Abstract
I seek to determine whether race is a factor in how black representatives vote in the United States House of Representatives; if so, this suggests electing more black representatives may improve the economic and political position of blacks if policy positions taken by black representatives on bills that fail to pass would provide tangible positive impacts to members of the black community if passed. Confounding the impact of legislator race, districts represented by blacks on average are quite different than those represented by whites. While past research on this topic uses linear regression techniques with undesirable properties, I improve on past research using matching techniques with more desirable properties. Utilizing a combination of Mahalanobis and propensity score matching, within-caliper matching, and exact matching using data from the 100th–113th Congress, I show black representatives are more likely to vote in agreement with the majority of the Congressional Black Caucus on all votes and on Leadership Conference on Civil and Human Rights, Americans for Democratic Action, and Congressional Quarterly key votes, indicating a substantive racial impact on roll-call voting.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
This is the range of average treatment effects (ATEs) from Mahalanobis and propensity score matching within the optimal radius of the logit of the propensity score, matching exactly on a congressperson’s gender and whether or not he or she represent a Southern state.
This is the range of average treatment effects on the treated (ATETs) from Mahalanobis and propensity score matching within the optimal radius of the logit of the propensity score, matching exactly on a congressperson’s gender and whether or not he or she represent a Southern state.
A number of studies look at the impact of a district’s black population on the roll-call votes of its representative, without regards for the race of the representative. See Fleisher (1993), Hood and Morris (1998), Hutchings (1998), Lublin (1997), Overby and Cosgrove (1996), Sharpe and Garand (2001), Swain (1995), and Whitby (1985).
However, possibly due to strong multicollinearity between a district’s racial makeup and the race of its elected representative, Canon (1999) finds that the fraction of black constituents in district is not a statistically significant indicator of whether a representative votes in favor of civil rights legislation.
These data are downloaded from the Vote View website (voteview.com).
This includes data from the 1980 STF 3D Congressional District-level Extract for the 98th Congress, the Census 1980 Congressional District Equivalency File for the 99th Congress, Census 1990 Summary Tape File 1D for the 103rd, 104th, and 105th Congresses, Census 2000 Congressional District Summary File for the 108th, 109th, and 110th Congresses, and Census 2010 113th Congress 100% Data.
Within these formulae, I allow \( {\varepsilon}_i^2 \), the variance of y Ti conditional on the covariates, to vary by treatment and covariates in the full-sample matched estimates found in Appendix A. To estimate \( {\varepsilon}_i^2 \) allowing for heteroskedasticity I use a second Mahalanobis matching procedure to find the nearest neighbors within the same treatment group, as in Abadie et al. (2004); in the full-sample matched estimates found in Appendix A, I estimate \( {\varepsilon}_i^2 \) using the closest two matches. Formally, define the set of nearest neighbor matches within the same treatment group for observation i as \( {\varOmega}_i=\left\{{m}_1,{m}_2\ \right|\ M\left( i,{m}_1\right)\le M\left( i, j\right),{T}_{m_1}={T}_i, M\left( i,{m}_2\right)\le M\left( i, j\right),{T}_{m_2}={T}_i\forall j\ni {T}_j={T}_i, j\ne {m}_1, j\ne {m}_2\ \Big\} \) and define \( {\varOmega}_i^{\prime } \) as the union of Ω i and observation i. Then \( {\varepsilon}_i^2 \) is estimated by \( \widehat{\varepsilon_i^2} \)= \( \frac{1}{2}{\sum}_{j\in {\varOmega}_i^{\prime }}{\left({y}_j-{\sum}_{k\in {\varOmega}_i^{\prime }}{y}_k/3\right)}^2. \)
In this article, I do not adjust for the fact that the propensity score is estimated. Abadie and Imbens (2016) show that standard errors on estimates from matching on the estimated propensity score, as is done in this article, are more conservative than those from matching on the true propensity score. In the case of the ATET, matching on the estimated propensity score may provide standard errors that are either too large or too small depending on the data generating process, but in this particular example not adjusting for the fact that the propensity score is estimated provides more conservative standard errors in the full sample when not using exact matching on congressional session.
For the sake of brevity in the body of this article, additional full-sample and within-caliper matched estimates have been relegated to Appendix A.
Minimizing the standardized difference in means for a particular variable is preferable to minimizing the t-statistic related to the difference in means for that particular variable since discarding data that has no effect on balance will result in a smaller t-statistic (Ho et al. 2007).
0.25 standard deviations of the pooled propensity score is the most common recommendation in the literature (Ho et al. 2007; Rosenbaum and Rubin 1985), and Austin (2011) recommends using calipers of 0.2 standard deviations of the logit of the propensity score, although there is no universal rule stating that these pre-specified radii will minimize bias regardless of the dataset they are applied to.
For the ATE, 0.1533 standard deviations of the logit of the propensity score minimizes this metric for Mahalanobis ATE and 0.1787 standard deviations of the logit of the propensity score minimizes this metric for the propensity score ATE. For the ATET, 0.0628 standard deviations of the logit of the propensity score minimizes this metric for the Mahalanobis ATET and 0.0647 standard deviations of the logit of the propensity score minimizes this metric for the propensity score ATET.
Using exact matching on Southern State and Female I am able to reduce the largest imbalances from within-caliper Mahalanobis matching (Civilian Unemployment Rate, Seniority) and within-caliper propensity score matching (Southern State).
These samples have substantially better balance than those using within-caliper matching alone, and should produce better causal estimates of the ATE.
Using within-caliper matching in conjunction with exact matching on Southern State and Female provides attenuated estimates compared to within-caliper matching alone for both methods, but a substantive racial impact remains between the well-balanced samples.
These samples also have substantially better balance than those using within-caliper matching alone, and should produce better causal estimates of the ATET. In particular, the Mahalanobis matching estimates, which contain no standardized differences in means above 0.25, should be a substantial upgrade to estimates using within-caliper matching alone.
For the ATE, 0.0302 standard deviations of the logit of the propensity score minimizes this metric for Mahalanobis ATE and 0.2202 standard deviations of the logit of the propensity score minimizes this metric for the propensity score ATE. For the ATET, 0.1253 standard deviations of the logit of the propensity score minimizes this metric for the Mahalanobis ATET and 0.01 standard deviations of the logit of the propensity score minimizes this metric for the propensity score ATET.
References
Abadie A, Imbens GW. Large sample properties of matching estimators for average treatment effects. Econometrica. 2006;74(1):235–67.
Abadie A, Imbens GW. Bias-corrected matching estimators for average treatment effects. J Bus Econ Stat. 2011;29(1):1–11.
Abadie A, Imbens GW. Matching on the estimated propensity score. Econometrica. 2016;84(2):781–807.
Abadie A, Drukker DM, Herr JL, Imbens GW. Implementing matching estimators for average treatment effects in stata. Stata J. 2004;4(3):290–311.
Angrist JD, Pischke J-S. Mostly harmless econometrics: an empiricist’s companion. Princeton: Princeton University Press; 2009.
Austin PC. Optimal caliper widths for propensity-score matching when estimating differences in means and differences in proportions in observational studies. Pharm Stat. 2011;10(2):150–61.
Baker A, Cook C. Representing black interests and promoting black culture. Du Bois Review. 2005;2(2):1–20.
Bratton K, Haynie K. Agenda setting and legislative success in state legislatures: the effects of gender and race. J Polit. 1999;61(3):658–79.
Cameron C, Epstein D, O’Halloran S. Do majority-minority districts maximize substantive black representation in congress? Am Polit Sci Rev. 1996;90(4):794–812.
Canon DT. Race, redistricting, and representation. Chicago: University of Chicago Press; 1999.
Cobb MD, Jenkins JA. Race and the representation of blacks’ interests during reconstruction. Political Research Quarterly. 2001;54(1):181–204.
Fleisher R. Explaining the change in roll-call voting behavior of southern Democrats. J Polit. 1993;55(2):327–41.
Gamble KL. Black political representation: an examination of legislative activity within U.S. house committees. Legis Stud Q. 2007;32(3):421–47.
Griffin J, Newman B. Minority report. Chicago: University of Chicago Press; 2008.
Grose CR. Disentangling constituency and legislator effects in legislative representation. Soc Sci Q. 2005;86(2):427–43.
Haynie KL. African American legislators in the American states. New York: Columbia University Press; 2001.
Herring M. Legislative responsiveness to black constituents in three deep south states. J Polit. 1990;52(3):740–58.
Ho DE, Imai K, King G, Stuart EA. Matching as nonparametric preprocessing for reducing model dependence in parametric causal inference. Polit Anal. 2007;15(3):199–236.
Hood MV III, Morris IL. Boll weevils and roll-call voting: a study in time and space. Legis Stud Q. 1998;23(2):245–69.
Hutchings VL. Issue salience and support for civil rights legislation among southern Democrats. Legis Stud Q. 1998;23(4):521–44.
Juenke EG, Preuhs RR. Irreplaceable legislators? Rethinking minority representatives in the new century. Am J Polit Sci. 2012;56(3):705–15.
Lublin D. The election of African Americans and Latinos to the U.S. House of Representatives, 1972–1994. American Politics Research. 1997;25(3):269–86.
Overby LM, Cosgrove KM. Unintended consequences? Racial redistricting and the representation of minority interests. J Polit. 1996;58(2):540–50.
Rosenbaum PR, Rubin DB. Constructing a control group using multivariate matched sampling methods that incorporate the propensity score. Am Stat. 1985;39(1):33–8.
Sharpe CLV, Garand JC. Race, roll calls, and redistricting: the impact of race-based redistricting on congressional roll call. Political Research Quarterly. 2001;54(1):31–51.
Stuart E. Matching methods for causal inference: a review and a look forward. Stat Sci. 2010;25(1):1–21.
Swain CM. Black faces and black interests: the representation of African Americans in congress. Cambridge: Harvard University Press; 1995.
Tate K. Black faces in the mirror: African Americans and their representatives in the U.S. Congress. Princeton: Princeton University Press; 2003.
Whitby KJ. Effects of the interaction between race and urbanization on votes of southern congressmen. Legis Stud Q. 1985;10(4):505–17.
Whitby KJ. The color of representation. Ann Arbor: University of Michigan Press; 1997.
Whitby KJ, Krause GA. Race, issue heterogeneity, and public policy: the Republican revolution in the 104th congress and the representation of African-American policy interests. Br J Polit Sci. 2001;31(3):555–72.
Author information
Authors and Affiliations
Corresponding author
Appendix A
Appendix A
In the following analysis, for the sake of showing the robustness of my estimates, I will first use one-to-one matching on the full sample. Then, I will use within-caliper matching in order to further reduce observable differences between districts. These semi-parametric methods lead to great reductions in bias in the majority of the covariates as compared to the full unweighted sample. However, these methods do not completely erase the observable differences between districts represented by blacks and whites and are in this sense less preferred than the estimates presented in the main analysis.
Matching using the full sample
To improve upon multiple regression results, I will use the most similar district represented by a legislator of opposite race to estimate the counterfactual outcome in each district in the full sample. To do this, I will use Mahalanobis nearest-neighbor matching and propensity-score matching using the methodology discussed in the Methodology section. Columns 1–4 of Table 6 show the reweighted black-white differences for the full sample using ATE weights and ATET weights; Mahalanobis ATE weights are used in column 1 and propensity score ATE weights are used in column 2. A comparison of column 1 of Table 6 to column 1 of Table 4 shows a large increase in balance between the two samples when Mahalanobis matching is used; bias in each covariate is improved except for seniority and fraction of the population other race. Likewise, a comparison of column 2 of Table 6 to column 1 of Table 4 shows a large increase in balance between the two samples when propensity score matching is used, as well; again bias in each covariate is improved except for seniority and fraction of the population other race.
Columns 3 and 4 of Table 6 show the analogous summary statistics when ATET weights are used. The Mahalanobis ATET matched sample shows reduced bias in each covariate in the sample, and the propensity score matched sample shows a reduction in bias in each covariate in the sample except seniority and gender, as compared to the unweighted sample. While bias is reduced in the majority of the congressperson and district covariates, thus providing less-biased estimates, it is important to note that since substantial differences still remain in many of the covariates the resulting matching estimates may still be biased. In order to further reduce bias in the matching estimates, I estimate within-caliper Mahalanobis and propensity score matches below (and in conjunction with exact matching on Southern State and Female in the main results).
Columns 1–4 of Table 7 shows the matching estimates for each outcome utilizing matches from the full sample. Under Mahalanobis matching, which uses the most similar district represented by a legislator of opposite race to estimate the counterfactual outcome in each district, black Democrats are more likely than white Democrats to vote in agreement with the majority of the CBC with regards to all votes by 5.9 percentage points, LCCR votes by 9.8 percentage points, ADA votes by 13.7 percentage points, and CQ votes by 11.8 percentage points and each estimate is statistically significant at the 1% level. The results from propensity score matching are not substantively different; under propensity score matching, black Democrats are more likely than white Democrats to vote in agreement with the majority of the CBC with regards to all votes by 4.6 percentage points, LCCR votes by 9.0 percentage points, ADA votes by 10.0 percentage points, and CQ votes by 10.1 percentage points and each estimate is statistically significant at the 1% level. Estimates from both Mahalanobis and propensity score matching reveal relatively large and statistically significant differences for LCCR, ADA, and CQ votes and relatively smaller, statistically significant differences for all votes.
As opposed to the average treatment effect, which shows the average impact of legislator race across all districts if each legislator were black as opposed to white, the average treatment effect on the treated shows the impact of legislator race across all districts represented by black congressmen as opposed to if they were represented by white congressmen. The average treatment effect on the treated is generally smaller than the average treatment effect in sample in this example. Under Mahalanobis matching, black Democrats are more likely than white Democrats to vote in agreement with the majority of the CBC with regards to all votes by 4.7 percentage points, LCCR votes by 8.0 percentage points, ADA votes by 9.9 percentage points, and CQ votes by 9.0 percentage points (each estimate is statistically significant at the 1% level), and under propensity score matching, black Democrats are more likely than white Democrats to vote in agreement with the majority of the CBC with regards to all votes by 4.5 percentage points, LCCR votes by 6.7 percentage points, ADA votes by 7.1 percentage points, and CQ votes by 7.0 percentage points (each estimate is statistically significant at the 10% level and the all votes estimate is statistically significant at the 1% level). Once again, estimates from both Mahalanobis and propensity score matching reveal relatively large and statistically significant differences for LCCR, ADA, and CQ votes and relatively smaller, statistically significant differences for all votes.
Within-caliper matching
While matching on the full sample is able to reduce bias significantly, significant differences still exist between many of the observable covariates, which might cause worry that unobservable characteristics between districts represented by black legislators and white legislators are also dissimilar. In order to obtain more similar matched samples of districts represented by black legislators and districts represented by white legislators, I next limit the sample to just those representative-district observations with “very close” matches. Specifically, I estimate the closest Mahalanobis and propensity score match only for those observations that contain at least one counterfactual match within a specified radius of the logit of the propensity score; observations that do not contain at least one match within a specified radius of the logit of the propensity score are omitted from the analysis. In this way, I estimate a local ATE and a local ATET for those districts that are quite similar to districts in the opposite treatment group. To determine the “ideal” caliper, I use the same methodology discussed in the main body of this article.Footnote 19
Columns 5 and 6 of Table 6 show the reweighted summary statistics using ATE weights; Mahalanobis weights are used in column 5 and propensity score weights are used in column 6. A comparison to column 1 of Table 4 shows a large increase in balance between the two samples when Mahalanobis matching or propensity score matching within caliper is used; bias in each covariate is improved except for seniority, which was not significantly different between the two samples to start with. Regardless of whether Mahalanobis or propensity score matching within caliper is used no significant differences remain and all standardized differences in means are below 0.25.
Columns 7 and 8 of Table 6 show the corresponding summary statistics when ATET weights are used instead. The Mahalanobis ATET matched sample shows reduced bias in each covariate in the sample except for seniority and gender while the propensity score ATET matched sample shows reduced bias in each covariate except for seniority and fraction other race. The only statistically significant differences remaining are gender in the Mahalanobis ATET matched sample and seniority in the propensity score ATET matched sample. While bias reduction for the ATET matched samples is not as great as in the ATE case for either method, the sum of squared standardized differences in means between black and white Democrats is still reduced by over 97% from the full sample regardless of which method is used. Because the observable representative and district characteristics are very similar between the matched samples, it should provide confidence that the unobservable characteristics between the two samples are also quite similar, particularly for the ATE estimates.
Columns 5 and 6 of Table 7 show the within-caliper matching estimates for each outcome using ATE weights. Under Mahalanobis matching, black Democrats are more likely than white Democrats to vote in agreement with the majority of the CBC with regards to all votes by 4.7 percentage points, LCCR votes by 6.7 percentage points, ADA votes by 9.1 percentage points, and CQ votes by 9.5 percentage points, and each estimate is statistically significant at the 1% level. The results from propensity score matching are not substantively different than those from Mahalanobis matching; under propensity score matching, black Democrats are more likely than white Democrats to vote in agreement with the majority of the CBC with regards to all votes by 4.8 percentage points, LCCR votes by 6.9 percentage points, ADA votes by 9.1 percentage points, and CQ votes by 9.4 percentage points, and each estimate is statistically significant at the 1% level. In terms of balance, propensity score matching within caliper provides a greater bias reduction (in terms of the sum of standardized differences in means) than Mahalanobis matching. However, both methods yield approximately the same estimates from different samples, providing further confidence in the results.
Columns 7 and 8 of Table 7 show the within-caliper matching estimates for each outcome using ATET weights. Under Mahalanobis matching, black Democrats are more likely than white Democrats to vote in agreement with the majority of the CBC with regards to all votes by 2.8 percentage points, LCCR votes by 4.5 percentage points, ADA votes by 4.4 percentage points, and CQ votes by 5.5 percentage points; the estimates for all votes, LCCR votes, and CQ key votes are each statistically significant at the 1% level and the estimate for ADA votes is statistically significant at the 5% level. Propensity score matching provides somewhat larger estimates than those from Mahalanobis matching; under propensity score matching, black Democrats are more likely than white Democrats to vote in agreement with the majority of the CBC with regards to all votes by 5.0 percentage points, LCCR votes by 9.8 percentage points, ADA votes by 11.4 percentage points, and CQ votes by 13.0 percentage points (the estimate for CQ key votes is statistically significant at the 1% level, the estimates for all votes and LCCR key votes are statistically significant at the 5% level, and the estimate for ADA votes is statistically significant at the 10% level).
In terms of balance, Mahalanobis matching within caliper provides a greater bias reduction (in terms of the sum of standardized differences in means) than propensity score matching and likely provides a closer approximation to the true values. Nonetheless, both ATET estimates should be taken with a grain of salt since large differences in covariates persist. Therefore, in the main results, I show estimates resulting from caliper matching in conjunction with exact matching on Southern State and Female, which further reduces differences in covariates between matched samples. This is particularly useful in providing better ATET estimates, but also helps provide better ATE estimates, as well. Although the ATE within-caliper matched sample contained no statistically significant differences and all standardized differences in means were below 0.25, even insignificant imbalances can translate into biases in causal estimates, so there is no reason to stop looking for better balance if it can be achieved (Ho et al. 2007).
About this article
Cite this article
Kopkin, N. Substantive Black Political Representation: Evidence from Matching Estimates in the United States House of Representatives. Rev Black Polit Econ 44, 203–232 (2017). https://doi.org/10.1007/s12114-017-9250-4
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12114-017-9250-4