TURNOUT BY RACE IN VIRGINIA ELECTIONS

112 Jeffrey B. Lewis grows, although some advantage is found even ifXis fixed across elections. On the the other hand, I would have found smaller reductions in MSE from SUEI if the estimated precinct effects had been smaller relative to the election-specific effects.²²

Extending King’s Ecological Inference Model to Multiple Elections Using Markov Chain Monte Carlo 113

1976 1978 1980 1982 1984 1986 1988 1990

020406080100

Year

Turnout

Figure 4.8. Estimates of black and white voter turnout from Sabato (1991). The dotted line shows white turnout, and the dashed line shows black turnout, in each case as a fraction of voter registration.

The solid line shows total turnout as a fraction of the voting age population.

these precincts is taken as an estimate of black turnout statewide. Unfortunately, these esti- mates are for the percentage of registered voters that turn out to vote and not percentages of the total voting age populations. Because population data for the precincts are not available, the turnout rates as a fraction of voting age population cannot be estimated in a comparable way.²⁵Turnout rates for blacks reported by Sabato are shown in Figure 4.8.²⁶Interestingly, Sabato’s results suggest that black turnout was higher than white turnout in the 1985 and 1989 races, in which Wilder was a candidate for lieutenant governor and governor. Black turnout was estimated to be lower than white turnout in 1986, when the black Republican Dawkins was a candidate for U.S. Senate, and in all of the other years in the eighties except 1981. By these estimates black turnout never exceeds white turnout by more than about 7.5 percentage points, though in some elections white turnout exceeds black turnout by as much as 17 percentage points.

In order to analyze turnout rates among whites and nonwhites using the ecological infer- ence estimators developed above, I require election returns and racial composition data for a set of geographic units. Practically, this requires aggregating electoral returns to a level that corresponds to geographical units recognized by the Census Bureau. In the ROAD project, King et al. (1997) published electoral data for Virginia elections from 1984 to 1990 that are aggregated to the minor civil division (MCD) group level. In the main these are simply the Census Bureau’s MCDs (for example, Alexandria, Berryville, or Quantico) except in cases where one or more electoral precincts (the lowest level of electoral aggregation) were shared across two or more MCDs. In these cases, the MCDs sharing precincts are grouped so that no electoral precinct is split across groupings. In total there are 257 MCD groups in the Virginia data, ranging widely in size from 506 to 183,000 voting age residents. The median Virginia MCD group has 7,363 voting age residents. Nonwhites make up 22 percent of the voting age residents statewide. The distribution of the nonwhite population across the MCD groups is shown in Figure 4.9. While many of the MCD groups have very small nonwhite populations, a small number of them are majority-minority.

25Similarly, because registration-by-race data are not available, ecological analysis of the sort developed here cannot be undertaken on the precinct-level data.

26Sabato does not give turnout rates for whites. In the figure, the white turnout rate is imputed from the total turnout rate and Sabato’s black turnout rate under the assumption that 18 percent of the registered voters in Virginia were black during this period.

114 Jeffrey B. Lewis

Fraction nonwhite

Frequency

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020406080100

(a)

Year

Turnout

1984 1985 1986 1987 1988 1989 1990

(b)

0.00.40.60.81.00.2

Figure 4.9. Virginia Ecological Election Data, 1984–1990: (a) racial composition, (b) turnout rates.

Here (a) shows the distribution of nonwhite voters across Virginia minor civil division groups (MCD groups; see text for definition), and (b) shows boxplots for the turnout rates in each of the seven elections considered (as a percentage of voting age populations). Each gray line in (b) represents an MCD group.

The distribution of voter turnout across the elections is also shown in Figure 4.9.²⁷ The figure reveals cross-election and cross-precinct variation in overall voter turnout at the MCD-group level. As one would expect, voter turnout was highest in the presidential election years 1984 and 1988. Interestingly, the midterm elections of 1986 and 1990 had the lowest rate of turnout, even lower than the 1987 election in which no federal or statewide offices were contested. Closer inspection reveals that the 1987 election included a hotly contested statewide proposition that established the Virginia lottery, whereas the 1986 election did not involve a U.S. Senate contest, and Senator John Warner faced no Democratic opposition in his 1990 reelection campaign (Sabato, 1991). The gray lines in Figure 4.9 trace the turnout rates within each precinct over time. Notice that there appear to be many high- and low-turnout precincts. For example, the high and low outliers tend to be the same MCD groups over time. While not sufficient to demonstrate MCD-group effects in turnout by race, persistent differences in total turnout are consistent with the existence of those effects.

Table 4.2 presents estimates of the main truncated bivariate normal parameters as es- timated by King’s EI and SUEI. In all but one election, the 1986 midterm, the estimated parameters are very similar. The 1984 presidential election presents a good case of what we expect to find if the data are well conditioned and the degree of truncation in the assumed TBVN distributions is small.²⁸The election-specific estimated location parameters,B^band B^w, are identical, and the estimated election-specific standard deviations are larger for King’s EI than for SUEI. This is because some of the precinct-level variation in turnout that is captured by these parameters in King’s EI is attributed to the precinct effect in SUEI. Table 4.3 shows the estimated standard deviations of the precinct effects. The standard deviation of the precinct effects for both whites and nonwhites is estimated to be about 0.09. Thus, in the 1984 presidential election, the estimates are consistent with the notion that the esti- matedσ^bfrom King’s EI is decomposed to into election- and precinct-specific components

27Presentation of the turnout data in this way was suggested to me by James DeNardo.

28This should not be taken as implying that the data are in fact well conditioned. In particular, the these results are not informative about the existence of aggregation bias in the results.

Extending King’s Ecological Inference Model to Multiple Elections Using Markov Chain Monte Carlo 115

Table 4.2 Estimates of truncated bivariate normal parameters for Virginia elections data: turnout by race, 1984–1990

King EI Precinct-effects EI

Parameter Mean Std. Dev. 95% CI Mean Std. Dev. 95% CI 1984 Presidential

B¯^b 0.55 0.02 (0.52, 0.59) 0.55 0.03 (0.49, 0.60)

B¯^w 0.46 0.01 (0.44, 0.47) 0.46 0.01 (0.47, 0.48)

σ˘^b 0.12 0.02 (0.08, 0.16) 0.07 0.02 (0.04, 0.10)

σ˘^w 0.12 0.005 (0.11, 0.13) 0.06 0.004 (0.06, 0.07)

1985 Gubernatorial

B¯^b 0.47 0.01 (0.45, 0.50) 0.46 0.04 (0.42, 0.51)

B¯^w 0.27 0.01 (0.27, 0.29) 0.29 0.01 (0.27, 0.30)

σ˘^b 0.03 0.02 (0.01, 0.07) 0.05 0.01 (0.03, 0.07)

σ˘^w 0.10 0.003 (0.10, 0.11) 0.05 0.003 (0.04, 0.05)

1986 Midterm

B¯^b 0.25 0.02 (0.21, 0.27) −0.04 0.22 (−0.44, 0.27)

B¯^w 0.18 0.01 (0.16, 0.19) 0.19 0.01 (0.18, 0.22)

σ˘^b 0.09 0.02 (0.05, 0.13) 0.35 0.11 (0.19, 0.53)

σ˘^w 0.14 0.01 (0.13, 0.16) 0.10 0.01 (0.08, 0.11)

1987 State legislative

B¯^b 0.25 0.03 (0.21, 0.30) 0.20 0.07 (0.09, 0.29)

B¯^w 0.36 0.01 (0.35, 0.37) 0.37 0.01 (0.35, 0.39)

σ˘^b 0.10 0.02 (0.04, 0.14) 0.13 0.04 (0.08, 0.20)

σ˘^w 0.12 0.005 (0.12, 0.13) 0.08 0.01 (0.07, 0.09)

1988 Presidential

B¯^b 0.48 0.02 (0.45, 0.51) 0.48 0.03 (0.43, 0.53)

B¯^w 0.48 0.01 (0.47, 0.48) 0.48 0.01 (0.47, 0.50)

σ˘^b 0.10 0.02 (0.07, 0.13) 0.03 0.01 (0.02, 0.06)

σ˘^w 0.09 0.003 (0.09, 0.10) 0.03 0.003 (0.03, 0.04)

1989 Gubernatorial

B¯^b 0.55 0.02 (0.52, 0.57) 0.55 0.03 (0.50, 0.60)

B¯^w 0.39 0.01 (0.38, 0.40) 0.39 0.01 (0.37, 0.40)

σ˘^b 0.08 0.02 (0.05, 0.12) 0.06 0.02 (0.04, 0.09)

σ˘^w 0.10 0.003 (0.10, 0.11) 0.04 0.003 (0.03, 0.04)

1990 Midterm

B¯^b ₋0.13 0.24 (−0.56, 0.16) −0.10 0.23 (−0.46, 0.25)

B¯^w 0.27 0.01 (0.26, 0.28) 0.27 0.02 (0.27, 0.29)

σ˘^b 0.29 0.07 (0.19, 0.42) 0.29 0.09 (0.15, 0.43)

σ˘^w 0.10 0.003 (0.09, 0.11) 0.11 0.01 (0.10, 0.12)

Note: Posterior means, standard deviations, and credible intervals were calculated using King’s computer procedures and the MCMC estimator described in the text.

116 Jeffrey B. Lewis

Table 4.3 Estimated standard deviations of the precinct-specific effects on turnout by race across the seven elections, Virginia, 1984–1990

Parameter Mean Std. Dev. 95% CI

ωb 0.09 0.04 (0.01,0.14)

ωw 0.09 0.01 (0.08,0.10)

in SUEI. For example, the total nonwhite precinct-level variance is estimated in King’s EI to be 0.12, and by SUEI to be√

0.07²+0.09²≈0.11. As mentioned above, when the degree of truncation is negligible, both King’s EI and SUEI imply that the precinct parameters follow bivariate normal distributions (both conditional and unconditional on the precinct effect).

In such cases, precinct-level variance in King’s EI will be decomposed into election- and precinct specific components as it is in the 1984 presidential election. Similar, results are obtained for the 1988 presidential election and the 1989 gubernatorial election.

In the remaining elections, differences in the estimated election-specific variance com- ponents between the two models cannot be directly attributed to the sort of decomposition described above. In these elections, the estimated election-specific variance components are larger in SUEI than in King’s EI for at least one of the two racial groups. In the 1985 gubernatorial election, the EI estimated election-specific variance ofβ^bis not even larger than the precinct-specific variation found using SUEI. In most cases, the differences can be attributed to greater degrees of truncation combined with differences in the ways the two models respond to violations in the their distributional assumptions.

Despite differences in the estimated parameters of the underlying TBVN distributions, estimates of the aggregate quantities of interest are quite similar, as seen in Table 4.4. The maximum difference between the EI estimates and SUEI estimates are 5 percentage points for nonwhites and 1 percentage point for whites.²⁹ Interestingly, despite the additional efficiency that should be obtained from SUEI, the estimated posterior uncertainties in the EI estimates is generally smaller than those found for SUEI. This finding results in part from an understatement of posterior uncertainty from King’s use of importance resampling and normal theory to construct estimates of the posterior uncertainty. The larger posterior uncertainties in SUEI also result from differing reactions of the two models to violations of their distributional assumptions.

The results presented in Table 4.4 support the notion that black turnout was elevated relative to white turnout in the two elections involving Douglas Wilder. In the 1985 and 1989 elections black turnout is estimated to have exceeded white turnout by about 15 to 25 percentage points. By comparison, in the 1987 state election, white turnout was estimated to exceeded nonwhite turnout by about 5 to 15 percentage points. In the two midterm elections, black and white turnout is estimated to have been quite similar. Although black turnout is estimated to have exceeded white turnout in 1986 and white turnout to have exceeded black turnout in 1990, in neither case is the difference within the 95 percent credible interval. The most anomalous case is the 1984 presidential election, in which black turnout is estimated to have exceeded white turnout by about 15 to 25 percent. While Jesse Jackson ran a strong campaign in the 1984 presidential primary, winning the Virginia caucus vote, it is not obvious that the effect of his campaign would extend to the general election six months later.

29That the maximum difference between EI and SUEI for whites is about 5 times smaller than for nonwhites follows directly from the fact that nonwhites comprise about 1/5 of the population.

Extending King’s Ecological Inference Model to Multiple Elections Using Markov Chain Monte Carlo 117

Table 4.4 Estimates of the statewide quantities of interest: fractions of whites and nonwhites voting statewide

King EI Precinct-effects EI

Parameter Mean Std. Dev. 95% CI Mean Std. Dev. 95% CI 1984 Presidential

B^b 0.54 0.03 (0.50, 0.58) 0.53 0.04 (0.46, 0.59)

B^w 0.41 0.01 (0.40, 0.42) 0.42 0.01 (0.39, 0.44)

1985 Gubernatorial

B^b 0.47 0.02 (0.44, 0.50) 0.44 0.04 (0.38, 0.50)

B^w 0.23 0.004 (0.22, 0.24) 0.24 0.01 (0.22, 0.26)

1986 Midterm

B^b 0.25 0.02 (0.21, 0.27) 0.30 0.05 (0.22, 0.39)

B^w 0.21 0.01 (0.20, 0.22) 0.20 0.01 (0.17, 0.22)

1987 State legislative

B^b 0.25 0.03 (0.20, 0.30) 0.22 0.04 (0.16, 0.28)

B^w 0.31 0.01 (0.29, 0.32) 0.32 0.01 (0.29, 0.33)

1988 Presidential

B^b 0.46 0.02 (0.42, 0.43) 0.46 0.04 (0.40, 0.52)

B^w 0.45 0.01 (0.44, 0.46) 0.45 0.01 (0.43, 0.47)

1989 Gubernatorial

B^b 0.53 0.02 (0.49, 0.56) 0.52 0.04 (0.46, 0.58)

B^w 0.34 0.01 (0.32, 0.36) 0.35 0.01 (0.33, 0.36)

1990 Midterm

B^b 0.17 0.03 (0.14, 0.22) 0.22 0.04 (0.15, 0.30)

B^w 0.27 0.01 (0.25, 0.28) 0.26 0.01 (0.23, 0.28)

Overall, these estimates suggest that black voter turnout is systematically higher relative to white voter turnout than Sabato’s estimates suggest. Several factors might account for these differences. The 44 predominantly black precincts use by Sabato could be atypical of turnout patterns statewide. Also, Sabato assumes that nonwhite and white behavior in these precincts is the same.³⁰ On the other hand, it is also quite possible that there is a relationship between voter turnout and racial composition. Key’s (1949) racial threat hypothesis asserts that whites will be most motivated to vote against blacks in areas where blacks are most prevalent. Consistent with Key’s hypothesis, Hertzog (1994) argues that

“the single most significant factor in determining how white Virginians would vote in the 1980s was the percentage of black people living the voter’s locality” (p. 163). If this is true, it is quite possible that for elections in which blacks are particularly mobilized, whites in predominantly black areas will be mobilized to vote as well (for the opposing candidate).

In that case, the ecological inference models considered here, which assume that racial composition and turnout by each racial group are independent, will fail in such a way that the additional white turnout in areas with large black populations will be attributed to black voters. This effect is opposite to the usual aggregation bias result, in which voting rates in predominantly black areas are lower for both blacks and whites than in predominantly

30Without knowing the racial composition of these precincts, the influence of white turnout on Sabato’s estimates cannot be assessed.

118 Jeffrey B. Lewis

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βw

Tomography Plot Estimates of β^b Estimates of β^w

Figure 4.10. MCDgroup level tomography plots and estimates from King’sEIand the precinct-effects EImodel estimated byMCMC. The left panels show tomography plots of feasible values ofβ^band β^wfor eachMCDgroup. The ellipses show probability contours of theTBVNparameters estimated by King’sEI. The center and right panels show theEAPestimates ofβ^bandβ^wrespectively for each MCDgroup.

Extending King’s Ecological Inference Model to Multiple Elections Using Markov Chain Monte Carlo 119

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Tomography Plot Estimates of β^b Estimates of β^w

Figure 4.10. (continued)

white areas, leading the estimated black turnout to be lower relative to white turnout than is the true black turnout. Interestingly, Sabato’s estimates indicates that black turnout is lower than the SUEI or EI estimates, not only in elections that involve black candidates, but in other elections as well, which undermines the idea that the differences between the two sets of estimates are due to aggregation bias resulting from racial threat. Further, the fact that Sabato’s estimates which result in lower estimates of black turnout are based on the behavior of blacks (and whites) in themostheavily black precincts, makes less plausible the notion that there is a positive correlation between black or white turnout rates in an area and the fraction of blacks in that area. Overall, the EI and SUEI results regarding the aggregate quantities of interest are quite similar. Further, consistent with Sabato, the EI and SUEI results show higher black turnout relative to white turnout when Wilder was on the ballot.

As seen in the simulation, the real advantage in the SUEI estimator is in the improvement to the precinct-level (MCD-group-level) predictions. Figure 4.10 shows the MCD group

120 Jeffrey B. Lewis turnout rates for whites and nonwhites as estimated by EI and SUEI along with King’s so-calledtomography plotfor each election. In the tomography plot, each line represents the feasible values of black and white turnout given the total turnout rate and the racial composition in a particular MCD group. The ellipses show contour lines of the truncated normal distributions that are assumed to govern the joint distribution of white and nonwhite turnout (as estimated by EI). Notice that many of the precinct lines are very flat, indicating the feasible range of white turnout rates (plotted on the y-axis) is typically small and the range of feasible black turnout rates is very large (often the entire interval [0, 1]). Thus, inferring white turnout rates is a considerably easier task than inferring black turnout rates in these data. Consequently, EI- and SUEI-estimated white turnout rates in each precinct and election are quite similar, as indicated by the fact that most of the points in the white turnout (β^w) panels fall near the 45 degree lines. In the case of white turnout, borrowing strength across elections had very little effect on the estimated quantities of interest. Not that the precinct effects are not present; rather the additional information that they yield with respect to estimating white turnout rates is small. On the other hand, in several of the elections, the inclusion of precinct effects greatly increases the variation in the estimated turnout rates among blacks. That is, the posterior estimates are greatly effected by the borrowing of strength across elections. Particularly in 1985 and 1986, and to a lesser extent in 1987 and 1989, SUEI finds much greater variation in black turnout than does EI. In the 1984 and 1988 elections, variation in estimated black turnout rates made by EI and SUEI are similar, and in the 1990 election the EI estimates exhibit somewhat more variation than the SUEI estimates.

Overall, when the variation in black turnout rates is estimated to be large relative to the variation in white turnout rates (when the ellipses in the tomography plots are wide), the precinct effects add relatively less, and when the variation in black turnout rates is estimated to be small relative to the variation in white turnout rates (when the ellipses in the tomography plots are tall) the precinct effects add relatively more. Also, as noted above, when the degree of truncation is large (as in 1986 or 1990), the relationship between the EI and SUEI estimates becomes more complex due to the asymmetric effect that positive and negative precinct effects have on the precinct-level prediction in cases in which the election specific effect (B^borB^w) is estimated to lie near the boundary of or off the unit square.

Of course, without knowledge of the true turnout by whites and nonwhites in each MCD group it is not possible to ascertain the degree to which the additional variation in the SUEI estimates versus the EI estimates comports with “true” cross-MCD group variation in turnout rates. However, the estimates do suggest the existence of persistent cross-election variation in turnout rates, and those difference are reflected in the SUEI MCD group-level data predictions. Thus, the results presented here demonstrate how the analysis of several elections at once can be used to gain leverage on the behavior of voters within each precinct (MCD group).

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