison also means that, while I focus on rates of participation in election t, the pre-treatment difference in turnout between matched treatment and control individuals is precisely 0. The matched results found in the study are thus a non-parametric difference-in-differences (DID) estimate as well. 4 Section B of this Appendix also demonstrates pre-matching imbalance on each of these variables. 5

7 A.4 Aggregation of Trials The main text notes that the fundamental unit of analysis in the study is the individual, who is identified as part of either the treatment or control group when contrasting turnout within a pair of 2012 districts. As Figure A.1 indicates, each pair of 2012 districts is considered to be a trial (k), and thus I calculate AT T D for each k. Since we are interested in the overall average treatment effect on the treated, we must combine the results of all trials k in some fashion. However, all trials are not created equal; we likely believe that a superior estimate of AT T D is provided by trials with a larger sample size and/or lower variance (Hedges and Vevea 1998), and we need a manner of estimating the overall uncertainty of our estimates. Also, if we are interested in individual-level behavior, we want to ensure that our estimated effects approximate what the average individual (in the sample) experienced as a result of treatment, not the trial-level average. As a first step, I calculate the standard error for the difference of means observed when contrasting treatment and control groups within each trial. Recall the difference of means was constructed by contrasting the rate of turnout for individuals in the treatment group with those from the control group. Using the unmatched results as an illustration, AT T D was expressed as follows: AT T D = E[Y 1 i Y 0 it D i = 1] = E[Y i D i = 1] E[Y i D i = 0] (A.11) In practice, AT T D k is estimated as Y d=1 - Y d=0 for each trial k, which is unbiased estimate of the average causal effect for a randomized trial (Dunning 2012, 115; Imbens and Rubin 2015, 87). The standard error for this difference in means is the root of the sum of the sampling variances observed for the treatment and control groups within each 6

8 trial: σ 2 k = σ 2 d=1 n d=1 + σ 2 d=0 n d=0, and SE k = σ 2 d=1 n d=1 + σ 2 d=0 n d=0 (A.12) Which, importantly, is likely to serve as a conservative or upwardly biased estimate of error with large samples (Dunning 2012, 171; Imbens and Rubin 2015, 93). Drawing on the interdisciplinary technique known as meta-analysis, and most especially the psychology literature (Hedges and Vevea 1998), I take all of the trial-level estimates of AT T D and generate a mean average treatment effect on the treated to summarize my results: AT T D = AT T D k k (A.13) The above simple mean of the trial-level effects may not account for the aforementioned heterogeneity across trials, especially differences in the size of treatment and control groups across trials. To do so, I instead make use of the trial-level standard errors computed above to construct a weighted mean of the effects, which is also known as a fixed-effects meta-analysis (Hedges and Vevea 1998, 489; Stanley and Doucouliagos 2015, 2117): AT T D W = (wk AT T D k ) wk (A.14) Weights are defined as the inverse of the variance for each trial k, w k = 1/σ 2 k and thus the standard error of AT T D W is the square root of the reciprocal of the sum of the weights: SE(AT T D W ) = 1 wk (A.15) 7

9 AT T D W for each racial/ethnic group and treatment serves as the point estimate found in Figures 2-4 of the main text. SE(AT T D W ) is used in construction of the 95% confidence interval that extends outward from these points. Two alternative methods of aggregating the results were considered. The primary alternative would be a random-effects meta analysis, where AT T D is understood as representing only a (random) sample of possible AT T D. From a practical standpoint, the fixed-effects approach assumes that there is no excess heterogeneity in the variance of effects that is not captured in the observed trial-level variance (Stanley and Doucouliagos 2015, 2117). Thus the difference between these approaches is a function of views regarding the representativeness of the trials included in the study: while a fixed-effects meta-analysis yields results that are conditional on the individual being included in the trials, and thus accurately reflects variation that is observed across trials, random-effects would produce an unconditional estimate that assumes the trials are representative of some larger population of trials. While few studies have examined the effect of district ethnoracial context across states, we may indeed expect differential results if an alternative set of states was included in the analysis. That means that the trials included in the study may not be representative of some broader population, and thus the fixed-effects approach is more realistic. Instead, future researchers should examine whether the effects found in the study can be reproduced in other states, or at other points in time. A second alternative would be to abandon any effort to aggregate the results, and instead examine cases deemed by the researcher to be superior to others (Slavin 1995). While a fuller discussion of such an approach is beyond the scope of this study, future work should examine additional elections, states, or cases, which may enhance our understanding of the underlying mechanisms at work. 8

10 Appendix B Covariate Balance between Treatment and Control Groups Tables B.1, B.2, and B.3 indicate how treatment and control groups differ in terms of gender, age, and previous voting participation, for each of the three treatment conditions and broken down by racial/ethnic group. For most individual demographic traits, we see few differences between the treatment and control conditions prior to exact matching. The p-values listed under the Baseline set of columns are generally only below 0.05 (a conventional measure of statistical significance) for variables related to previous turnout for Whites and Latinos. As noted in the main text, this supports an argument of nonrandom assignment under redistricting, as those in charge of the process may account for previous turnout when assessing which areas to place in new political contexts (Li 2012; Henderson, Sekhon and Titiunik 2013). Exact matching fully removes these, and other, imbalances. 9

11 Table B.1: Covariate Balance, Co-Ethnic Incumbent Treatment White Registrants Baseline Matched Treatment Control p-value Treatment Control p-value N 668,781 2,077, ,643 2,065,943 District Pairs % Female % Age % Age % Turnout % Turnout % Turnout % Turnout Black Registrants N 363,794 1,461, ,441 1,455,953 District Pairs % Female % Age % Age % Turnout % Turnout % Turnout % Turnout Latino Registrants N 156, , , ,278 District Pairs % Female % Age % Age % Turnout % Turnout % Turnout % Turnout Asian Registrants N 56, ,336 56, ,020 District Pairs % Female % Age % Age % Turnout % Turnout % Turnout % Turnout Note: p-value reflects t-test for differences between district pairs on covariate. All variables listed are exact matched in Matched, except number of registrants and 2012 turnout. 10

12 Table B.2: Covariate Balance, Co-Ethnic Candidate Treatment White Registrants Baseline Matched Treatment Control p-value Treatment Control p-value N 81, ,296 81, ,259 District Pairs % Female % Age % Age % Turnout % Turnout % Turnout % Turnout Black Registrants N 821,925 1,630, ,262 1,622,318 District Pairs % Female % Age % Age % Turnout % Turnout % Turnout % Turnout Latino Registrants N 441,898 1,076, ,541 1,072,644 District Pairs % Female % Age % Age % Turnout % Turnout % Turnout % Turnout Asian Registrants N 126, , , ,818 District Pairs % Female % Age % Age % Turnout % Turnout % Turnout % Turnout Note: p-value reflects t-test of no difference between district pairs on covariate. All variables listed are exact matched in Matched, except number of registrants and 2012 turnout. 11

13 Table B.3: Covariate Balance, Majority-[Group] District Treatment White Registrants Baseline Matched Treatment Control p-value Treatment Control p-value N 195, , , ,596 District Pairs % Female % Age % Age % Turnout % Turnout % Turnout % Turnout Black Registrants N 164, , , ,941 District Pairs % Female % Age % Age % Turnout % Turnout % Turnout % Turnout Latino Registrants N 154, , , ,380 District Pairs % Female % Age % Age % Turnout % Turnout % Turnout % Turnout Asian Registrants - No Majority-Asian Districts in Dataset Note: p-value reflects t-test of no difference between district pairs on covariate. All variables listed are exact matched in Matched, except number of registrants and 2012 turnout. 12

14 Appendix C District Demographic Composition as a Continuous Variable In the main text, H3 is evaluated using a binary indicator for whether a registrant resides in a majority-white, Black or Latino district in However, such a measure may not capture the impact of smaller changes in district ethnic composition (Fraga 2015). As alternative, we may revise H3 to instead indicate that registrants should be more likely to vote when placed in districts with an increased proportion of co-ethnic individuals: H3b (D = V AP ): Individuals are more likely to turn out to vote when their share of the congressional district s voting-age population is increased, ceteris paribus. The data used to evaluate this hypothesis is drawn from the 2010 Census, as with the original conceptualization of H3 in the main text. For each 2012 district, I first calculate the proportion of the voting-age population (VAP) that is non-hispanic White, Black, Latino, or Asian. Then, for each group of voters I evaluate whether turnout is higher when placed in a district with a greater proportion of the VAP corresponding to the voter s ethnic group relative to voters placed in a district with a smaller co-ethnic VAP. As with the other treatments, comparison is only made between voters who shared the same district pre-redistricting. I define the treatment district for election t as the district with a higher proportion of the population belonging to the individual i s ethnic group: AT T V AP = E[Yi 1 Yi 0 Di V AP AT T V AP X = E[Y i D V AP i = 1,D V AP i = 0] = E[Y i D V AP i = 1] E[Y i D V AP i = 0] (C.1) = 1,X] E[Y i D V AP i = 0,X] (C.2) As with the other treatments, for each trial k, AT T k D σd=1 standard error as SE k = 2 n d=1 + σ d=0 2 n d=0. is estimated as Y d=1 - Y d=0, and the 13

15 Aggregation of the results accounts for the continuous nature of the difference in the VAP. 5 When combining trials, I preserve the continuous scaling of the VAP difference between treated and control districts through minimizing the weighted sum of squares as w k (y k x k β) 2, with y k equal to AT T V AP for each trial, x k as D between the 2012 district having a greater population proportion for the group and the district with a lesser population proportion, and w k as the inverse of the variance in estimation of AT T V AP k. The weighted least-squares regression coefficient resulting from analysis of the magnitude of the difference in district demographics ( ˆβ) is rescaled such that the overall average treatment effect on the treated (AT T D W ) reflects a 30 percentage point positive difference in the group s share of the voting-age population, relative to the control district. This quantity was chosen because it approximates a feasible shift occurring through the redistricting process. The effect is averaged over the entire continuum of observed VAP differences, then rescaled to reflect the average impact of a 30 percentage point increase. With treatment defined as placement in a district with an increased share of the individual s ethnic group relative to the control 2012 district, even the slightest difference will allow a pair to have treatment and control conditions. Thus nearly all jurisdictions in the dataset are included under this test. Despite the large number of district pairs included when testing H3b, a t-test reveals striking differences between treatment and control individuals, on average. White, African American, and Latino registrants with higher turnout have substantially different rates of prior participation in the treatment group, again with Whites moved to a more White district having higher turnout, on average, and Black and Latino individuals with significantly lower prior turnout being more likely to have a more heavily-black or Latino district in Table C.1 displays these differences. 5 Treatment could also be conceptualized as a non-binary dosage, with D [d 0,d 1 ] (Hirano and Imbens 2004). However, to align with the methodology used in the main text I instead account for differences in the magnitude of the change in the aggregation stage. 14

16 The overall average treatment effects for H3b align with results in the main text for some groups, but show a different pattern from the binary conceptualization taken in the main text in some circumstances. Figure C.1 indicates that White turnout increases approximately one percentage point when increasing the White voting-age population in the district 30 percentage points, an increase that did not appear in the matched condition when using the binary majority-white versus non majority treatment criterion. The effect of increasing the co-ethnic population for African Americans is roughly proportional to what is reported in Figure 3 of the main text, though uncertainty has increased as well. Latinos, whose turnout decreased about one percentage point when assigned to a majority-latino district, also display proportionately lower turnout when conceptualizing district demographics as a continuous variable. Asian Americans, who were not included in the analysis of district demographic composition in the main text, show signs of higher turnout that again point to a pattern most similar to African Americans. Figure C.1: Overall Average Treatment Effect on the Treated (ATT), Dist Demographics White Turnout, White VAP +30pp Matched Baseline Black Turnout, Black VAP +30pp Latino Turnout, Latino VAP +30pp Asian Turnout, Asian VAP +30pp Difference in Turnout 2012 (Tr-Co), percentage points Note: Points indicate average effect of a shift in district demographics, with 95% confidence interval extending outward. Gray points reflect the unmatched analysis, blue points the results after exact matching individuals in treatment and control conditions. Results reflect simulated 30 point increase in voting-age population for each ethnic group, based on results from an inverse-variance weighted least-squares regression with the difference between treatment and control 2012 district VAP as the independent variable. 15

17 Table C.1: Covariate Balance, District Demographics as a Continuous Variable White Registrants Baseline Matched Treatment Control p-value Treatment Control p-value N 28,434,413 23,042,191 28,372,815 22,984,262 District Pairs 1,292 1,292 1,292 1,292 % Female % Age % Age % Turnout % Turnout % Turnout % Turnout Black Registrants N 5,531,647 3,213,437 5,492,208 3,198,872 District Pairs % Female % Age % Age % Turnout % Turnout % Turnout % Turnout Latino Registrants N 5,225,087 3,819,895 5,187,422 3,803,972 District Pairs 1,068 1,068 1,068 1,068 % Female % Age % Age % Turnout % Turnout % Turnout % Turnout Asian Registrants N 1,041, ,806 1,021, ,888 District Pairs % Female % Age % Age % Turnout % Turnout % Turnout % Turnout Note: p-value reflects t-test of no difference between district pairs on covariate. All variables listed are exact matched in Matched, except number of registrants/pairs and 2012 turnout. 16

18 Appendix D Accounting for Electoral Competition The main text presents evidence for an impact of district ethnoracial context on voter turnout. However, as indicated in the Research Design section of the study, there may be factors that are correlated with ethnoracial context that influence the results. Of great concern may be electoral competition, which may influence turnout (Franklin 2004), influence the impact of other turnout correlates (Fraga and Hersh 2011), and most importantly, influence the impact of race on voter turnout (Tate 1991, 1994; Gay 2001). Below I test for heterogeneity in the effect of co-ethnic incumbents, candidates, or majority-[group] districts on voter turnout, depending on the level of electoral competition we see in the congressional district. One concern when studying the impact of electoral competition is the risk that the race of candidates or the demographic composition of districts may influence the level of competition with in a district; we should not treat the actual level of competition found post-election as entirely independent of the levels of turnout witnessed by various groups. Therefore, I use a predicted measure of competition to distinguish between competitive and uncompetitive environments, drawing on the Cook Political Report Partisan Voting Index (Cook PVI). 6 Cook PVI is constructed by taking each congressional district s two-party Democratic vote share from 2004 and 2008, subtracting the national Democratic vote share, and taking the average deviation over both elections. 7 I rescale this value as 1 P V I 0.5, such that a value of 1 would be found in a district with an exact 50%-50% split of the voteshare between the Democratic and Republican party candidates. Figures D.1-D.4 provide two sets of results. The first set uses the same districts as Figures 2-5 in the main text, that is to say, all available district pairs regardless of dif Cook PVI is widely used by campaigns, media outlets, and to a lesser degree political scientists, as an ex ante measure of district competitiveness. For 2012, the measure was recalculated to reflect 2012 congressional district boundaries. 17

19 fering levels of competition. The second set restricts the analysis to places where both the treatment and control groups post-redistricting districts were predicted to be competitive, with competitiveness being defined as a 20 percentage point margin of victory or smaller (0.8 with the rescaled PVI). Thus, the treatment and control groups varied as to the ethnoracial context found in 2012, but both groups faced a competitive electoral context nonetheless. 8 Highly uncompetitive districts, blamed for past null or negative findings regarding minority voter turnout in contexts of empowerment (Tate 1991, 1994; Gay 2001), have been removed in the Competitive Only condition. Figure D.1: Overall ATT, White Registrants by Level of Competitiveness, Matched Only H1: Co-Ethnic Incumbent All Cases Competitive Only H2: Co-Ethnic Candidate H3: Majority-White District Difference in White Turnout 2012 (Tr-Co), percentage points Note: Points indicate average treatment effect when using co-ethnic incumbency, candidacy, or majority- White district to define the treatment condition, with 95% confidence interval extending outward. Competitive Only subsets to cases where the losing candidate was predicted to receive at least 40% of the two-party vote in both the treatment and control district. Figure reflects inverse-variance weighted means of the average treatment effect on the treated for exact matched individuals; see main text for baseline results in national dataset. Do we see heterogeneous effects of ethnoracial context in competitive districts? Only in a few instances. Figure D.1 does indicate that when non-hispanic Whites are confronted with a co-ethnic candidate for the first time in a competitive district, we do not 8 Both sets of findings reflect Matched results, as indicated in the notes to the Figures. 18

20 Figure D.2: Overall ATT, Black Registrants by Level of Competitiveness, Matched Only H1: Co-Ethnic Incumbent All Cases Competitive Only H2: Co-Ethnic Candidate H3: Majority-Black District Co-Ethnic Cand + Majority-Black Difference in Black Turnout 2012 (Tr-Co), percentage points Note: Points indicate average treatment effect when using co-ethnic incumbency, candidacy, or majority- Black district to define the treatment condition, with 95% confidence interval extending outward. Competitive Only subsets to cases where the losing candidate was predicted to receive at least 40% of the two-party vote in both the treatment and control district. Figure reflects inverse-variance weighted means of the average treatment effect on the treated for exact matched individuals; see main text for baseline results in national dataset. see a significant change in behavior versus a competitive district without a White candidate. Instead, assignment to a majority-white district, which had a small, negative impact on participation when including all eligible district pairs, boosts turnout about one percentage point on average. Did competitiveness cause this change in results? Perhaps, but it is worth noting that Figure C.1 in the previous section of this Appendix also found that a substantial shift in percent White within a district resulted in a positive change in White turnout. While competitiveness may influence the instances in which ethnoracial context influences White turnout, the small number of Whites in non-majority White districts (pre or post-redistricting) may be a more likely explanation for heterogeneity. African American and Latino registrants, however, show a statistically indistinguishable pattern of participation when compared to the main text. Removing the most un- 19

21 Figure D.3: Overall ATT, Latino Registrants by Level of Competitiveness, Matched Only H1: Co-Ethnic Incumbent All Cases Competitive Only H2: Co-Ethnic Candidate H3: Majority-Latino District Co-Ethnic Cand + Majority-Latino Difference in Latino Turnout 2012 (Tr-Co), percentage points Note: Points indicate average treatment effect when using co-ethnic incumbency, candidacy, or majority- Latino district to define the treatment condition, with 95% confidence interval extending outward. Competitive Only subsets to cases where the losing candidate was predicted to receive at least 40% of the two-party vote in both the treatment and control district. Figure reflects inverse-variance weighted means of the average treatment effect on the treated for exact matched individuals; see main text for baseline results in national dataset. Figure D.4: Overall ATT, Asian Registrants by Level of Competitiveness, Matched Only H1: Co-Ethnic Incumbent All Cases Competitive Only H2: Co-Ethnic Candidate Difference in Asian Turnout 2012 (Tr-Co), percentage points Note: Points indicate average treatment effect when using co-ethnic incumbency or candidacy to define the treatment condition, with 95% confidence interval extending outward. Competitive Only subsets to cases where the losing candidate was predicted to receive at least 40% of the two-party vote in both the treatment and control district. Figure reflects inverse-variance weighted means of the average treatment effect on the treated for exact matched individuals; see main text for baseline results in national dataset. 20

22 competitive districts does not explain why Latino turnout is lower in contexts of Empowerment, as demonstrated by the largely similar findings in Figure D.3. That said, Asian Americans in competitive districts have slightly lower turnout when gaining a co-ethnic for the first time, the opposite of what was found in the main text. As with Whites, future work should examine why Asian American candidates do not boost co-ethnic turnout in competitive elections. While it is beyond the scope of this project to explore all ways in which competition can influence voter turnout, these findings indicate that uncompetitive districts are not driving the key results discussed in the main text, at least for Black and Latino registrants. 21

23 Appendix E Cross-Group Matching as a Placebo Test The identification strategy implemented in the main text compares voter turnout among registrants from the same ethnic group, but who are assigned to districts with differing ethnoracial contexts in the 2012 election. Such a strategy approximates random assignment and allows for the construction of treatment and control populations, who are then compared to produce the average treatment effects used throughout the study. However, factors outside of group-specific ethnoracial context also shift when contrasting treatment conditions, as noted above. Might some combination of these factors not directly related to ethnoracial context produce the findings found in the study? To address such concerns, we may conduct an alternative identification strategy that qualifies as a racial placebo test. 9 Since the three tests examined in the study are groupspecific, placement in a treatment district should not impact turnout for non-group members. If we find that turnout by group members is robustly higher than non-group members within treated districts, then we may believe this to be substantial evidence that H1, H2, and/or H3 have been validated for the group in question. Furthermore, since comparisons can be made among populations with the same post-redistricting district, then the electoral environment is held constant and alternative factors are unlikely to have produced the results. Such a strategy also recalls previous work that compared group to non-group turnout in majority-minority districts (Gay 2001; Barreto, Segura and Woods 2004; Henderson, Sekhon and Titiunik 2013). In these studies, turnout for the minority group in question was presented along with turnout for non-group members. In each instance, turnout by non-group members was not significantly different or was lower than the group that constituted a majority of the district or had co-ethnic representation. However, there are issues with this technique, many of which are noted in the Ig- 9 I am grateful to an anonymous reviewer for suggesting an identification strategy similar to that which is presented in this section. 22

24 norability section of the main text. Pre-treatment differences between the treatment population and control population create challenges for a redistricting design, but such difficulties are exacerbated when we also need to compare turnout rates across groups. It is a well-known fact that minority turnout lags non-hispanic White turnout substantially more in midterm elections than presidential elections (File 2013). 10 Thus, a simple difference-in-differences (DID) design that assumes a parallel trend in turnout between 2010 and 2012 in the absence of treatment is certainly not a valid inference strategy. Matching can alleviate some of these concerns, as we can exact match on turnout in both midterms and a presidential election, along with age and gender, to produce pre-redistricting balance across ethnic groups. Yet such matching is an attempt to randomize race by eliminating what is likely to be post-treatment (that is, post assignment of race) differences in participation caused by race (see Sen and Wasow 2016); the racial difference we find likely does not reflect how treatment would influence the average White, Black, Latino, or Asian registrant. Figures E.1 through E.4 present the cross-group effect of each treatment condition, broken down by race of the group that is hypothesized to be receptive to the groupspecific treatment condition. Points represent the inverse-variance weighted overall average treatment effect on the treated, as found when comparing group versus non-group turnout in treated districts. For example, the points in Figure E.1 denote the average difference in White versus non-white turnout in districts with a White incumbent, co-ethnic candidate, or where Whites constituted a majority of the voting-age population, respectively. As in the main text, I only include individuals whose pre-redistricting district did not have these conditions; a substantial change in ethnoracial context was experienced by both group and non-group members in each case. Furthermore, the shift in districts 10 Tables 1-3 above also indicate variation in turnout across ethnic groups and across elections, within ethnic groups. 23

25 is the same for both populations, as this tracks group and non-group members who were assigned to the same district as each other across the 2006, 2008, 2010, and 2012 elections. The gray points reflect an unmatched analysis, while the blue points exact match group and non-group members on previous turnout, age, and gender. Matched results may therefore be understood as a difference-in-differences analysis, subject to the caveats mentioned above. Figure E.1: Difference in White vs. Non-White Turnout in Treated Districts, 2012 H1: Co-Ethnic Incumbent Matched Baseline H2: Co-Ethnic Candidate H3: Majority-White District White Turnout - Non-White Turnout, percentage points Note: Points indicate inverse-variance weighted mean difference between White and non-white turnout in treated districts, when using co-ethnic incumbency, candidacy, or a majority-white district to define treatment condition. Gray points reflect the unmatched (baseline) analysis, blue points the results after exact matching individuals on previous turnout, age group, and gender. 95% confidence interval extending outward. Examining Figure E.1 first, we see a substantial difference between the Baseline and Matched results. While in the unmatched analysis White turnout is far higher than non-white turnout in districts with White incumbents, candidates, or a majority, after exact matching White and non-white registrants on previous turnout and demographics, the results reverse. To some degree, at least, the exact matching of White and non-white voters may create an unrealistic comparison set. Ignoring this issue, however, these results may not be surprising when considering the broader context of the 2012 election. 24

26 According to media reports, Black turnout exceeded White turnout for the first time on record, reversing a longstanding gap in participation (Wheaton 2013). If African American turnout was higher than expected based on past trends, it should not be surprising that it may have been higher than expected even in majority-white districts. Furthermore, given that these places had a non-white majority, incumbent, and/or candidate for at least three elections prior to 2012, these may be areas where minority voters are most likely to be targeted for mobilization (Fraga 2015). Figure E.2: Difference in Black vs. Non-Black Turnout in Treated Districts, 2012 H1: Co-Ethnic Incumbent Matched Baseline H2: Co-Ethnic Candidate H3: Majority-Black District Co-Ethnic Cand + Majority-Black Black Turnout - Non-Black Turnout, percentage points Note: Points indicate inverse-variance weighted mean difference between Black and non-black turnout in treated districts, when using co-ethnic incumbency, candidacy, or a majority-black district to define treatment condition. Gray points reflect the unmatched (baseline) analysis, blue points the results after exact matching individuals on previous turnout, age group, and gender. 95% confidence interval extending outward. African American relative turnout, as featured in Figure E.2, bears more of a resemblance to the results in the main text. Relative to non-black registrants, Black registrants turned out at substantially higher rates in majority-black districts, or those with a Black incumbent or candidate. Relative turnout is 4-5 points higher in districts with a Black 25

27 candidate, and 5-6 points higher in Black-majority or Black represented districts when using the matched results. Comparison with Figure 3 of the main text indicates a pattern that is unlikely to have appeared by chance: Black turnout is robustly higher in treated versus control districts (main text), and in treated districts when compared to non-black turnout (present analysis). While the magnitude of the effect is likely influenced by the aforementioned increase in African American turnout nationwide in 2012, these results also demonstrate non-racial electoral factors are an unlikely explanation. Figure E.3: Difference in Latino vs. Non-Latino Turnout in Treated Districts, 2012 H1: Co-Ethnic Incumbent Baseline Matched H2: Co-Ethnic Candidate H3: Majority-Latino District Co-Ethnic Cand + Majority-Latino Latino Turnout - Non-Latino Turnout, percentage points Note: Points indicate inverse-variance weighted mean difference between Latino and non-latino turnout in treated districts, when using co-ethnic incumbency, candidacy, or a majority-latino district to define treatment condition. Gray points reflect the unmatched (baseline) analysis, blue points the results after exact matching individuals on previous turnout, age group, and gender. 95% confidence interval extending outward. Latino (Figure E.3) and Asian American (Figure E.4) turnout in the Baseline analysis reflects the fact that turnout for these groups lagged both African Americans and non- Hispanic Whites substantially in 2012 (File 2013). The matched results, for Latinos at least, approximate what was found using the main text s methodology, as turnout does not 26

28 increase, and often decreases, in the presence of Latino candidates, incumbents, or when assigned to a Latino-majority district as compared to non-latinos. For Asian Americans, we now see evidence that points to a pattern more similar to Latinos, as turnout is lower when compared to non-asians in treated districts. Figure E.4: Difference in Asian vs. Non-Asian Turnout in Treated Districts, 2012 H1: Co-Ethnic Incumbent Baseline Matched H2: Co-Ethnic Candidate Asian Turnout - Non-Asian Turnout, percentage points Note: Points indicate inverse-variance weighted mean difference between Asian and non-asian turnout in treated districts, when using co-ethnic incumbency or candidacy to define treatment conditions. Gray points reflect the unmatched (baseline) analysis, blue points the results after exact matching individuals on previous turnout, age group, and gender. 95% confidence interval extending outward. What is the main takeaway from this racial placebo test? First, it appears unlikely that results for African American and Latino registrants are contingent upon alternative electoral factors that are associated with, but not directly attributable to, the ethnoracial contextual features examined here. However, evidence also suggests that, in line with theoretical and methodological understandings, a comparison of group to non-group turnout may not be as useful of a methodology for studying the impact of redistricting on voter turnout. Simply put, the reasons for cross-group differences in participation in 2012 (or any other election) are likely not captured by the study in a manner sufficient for isolating ethnoracial context. 27

29 Appendix F Matching on State Lower House District As a final test, we may also further match registrants within treatment districts to ensure that comparison is made only between group and non-group voters who were placed into the same State Legislative district. The methodology used in the main text cannot effectively account for lower level geographic variation, as it leverages the placement of individuals with the same pre-redistricting district into different districts for 2012 and in almost all instances this also induces a shift in state legislative districts. However, using the cross-group methodology noted above, we can check to see if the results featured in Figures E.1-E.4 shift when matching voters on lower level geography in treated districts. The blue points in Figures F.1 to F.4 require that comparison is made only between voters who are assigned to the same state lower house district, even after exact matching as in the Matched condition. Compared to the matched results in Figures E.1-E.4, we see no substantive or significant difference attributable to the lower level electoral context, across groups and treatment conditions. While not necessarily precluding some influence of alternative electoral contexts on the results featured in the main text, such similarity in results indicates no evidence of systematic bias that would shift our interpretation of the study s core findings. 28

30 Figure F.1: White vs. Non-White Turnout in Treated Districts, Same SL District H1: Co-Ethnic Incumbent Matched Only Same SL Dist H2: Co-Ethnic Candidate H3: Majority-White District White Turnout - Non-White Turnout, percentage points Note: Points indicate inverse-variance weighted mean difference between White and non-white turnout in treated districts, when using co-ethnic incumbency, candidacy, or a majority-white district to define treatment condition. Gray points reflect results after exact matching individuals on previous turnout, age group, and gender. Blue points the results after matching on state lower house district as well. 95% confidence interval extending outward. Figure F.2: Black vs. Non-Black Turnout in Treated Districts, Same SL District H1: Co-Ethnic Incumbent Matched Only Same SL Dist H2: Co-Ethnic Candidate H3: Majority-Black District Co-Ethnic Cand + Majority-Black Black Turnout - Non-Black Turnout, percentage points Note: Points indicate inverse-variance weighted mean difference between Black and non-black turnout in treated districts, when using co-ethnic incumbency, candidacy, or a majority-black district to define treatment condition. Gray points reflect results after exact matching individuals on previous turnout, age group, and gender. Blue points the results after matching on state lower house district as well. 95% confidence interval extending outward. 29