RACE AND TURNOUT IN U.S. ELECTIONS EXPOSING HIDDEN EFFECTS

Transcription

1 Public Opinion Quarterly, Vol. 74, No. 2, Summer 2010, pp RACE AND TURNOUT IN U.S. ELECTIONS EXPOSING HIDDEN EFFECTS BENJAMIN J. DEUFEL ORIT KEDAR* Abstract We demonstrate that the use of self-reported data often results in misleading inferences about racial differences in. We theorize about the mechanism driving report of and, utilizing ANES data in presidential elections from 1976 to 1988 (all years for which comparable validated data are available), we empirically model report of as well as the relationship between reported and actual. We apply the model to the two subsequent presidential elections in which validated data are not available, 1992 and Our findings suggest that African Americans turned out almost 20 percentage points less than did Whites in the 1992 and 1996 U.S. presidential elections almost double the gap that the self-reported data indicates. In contrast with previous research, we show that racial differences in factors predicting make African Americans less likely to vote compared to Whites and thus increase their probability of overreporting. At the same time, when controlling for this effect, other things equal, African Americans overreport electoral participation more than Whites. BENJAMIN J. DEUFEL directs quantitative analysis for the Financial Services Practice at the Corporate Executive Board, Arlington, VA, USA. ORIT KEDAR is an Associate Professor in the Department of Political Science at the Massachusetts Institute of Technology, Cambridge, MA, USA, and the Hebrew University of Jerusalem, Jerusalem, Israel. Benjamin Deufel benefited from financial support by the Jacob K. Javits Fellowship Program of the U.S. Department of Education and the Multidisciplinary Program in Inequality and Social Policy at Harvard University, sponsored by the National Science Foundation. Orit Kedar benefited from the V.O.K. Fellowship and Dellon Fellowship, Harvard University. The authors would like to thank the Center for American Political Studies at Harvard University for a seed grant. For helpful comments and suggestions, they thank Chris Achen, Barry Burden, Don Green, Jonathan Katz, Gary King, Matthew Lebo, Skip Lupia, Jonathan Nagler, Ken Scheve, Nick Valentino, Lynn Vavreck, and Jonathan Wand. They also thank Greg Distelhorst and Mike Sances for superb research assistance. Accompanying materials can be found on the authors Web site at okedar/www/. *Address correspondence to Orit Kedar, Massachusetts Institute of Technology, Department of Political Science, 77 Massachusetts Ave., E53-429, Cambridge, MA 02139, USA; okedar@mit.edu. doi: /poq/nfq017 Advance Access publication April 22, 2010 The Author Published by Oxford University Press on behalf of the American Association for Public Opinion Research. All rights reserved. For permissions, please journals.permissions@oxfordjournals.org

2 Race and Turnout in U.S. Elections 287 Introduction The question Who votes? has been the focus of numerous studies. Out of both positive and normative motivations, political scientists have examined voter over time, across electoral institutions, and across segments of the population. For the most part, however, the secret ballot prevents political scientists from observing what we seek to explain; we know who reports voting in surveys, but we do not know who actually votes. The vast majority of studies simply assume that the missing piece individual is identical to the observed piece self-reported. In the absence of any further information, this is, of course, a reasonable assumption. However, auxiliary information reveals not only that a substantial proportion of American survey respondents report turning out when they do not, but also that their propensity to misreport is related to their propensity to vote, which may lead to mistaken inferences. Two steps are thus required in order to explain who votes. First, we need to comprehend the mechanism that drives the observed piece reported. And second, the relationship between the observed and unobserved, reported and actual, should be modeled. Although much energy has been focused on the former, the latter has been largely ignored. In this study, we take up this challenge, focusing on racial differences in. Numerous studies provide evidence that African Americans overreport at higher rates than Whites. Building on these studies, we develop a theoretical account that explicitly models both the reporting process and its relationship to actual. We employ this theory to model the relationship between and report of in those years in which the two are available at the individual level. We contend that African Americans overreport their more than Whites for two reasons. First, African Americans overreport more because they simply have more of an opportunity to do so. Group differences in other predictors of, such as socioeconomic status, cause African Americans to be less likely to turn out compared to Whites, and a lower propensity to vote actually makes African Americans more likely to overreport. Furthermore, holding constant other predictors of, African Americans still overreport more than Whites. We argue that, because of the importance of race in American politics and elections in particular, the social desirability of voting is higher for African Americans. After establishing our theory empirically, we employ it to deflate selfreported figures in the 1990s where validated data are not available. Our findings suggest that throughout the 1980s and 1990s, the overreporting bias in self-reports masks a large gap between Whites and African Americans. On the other hand, this gap narrows considerably after accounting for other predictors of.

3 288 Deufel and Kedar Finally, a side benefit of our venture to expose hidden effects is methodological. Modeling the relationship between validated and self-reported in the 1970s and 1980s, we produce a function that probabilistically deflates reported. We test the performance of our deflating function and show that our algorithm predicts more accurately than self-reports. WHAT WE KNOW (AND DON T KNOW) ABOUT OVERREPORTING Studies of voter are in agreement that misreporting of exists and is almost entirely in one direction. The fraction of respondents voting but reporting they did not ( underreporters ) is negligible and, importantly, these discrepancies are usually random (Silver, Anderson, and Abramson 1986; Presser and Traugott 1992). Overreporting of is different: it is of substantial magnitude and, most students of voting behavior agree, it is systematically related to voters characteristics. However, several issues make it difficult to develop theories about the relationship between self-reports (R) and verified (V). The appropriate quantities of interest, the mechanism that generates overreporting, and the substantive effects of overreporting are all disputed in the literature. While these issues are mostly empirical, they muddle the theoretical waters. Before we outline our theory, we need to first wrestle with these issues. The first hurdle is determining the population of interest, as choices on this front may change inferences about the nature of overreporting. Focusing on overreporting as their ultimate variable of interest, some (e.g., Silver et al., 1986) argue that overreporting should be calculated among nonvoters only, the actual group at risk of overreporting. Another advantage of this procedure is that it controls for rate. Given our motivation, however, a different strategy is in order. Because our goal is to explain voter rather than overreporting, we estimate the hypothetical probability of all respondents to overreport. In line with standard treatment of binary variables (Greene 1993, pp ), we acknowledge that every observed binary variable (here, both validated and reported ) is a realization of an unobserved continuous proclivity (a probability of actually turning out, and a probability of reporting turning out). Therefore, every individual has both an underlying unobserved probability, and a realization the observed binary outcome. Whether they turned out or not, it is possible for an individual to have a probability of turning out of, say, 0.65, and a probability of reporting of, say, Thus, the relevant group by which we calculate overreporting of is the general voting-eligible population, and in the sample, the entire group of respondents eligible to vote. The second hurdle is understanding the sources of systematic components of overreporting. The standard argument, perhaps most clearly represented in

4 Race and Turnout in U.S. Elections 289 Silver et al. (1986), employs the concept of social desirability. The basic idea is that respondents report their behavior untruthfully because they wish to portray themselves as engaged in a socially desirable activity. This wish is unevenly felt across respondents; the very factors that make respondents likely to vote also reinforce their desire to portray themselves as voters, regardless of their actual behavior. 1 Thus, those who are more likely to vote are more likely to misreport when they did not actually participate. 2 This argument implies that the use of self-reported (R) data will lead to overestimation of partial correlations with regard to (Cassel 2003). For example, if education makes people both more likely to vote and more likely to exaggerate the extent of their participation, use of R will result in overestimation of the effect of education on the propensity to turn out. Indeed, Presser and Traugott (1992) show that, using R, political scientists overestimate partial correlations with regard to. Nonetheless, Sigelman (1982) argues that substantive conclusions about the predictors of voting, despite biased coefficients, are mostly unchanged by the use of validated as opposed to reported voting data. Racial effects are a seeming exception to this general pattern. Repeated studies have shown that African Americans are more likely to overreport than Whites, despite possibly being less likely to turn out (Sigelman 1982; Hill and Hurley 1984; Bernstein, Chadha, and Montjoy 2001). In a series of articles, Abramson and Claggett (1984, 1986, 1989, 1991) find that although selfreported data indicate no racial difference in after accounting for education and region, use of validated data reveals otherwise. In other words, African Americans overreport at higher rates, yet are less likely to turn out compared to Whites. These two gaps in opposite directions mask each other, leading researchers using R to underestimate the effect of race on and often conclude that there is no relationship or even that African Americans turn out at higher rates than Whites do. 3 While much attention has been dedicated to empirical descriptions of this pattern, to our knowledge there has been no attempt to model how the relationship between and reported varies by race. Doing so allows 1. In the only comparative study of overreporting we are aware of, Karp and Brockington (2005) make a distinction between social desirability and opportunity of overreporting. Examining overreporting in Britain, New Zealand, Norway, Sweden, and the United States, the authors show that where is high, social desirability is higher as well, yet high also leaves fewer nonvoters with the opportunity to overreport their participation. 2. Bernstein, Chadha, and Montjoy (2001) propose an alternate possibility. They argue that respondents misreport out of guilt from failure to fulfill a social obligation. 3. A review of the APSR, AJPS, JOP, and Political Behavior between 1993 and 2008 for studies estimating in U.S. presidential elections, employing individual-level data, and having race on the right-hand side yielded 13 studies; among them, five found no effect of race on, two found mixed effect, and among the six which found an effect, five found that African Americans were more likely to participate than Whites.

5 290 Deufel and Kedar us to understand how differential overreporting affects our inference of racial differences in. It is to this task that we now turn. Explaining the Reporting Gap: Two Mechanisms We expect the impact of social desirability to be nonlinear, where overreporting first increases and then decreases with propensity to vote. Those with the highest likelihood of voting have low levels of overreporting because they often actually do turn out. Those respondents who are moderately likely to turn out are those who overreport at the highest rates. They turn out at the polls less often than do those most likely to vote, which gives them more of an opportunity to overreport (for similar intuition, see also McDonald 2003, p. 185). These mid-range potential voters feel a greater need to report socially desirable behavior than those with a low likelihood of voting, and thus their level of overreporting is also higher than that of those who vote at low rates. In sum, opportunity to overreport, along with social desirability, produces a nonlinear relationship between propensity to vote and overreporting. Figure 1 graphically illustrates this relationship. Let us begin by examining curve I only. The top panel (panel A) presents the probability of turning out on the horizontal axis against the probability of overreporting on the vertical axis. This curve graphically presents the social desirability argument we discussed above. It asserts that as the probability of voting increases, the tendency to overreport, measured vertically, first increases and then decreases. (If one voted for sure, she has no chance of overreporting, and if we assume that people do not underreport, someone with zero probability of reporting having voted has an identical probability of actually voting.) If curve I holds for everyone in the population, the effect of race on reporting should diminish as more factors that account for the tendency to turn out are included in the analysis. In other words, any potential racial difference in overreporting is a product of opportunity and social desirability (on-the-curve effect). Panel B (still curve I) presents the latent propensity of turning out on the horizontal axis and the respondent s latent propensity to report having voted on the vertical axis. The diagonal represents the relationship between the two had there been no overreporting. The vertical difference between the curve and the 45-degree line is the overreporting gap presented in the first panel on the vertical axis. Suppose that on average Whites score higher on predictors of (e.g., homeownership) such that they are located around point A and that African Americans are located on average at a point like C or E. While an E-type voter is both less likely to vote and less likely to overreport than an A-type, C is less likely to vote yet more likely to overreport than A. This latter possibility is consistent with the empirical findings that African Americans may be more likely to overreport but less likely to vote. In sum, the account in curve I alone suggests that African Americans may overreport more than Whites because they are less likely to vote, not because of any

6 Race and Turnout in U.S. Elections 291 Figure 1. (a) Possible Relationships between Voting and Overreporting. (b) Possible Relationships between Voting and Report of Voting

7 292 Deufel and Kedar special propensity to overreport relative to Whites they are on a different point on the same overreporting function (curve I). However, previous studies also note that overreporting by African Americans may have an additional source (Bernstein et al., 2001). Because most African Americans effectively gained the right to vote in the 1960s after a hard-fought struggle that drew heavily upon group resources, other things equal, voting may be more of a socially desirable act for African Americans than for Whites. A high percentage of African American disenfranchisement compared to Whites (Uggen and Manza 2002) potentially serves as an additional source of social desirability, reducing the likelihood that those who did not turn out will report so to the pollster. More generally, though, American electoral politics is often about race. Electoral districts are drawn explicitly with race in mind, and race is important for electoral mobilization and demobilization (see, for example, Rosenstone and Hansen 1993; Dawson 1994; Tate 1994; and Kinder and Sanders 1996). According to this argument, African Americans have a different tendency to overreport, controlling for predictors of. Therefore, unlike the previous on-the-curve explanation, curve I represents overreporting for Whites and curve II represents overreporting for African Americans. For example, take two voters of different races but identical in their likelihood of voting E is White and D is African American. Although they are equally likely to vote, D is more likely to overreport than E. Technically, African Americans are located on a different reporting curve. We allow for both accounts and, therefore, for both on-the-curve and offthe-curve effects to affect racial differences in reporting. For example, perhaps the average White is at point A and the average African American is at point B. In this case, African Americans would be more likely to overreport because of the relationship between race and overreporting and because of differences in the values of predictors of between Whites and African Americans. A side issue we need to address is the consistency of the relationship over time. The relationship may change systematically as we move away from the height of civil rights movement activity, 4 or idiosyncratically, with events that alter the social desirability of voting by race. 5 This highlights the need to establish whether any of our expectations are met in the data before we can make inferences about race and. Analysis of survey and validation data will allow us to determine the extent of racial differences in reporting and voting, and the degree to which the two mechanisms account for gaps in reporting of. 4. For discussion of a related issue, the relationship between group consciousness and participation, see Verba, Schlozman, and Brady (1995, pp ), and their discussion of the departure of their findings from those of Verba and Nie (1972). 5. See Dawson (1994, pp ) for discussion of the effect of Jackson s candidacy and his treatment by the party. See also Tate (1994) and Kinder, Mendelberg, Dawson, et al. (1989).

8 Race and Turnout in U.S. Elections 293 REPORTED AND OFFICIAL TURNOUT: HOW BIG IS THE PROBLEM? The American National Election Studies (ANES) conducted vote validation studies in the 1964, , and election studies. In this article, we utilize validated data from the four most recent presidential elections where these data are available: 1976, 1980, 1984, and In appendix A, we justify the quality of the validation procedure and offer evidence that it provides an accurate means to address our research questions, and in appendices B and C, we report the question wording and sampling procedures along with response rates, respectively. Table 1 shows the official rate, the proportion of respondents reporting having voted (R), and the proportion validated as voting (V), with the latter two quantities broken down by race. 7 Each row presents these quantities for one of the four presidential elections: The first obvious point is that in the full sample, V is closer to figures of official than R is in all years. 9 Although at first glance there is still roughly a 10-percentage-point difference between validated in the full sample and official figures, this is not surprising, both because the latter includes in its denominator many who are ineligible to vote (McDonald and Popkin 2001) 10 and because of potential systematic nonresponse to the ANES. Examination of the differences between validated and reported over time in the full sample (as well as the gap between the two measures and official ) suggests no apparent secular trend across the four elections. The difference between R and V is around 10 percentage points in each elec- 6. We do not use the 1964 validation study since the validation procedure in that year was changed in the subsequent studies. 7. The respondent was included in our validation sample if her validation record indicated that she voted (coded as 1), did not vote, or no record of voting or registering was found, or if the respondent reported that she had not registered or SDR (coded as 0), but not if one of the latter four was found and the status of the office voting records was such that some or none of the records were inaccessible. The respondent was included in our reported sample if she reported that she had voted or that she did not vote. 8. In 1976 and 1980, the ANES attempted to validate each self-report, but in 1984 and 1988, selfreports were validated only if the respondent indicated that she was registered or had voted in localities without registration requirements. In (and for some respondents in 1976), the ANES also validated those who completed the pre-election interview but not the post-election one (leaving such respondents without R data), leading to the possibility of a V sample size greater than that of R (as is indeed the case in 1980, 1984, and 1988). 9. On this point, see also Clausen (1968). 10. In most official measures, the denominator is the Voting Age Population (VAP) as reported by the Bureau of the Census in their Current Population Reports, Series P-25. VAP includes all persons over the age of 18, including those ineligible to vote in federal elections, such as legal and illegal aliens, convicted felons, and individuals legally declared non compos mentis. The VAP is therefore considerably larger than the pool of potential voters (McDonald and Popkin 2001, although see Burden 2000). For related articles, see Burden (2003), Martinez (2003), and McDonald (2003).

9 294 Deufel and Kedar Table 1. Self-Reported Turnout, Validated Turnout, and Official Turnout by Year (95-percent confidence intervals in parentheses) Year Official Turnout* (R) Full Sample** Whites African Americans Validated (V) (R) Validated (V) (R) Validated (V) (71.3, 75.3) n =1, (69.4, 74.1) n = 1, (72.1, 76.0) n = 1, (68.2, 72.6) n = 1, (62.5, 66.9) n = 1, (56.4, 61.4) n = 1, (61.3, 65.5) n = 2, (60.9, 65.4) n = 1, (72.8, 76.0) n = 1, (69.8, 74.9) n = 1, (73.1, 77.2) n = 1, (69.7, 74.2) n = 1, (63.8, 68.4) n = 1, (57.3, 62.7) n = 1, (63.4, 67.7) n = 1, (63.3, 68.1) n = 1, (58.9, 73.2) n = (59.4, 73.9) n = (59.2, 72.0) n = (53.1, 66.3) n = (44.5, 59.7) n = (41.6, 57.2) n = (41.0, 53.6) n = (39.2, 52.3) n = 225 NOTE. Cell entries include rate, 95-percent confidence interval, and number of respondents, respectively. The R sample includes respondents who have reported data, while the V sample includes all those with validated data. This table does not use the post-stratification weights provided by the ANES. *Official figures are from the Federal Election Commission, **The full sample includes respondents who indicated they were either African American or White.

10 Race and Turnout in U.S. Elections 295 tion. Among African Americans, however, the gap is considerably greater than among Whites, falling between roughly 14 and 18 percentage points across the four elections. 11 Finally, note that at first glance there seems to be no trend in overreporting of African Americans over time. 12 While these figures expose a potential reporting gap, they do not provide a theoretical framework for understanding the sources of racial differences in reported or validated. In particular, the differences do not tell us whether the gap is simply a reflection of African Americans lower propensity to vote given other predictors of (an on-the-curve effect) or whether African Americans are more likely to overreport, even accounting for predictors of (an off-the-curve effect related to differing social desirability), or both. To get at this issue, we must model the relationship between reported and actual. UNMASKING RACIAL EFFECTS: REVEALING THE REPORTING GAP We now turn to examining whether our theory holds empirically. What is the underlying relationship between reported and actual? To capture this relationship, in each of the four years we first estimate a logistic model of and a model of reporting using validated (V) and self-reported (R), respectively, as dependent variables. We rely on an established empirical and theoretical literature in choosing our explanatory variables for these models (Rosenstone and Hansen 1993; Verba et al., 1995). These variables capture resources, in addition to social and political experiences and attachments that raise the benefits and lower the costs of voting, as well as standard demographic controls. In particular, the model includes party contact, church attendance, party attachment, age, education, income, homeownership, race, and gender. The estimated coefficients of the eight regressions are too much to be discussed in detail here and can be found in table D2 (appendix D). Nonetheless, some effects hold throughout the eight models, reflecting the systemic effects discussed in the literature. Resources such as education and income make voting more likely, as does community embeddedness measured as homeownership. By the same token, young adults (usually more mobile and less immersed in a stable community) are less likely to vote. Attachment to a party, voter mobilization, and church attendance all have a positive effect on the likelihood of turning out. Finally, once controlling for these effects, living in the South has a partial negative effect on one s likelihood of turning out. 11. In a thorough analysis combining data from both presidential and congressional elections, Belli, Traugott, and Beckmann (2001) find that non-whites overreport at higher rates than Whites do. 12. The inferences we make here are identical if one looks at only those respondents who have both reported and validated data.

11 296 Deufel and Kedar Figure 2. Discounting Functions: Next, we map the relationship between voting and reported voting. We pool the resulting predicted probabilities over the four years and model the relationship between voting and reporting as a quadratic function, allowing it to vary by race and year (including all relevant interaction effects for maximum flexibility). 13 The quadratic specification and the interactions allow us to examine if the relationship expected between overreporting and (as specified in figure 1) is found in the data and whether it varies by race and over time. Figure 2 presents this relationship for all four years by race. On the horizontal axis are the probabilities of voting using validated data, and on the vertical axis are predicted probabilities of reporting having voted. As in figure 1b, the 45-degree line in figure 2 represents a hypothetical relationship with no reporting gap. The four dashed lines present the relationship for Whites, while the four solid lines present the relationship for African Americans in the four years. The vertical gaps between the diagonal line and each of the eight lines are the respective overreporting gaps. The figure illuminates several aspects of the relationship between reported and actual. Examine the relationship for Whites first. The pattern is consistent with the theory 13. The full specification and coefficients are presented in table E1 of appendix E.

12 Race and Turnout in U.S. Elections 297 specified above: the line is, in general, above the diagonal, and the relationship is nonlinear; as the probability of voting increases, the probability of overreporting one s likelihood of voting first increases and then declines. Individuals in the middle range have a higher likelihood of overreporting than either those who are unlikely to vote or those who almost surely vote. Consistent with our expectation, the relationship between and report of for Whites is constant over time. The functions for 1976, 1980, and 1984 are almost identical, and the data expose no trend in the relationship. However, the overreporting function for 1988 is a curious exception to this stable pattern. The relationship for African Americans tells an even clearer story. Here, too, overreporting is in quadratic relation to voting, but the magnitude of overreporting is greater; the vertical gaps between the diagonal and each of the functions reaches almost 20 percentage points. Overreporting is not orthogonal to race. Although the coefficients bear large standard errors (partly because of the many interaction terms included), the point estimates (presented in figure 2) consistently suggest that African Americans reporting function is different than Whites (off-the-curve effect). Furthermore, the nature of overreporting by African Americans appears roughly similar across all four elections. Based on this consistency, in the next stage we eliminate the year variables, resulting in reduced estimation uncertainty and similar results (column 2 in table E1). In summary, we have presented evidence for two mechanisms at play. First is a quadratic relationship between voting and report of voting, supporting the importance of opportunity to overreport and social desirability. Second is a racial difference, which may be attributed to an additional social desirability variable related to racial history. Both effects are constant over time. Implications of the Reporting Gap So far we have established that there is a nonlinear tendency to overreport, and that this tendency differs for African Americans and for Whites. Our next step is to analyze the consequences of these patterns for inference about. To accomplish this task, we rely on three models of voter. The first two models come from Abramson and Claggett s studies of racial differences in overreporting and (1984, 1986, 1989, 1991). 14 Their first ( thin ) model has race only on the right-hand side. Their second ( thick ) model controls for education and region (South). Finally, based on recent advances in the study of (Rosenstone and Hansen 1993; Verba et al., 1995), we extend our analysis to a third ( full ) model that is identical to 14. Abramson and Claggett (1984, 1986, 1989, 1991) code the race variable as a dichotomous 1, 1 variable, while we employ the more common dummy approach (0, 1). Despite this difference, our results are very similar.

13 298 Deufel and Kedar the model of voting we used to construct figure 2 (for estimates, see tables D1 and D2 in appendix D). To reiterate, in addition to region and education, this model also includes variables that capture resources, social and political experience, and attachment that raise the benefits and lower the costs of voting, as well as standard demographic controls. 15 While the inclusion of these particular variables is not novel, in the context of our unpacking of overreporting, a comparison of the three models sheds light on our theoretical argument. Our theory implies that effects relating to opportunity and social desirability account for part of the racial reporting gap. According to this argument, as we move from the thin to the thick to the full model and control for more of the determinants of, and hence opportunity to overreport, using R, the reporting gap between the two racial groups should decline. In other words, if as we account for more factors that disproportionately reduce African Americans likelihood of voting, the gap in overreporting diminishes, then we may infer that African Americans overreport more because they vote less (on-the-curve effect). However, if the gap between reported and actual data holds even as we control for such factors, then it is an indication that African Americans indeed have a different reporting function, likely because of additional social desirability, as we discuss above. We focus below on 1984 and 1988, the two most recent presidential elections in which validated data are available. 16 Table 2 presents the results for The first and second rows in each section present the mean predicted probabilities for African Americans and Whites, respectively, with the values of other explanatory variables held at their mean. The third entry is the mean difference in between the two racial groups. A positive number indicates that Whites are estimated to turn out at higher rates than African Americans. As the table shows, in 1984, R and V (in the first and second columns, respectively) lead to different inferences about racial gaps in. In model 1, both R and V suggest that African Americans are less likely to turn out, yet using V, the racial difference is substantially greater (10 percentage points using R as opposed to 19 using V). In other words, validated data reveal a large effect of race on, an effect that is masked by selfreported data. The results of model 2 make an even stronger case: using R, there is no statistically significant racial gap in, and the predicted probabilities for both races are inflated (73 percentage points for African Americans, and 76 for Whites). V, however, exposes a different picture. First note that the predicted probability of African Americans turning out is substantially lower (57 percentage points) and significantly different from R. The figure for Whites is lower as well (69 percentage points). Most importantly, while 15. Likelihood Ratio Tests comparing the full model to the thick and the thin models are statistically significant in all years. 16. Results for 1976 and 1980 are similar to those reported below.

14 Race and Turnout in U.S. Elections 299 Table 2. Predicted Probabilities of Turning Out by Race: 1984 Presidential Elections (95-percent confidence intervals in parentheses) (R) Validated (V) Discounted self-reported ( ) Deflated self-reported ( , out of sample) Model 1 ( thin ) African Americans (0.595, 0.730) (0.429, 0.573) (0.338, 0.578) (0.354, 0.622) Whites (0.735, 0.777) (0.662, 0.709) (0.622, 0.713) (0.619, 0.708) Difference b/w African Americans and Whites (0.019, 0.166) (0.110, 0.260) (0.081, 0.331) (0.040, 0.323) Model 2 ( thick ) African Americans (0.665, 0.792) (0.484, 0.634) (0.414, 0.656) (0.431, 0.688) Whites (0.740, 0.786) (0.661, 0.710) (0.633, 0.717) (0.631, 0.713) Difference b/w African Americans and Whites (-0.035, 0.102) (0.046, 0.203) (0.012, 0.272) (-0.016, 0.243) Model 3 ( full ) African Americans (0.760, 0.872) (0.564, 0.727) (0.533, 0.764) (0.551, 0.775) Whites (0.781, 0.828) (0.682, 0.737) (0.673, 0.762) (0.676, 0.758) Difference b/w African Americans and White (-0.072, 0.044) (-0.022, 0.148) (-0.051, 0.190) (-0.069, 0.168) NOTE. Entries in the table are predicted probabilities of turning out. All other variables in the model are held at their respective means. Model 1: Race. Model 2: Race, education, and region (South vs. other). Model 3: Full model; see specification in table D2. For all models, see N and coefficients in tables D1 and D2.

15 300 Deufel and Kedar Table 3. Predicted Probabilities of Turning Out by Race: 1988 Presidential Elections (95-percent confidence intervals in parentheses) (R) Validated (V) Deflated self-reported ( ) Deflated self-reported ( , out of sample) Model 1 ( thin ) African Americans (0.528, 0.664) (0.386, 0.541) (0.283, 0.523) (0.304, 0.562) Whites (0.690, 0.739) (0.645, 0.697) (0.610, 0.697) (0.573, 0.666) Difference b/w African Americans and Whites (0.046, 0.193) (0.125, 0.287) (0.112, 0.387) (0.048, 0.331) Model 2 ( thick ) African Americans (0.587, 0.727) (0.389, 0.560) (0.339, 0.587) (0.363, 0.637) Whites (0.703, 0.753) (0.650, 0.706) (0.622, 0.709) (0.584, 0.680) Difference b/w African Americans and Whites (-0.010, 0.143) (0.114, 0.293) (0.072, 0.340) (-0.008, 0.273) Model 3 ( full ) African Americans (0.670, 0.839) (0.437, 0.614) (0.422, 0.690) (0.454, 0.733) Whites (0.746, 0.803) (0.674, 0.733) (0.663, 0.747) (0.638, 0.732) Difference b/w African Americans and White (-0.070, 0.105) (0.082, 0.275) (0.006, 0.297) (-0.058, 0.237) NOTE. Entries in the table are predicted probabilities of turning out. All other variables in the model are held at their respective means. Model 1: Race. Model 2: Race, education, and region (South vs. other). Model 3: Full model, see specification in table D2. For all models, see N and coefficients in tables D1 and D2.

16 Race and Turnout in U.S. Elections 301 Table 4. The Challenge of Partial Observation of Turnout Data available/period t t Validated +? using R alone there is no statistically significant effect of race on, V reveals an effect of 12 percentage points reporting is correlated with race. Finally, the full model shows the same trend, although the results fall slightly short of standard levels of statistical significance. As in the previous two models, the point estimates indicate that the racial gap hidden using self-reported figures is greater when is measured with validated figures, and the racial gap (which is six percentage points) is exposed by the use of validated figures. Table 3 repeats this exercise in The results are consistent with those of 1984, and we describe them here only briefly. Within each model, the racial difference exposed by V is substantively greater than the difference suggested by R. Even in the full model, use of validated data suggests an 18-percent gap while self-reported data suggests no difference. The findings using validated data are consistent with the findings of Dawson (1994) and Kinder and Sanders (1996) previously noted. In sum, with regard to our substantive issue of interest racial differences in a strong case can be made that the use of self-reported data can lead to mistaken inferences. Both opportunity and social desirability (on-thecurve effects) and an additional desirability related to race (off-the-curve effect) lead to biased inferences. As we control for opportunity to overreport, the gap declines, yet because of differing social desirability, some racial differences remain. Having revealed these effects, in the next section we devise a remedy for the biases produced by conventional investigation. DEFLATING SELF-REPORTS Table 4 summarizes the challenge we face. In some periods (t) both selfreported and verified data are observed, while in others (t + 1) only self-reported data are available. While the literature on overreporting bias is extensive, almost no attention has been given to potential solutions. Suggestions of measurement improvements ex ante (Belli et al. 1999; Duff, Hammer, Park, et al. 2007; Holbrook and Krosnick forthcoming), discussing issues such as poor memory and face-saving response options, produce more accurate reports, but the problem of bias with already collected data still holds. Our proposed algorithm is simple. Based on our theory and empirical evidence for the joint roles of opportunity and desirability, we model the relationship between voting and reporting of voting using all years in which reported and validated data from presidential elections are available (1976,

17 302 Deufel and Kedar 1980, 1984, and 1988). We then use the estimated relationship to deflate selfreported data at time t + 1 (1992 and 1996), where validated data are not available. We now turn to presenting our algorithm in greater detail. The Deflating Algorithm STEP 1: MODEL THE RELATIONSHIP BETWEEN VOTING AND REPORTING OF VOTE AT TIME t 1.1. We estimate a model of reported at time t: R t = f X1 t ; βt 1 ; ð1þ where X t 1 is a vector of voter characteristics, β t 1 is a vector of coefficients, and f ðþis a logistic function. 17 We then calculate the predicted probability of reported voting for each individual, P^rðR t =1Þ 1.2. Similarly, we estimate a model of validated at time t: V t = f X2 t ; βt 2 ; ð2þ and calculate the predicted probability of turning out for each individual P^rðV t =1Þ The deflating function: We model the relationship between voting (V) and reporting of vote (R) where the dependent variable is the estimated probability of actually voting calculated from equation (2). Given the racial differences in voting and report of voting established above, we let the voting be a quadratic function of selfreported voting and vary interactively by race. The right-hand side, then, is a vector of covariates such that P^rðV t =1Þ= δ t 0 + δt 1 racet + δ t 2 P^r ðr t =1Þ+ δ t 3 P^r 2 ðr t =1Þ h i h i + δ t 4 racet P^rðR t =1Þ + δ t 5 racet P^r 2 ðr t =1Þ ð3þ Equation (3) reflects how social desirability and opportunity affect racial differences in overreporting. The coefficients δ 0, δ 2,andδ 3 represent the quadratic relationship between voting and report of voting among Whites. 17. In our case, based on the observed consistent relationships observed over time, we pool data from 1976, 1980, 1984, and In our case, we use the same functional form and vector of voter characteristics as in equation 1, reported in table D2.

18 Race and Turnout in U.S. Elections 303 The coefficients δ 1, δ 4, and δ 5 represent the difference between the curve for Whites and the curve for African Americans. The additional effect of social desirability (off-the-curve) is carried out by the latter set of coefficients. The estimated coefficients are reported in the second column of table E1. We will next use these coefficients to deflate reported. STEP 2: DEFLATE REPORTED DATA AT t +1 In this stage, we first estimate the probability of turning out using reported data (the only data we have at t + 1). We then employ our deflator to deflate the estimated probabilities Similar to step 1.1, we estimate a model of reported at time t +1: R t +1 = f X3 t +1 ; β t 3 +1 ð4þ (in our case, 1992 or 1996). Here, too, we use a logistic function. We then compute predicted probabilities of reported for two hypothetical individuals: White ðp^rðr t +1 j W =1ÞÞ and African American ðp^rðr t +1 j Af :A =1ÞÞ, with all other variables held at their mean (six hypothetical individuals altogether). We repeat this step for three different model specifications corresponding with the models above ( thin, thick, and full ). The estimates are reported in tables D1 and D We apply the deflating function to the predicted probabilities generated in the previous step. For example, for a White individual: D t +1 = δ^t 0 + δ^t 1 ðrace = W Þ t +1 + δ^t 2 P^r R t +1 j W h + δ^t 4 ðrace = WÞ t +1 h P^r R t +1 j W Š + δ^t5 ðrace = W + δ^t3 P^r 2 R t +1 j W Þ t +1 P^r 2 R t +1 j W Šð5Þ The outcome D t+1 is the estimated individual s deflated probability of turning out. Multiple-Step Estimation The logic of our algorithm is straightforward. It is important to keep in mind, however, that each step produces a layer of uncertainty that should be taken into account. The first source is the uncertainty around the Maximum Likelihood estimates at time t (β^t andβ^t 1 2 ), which in turn produce the predicted probabilities for thetwo variables V and R (steps 1.1 and 1.2). We assume that β t 1 = f Multivar: Normal β^ t 1 ;, and drawing randomly from this distribution, β^t 1 we get a sample distribution of β^ t 1 (in this step, as in all other steps described below, we draw 1,000 times). We repeat the same procedure for β^ t 2, producing 1,000 predicted probabilities of turning out and 1,000 predicted

19 304 Deufel and Kedar probabilities of reporting to have turned out for each individual. Therefore, in step 1.3, we estimate 1,000 deflating functions. Similarly, we draw on the respective distribution of the coefficients on R at time t +1(β^t +1 3 ) and calculate predicted probabilities of two hypothetical respondents to be deflated. Finally, we employ the sets of coefficients of the deflating function δ^ to these 1,000 predicted probabilities and get deflated probabilities. The results we present are the mean of those deflated probabilities. 19 Evaluating Our Algorithm To evaluate our algorithm, we pose two questions. First, we examine whether the inferences we make about racial differences in using our method come closer to V than those we would make using R. Our measure of ought to produce quantities of interest that are closer to those produced by the use of V than those produced by the use of R, conditioning on the same model. Focusing on racial differences in, we turn back to tables 2 and 3. Recall that the use of R coefficients often led to underestimated effects of race on. We perform both in-sample and out-of-sample tests to examine the performance of our measure. For the in-sample tests, we deflate self-reports using the deflating function produced by validated data from For our out-of-sample tests, we estimate our deflating function in 1976 and use it to deflate self-reported data in These tests are particularly demanding for two reasons. First, we use auxiliary information from 1976 to correct bias in data produced eight and 12 years later. Second, we know from figure 2 that Whites overreported in a unique manner in 1988 compared to other years. Results of these estimations are presented in the third (in-sample) and fourth (out-of-sample) columns of table 2. We then repeat this exercise for 1988 (table 3). Tables 2 and 3 reveal that using information from 1976 to deflate self-reports in 1984 and 1988 produces substantially more accurate estimates of racial differences in than the use of R does. As expected, the results for 1984 are somewhat more accurate than those of 1988, but in all cases the point estimates using the deflated data (D) are considerably closer to V than those produced by R (the multiple stages of estimation acknowledge the uncertainty in these point estimates, leading to a few cases where the D confidence intervals overlap with zero). Notice in particular the figures for African American produced by our algorithm in the full model for While self-reports suggest no racial gap in, our algorithm exposes the particularly low of African Americans, consistent with previously cited accounts of alienation felt among the African American population in In sum, while keeping in mind the caveat that the same 19. We compute 95-percent confidence intervals by sorting the deflated probabilities and taking the 25th and 975th probabilities.

20 Race and Turnout in U.S. Elections 305 Figure 3. a and b. Model Fit Based on Self-Reported, Validated, and Deflated Data for 1984 (Panel a) and 1988 (Panel b)

21 306 Deufel and Kedar sampling frame was used both in 1976 and in 1984 and 1988, our method produces point estimates superior to those produced by R, although as expected, a fair amount of noise created in the process increases uncertainty. Second, we examine how well our model fits the data. In particular, we evaluate how predicted probabilities of turning out based on D produced by the out-of-sample procedure match observed data of based on validated figures. Figure 3 presents this evaluation for 1984 and 1988 in the top and bottom panels, respectively. To evaluate our model fit, for each of three measures, V, R, and D, we sort our observations by predicted probability of turning out produced by the respective measure (based on estimates in table D2), group them into 20 equal-length intervals, and plot on the horizontal axis the average predicted probability for that group, and on the vertical axis the actual observed fraction of votes in that group as indicated by validated data. A perfect fit (on average) will result in all points aligned right on the 45-degree line. As can be seen for 1984, results produced by the self-reported model do not fit the data well and overestimate the observed vote by up to 20 percentage points. Consistent with figure 2, the inaccuracy is largest in the middle range. It is reassuring that our model for validated data produces a good fit predicted probabilities are aligned close to the 45-degree line, and importantly, in cases where our predictions diverge from the line, they reveal no systematic bias but rather are scattered equally above and below the line. Finally, results produced by the deflated data are tightly clustered around the 45-degree line with no systematic deviation. Results for 1988 are similar. Recall that this is our hardest case: the out-ofsample test is based on data 12 years prior to the election, and the reporting pattern in 1988 is different than in other years. And although our prediction does involve more noise than in 1984, here too, while the prediction based on self-reports differs systematically from the observed vote, prediction based on our algorithm is in line with observed patterns. Exposing Hidden Effects in the 1990s Having established its validity, we reach the final stage of our analysis, applying our algorithm to deflate self-reports in the 1992 and 1996 presidential elections where validated data are unavailable. We do so exactly as we describe above: we estimate a model based on self-reports for 1992 (and 1996), calculate the predicted probability of turning out for each individual, and apply our deflator to those predicted probabilities. Table 5 compares the results based on self-reports to those based on the deflated self-reports produced by our algorithm for each of the three models, as above. The table presents two main findings. First, it shows that predicted probabilities produced by R are inflated compared to D across models in both elections. More importantly, our use of D exposes a larger racial gap in turn-