Hostname: page-component-7b7567c8c-2n9c9 Total loading time: 0 Render date: 2026-11-14T17:30:40.375Z Has data issue: false hasContentIssue false
  • English
  • Français

The Statistical Properties and Empirical Performance of Double Regression

Published online by Cambridge University Press:  04 January 2017

Jeffrey S. Zax
Jeffrey S. Zax*
Affiliation:
University of Colorado at Boulder, Department of Economics, 256 UCB, Boulder, CO 80309–0256. e-mail: zax@colorado.edu
Get accessRights & Permissions [Opens in a new window]

Abstract

Voting rights litigation requires ecological inference to estimate the voting preferences of minority and nonminority groups within the electorate. Double regression has been the procedure most commonly employed for this purpose. This article presents the first formal examination of this procedure. The underlying structural model reveals that double regression estimators are neither unbiased nor consistent estimators of true within-group vote preferences or polarization. Simulations demonstrate that they can substantially exaggerate the differences between minority and nonminority vote choices when none are present, and dramatically understate them when differences exist. In sum, double regression cannot meet conventional statistical standards for reliability. Consequently, it should be abandoned.

Information

Type
Research Article
Information
Political Analysis , Volume 13 , Issue 1 , Winter 2005, pp. 57 - 76
Copyright
Copyright © Society for Political Methodology 2005 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Cho, Wendy K. Tam. 1998. “If the Assumption Fits …: A Comment on the King Ecological Inference Solution.” Political Analysis 7: 143–164.Google Scholar
Epstein, David, and O'Halloran, Sharyn. 1999. “Measuring the Electoral and Policy Impact of Majority-Minority Voting Districts.” American Journal of Political Science 43: 367–395.CrossRefGoogle Scholar
Firebaugh, Glenn. 1993. “Are Bad Estimates Good Enough for the Courts?” Social Science Quarterly 74: 488–495.Google Scholar
Freedman, David A., Klein, Stephen P., Sacks, Jerome, Smyth, Charles A., and Everett, Charles G. 1991. “Ecological Regression and Voting Rights.” Evaluation Review 15: 673–711.CrossRefGoogle Scholar
Goldberger, Arthur S. 1998. Introductory Econometrics. Cambridge: Harvard University Press.Google Scholar
Goodman, Leo A. 1953. “Ecological Regressions and Behavior of Individual.” American Sociological Review 18: 663–664.CrossRefGoogle Scholar
Goodman, Leo A. 1959. “Some Alternatives to Ecological Correlation.” American Journal of Sociology 64: 610–625.CrossRefGoogle Scholar
Grofman, Bernard. 1991. “Multivariate Methods and the Analysis of Racially Polarized Voting: Pitfalls in the Use of Social Science by the Courts.” Social Science Quarterly 72: 826–833.Google Scholar
Grofman, Bernard. 1993. “The Use of Ecological Regression to Estimate Racial Bloc Voting.” University of San Francisco Law Review 27: 593–625.Google Scholar
Grofman, Bernard, Handley, Lisa, and Niemi, Richard G. 1992. Minority Representation and the Quest for Voting Equality. New York: Cambridge University Press.CrossRefGoogle Scholar
Grofman, Bernard, and Migalski, Michael. 1988. “Estimating the Extent of Racially-Polarized Voting in Multicandidate Contests.” Sociological Methods and Research 16: 427–453.CrossRefGoogle Scholar
Grofman, Bernard, Migalski, Michael, and Noviello, Nicholas. 1985. “The” Totality of the Circumstances Test’ in Section 2 of the 1982 Extension of the Voting Rights Act: A Social Science Perspective.” Law and Policy 7: 199–223.CrossRefGoogle Scholar
Gujarati, Damodar N. 2003. Basic Econometrics, 4th ed. Boston: McGraw-Hill.Google Scholar
Hill, R. Carter, Griffiths, William E., and Judge, George G. 2001. Undergraduate Econometrics, 2nd ed. New York: John Wiley & Sons.Google Scholar
Kennedy, Peter. 1998. A Guide to Econometrics, 4th ed. Cambridge, MA: MIT Press.Google Scholar
King, Gary. 1997. A Solution to the Ecological Inference Problem: Reconstructing Individual Behavior from Aggregate Data. Princeton, NJ: Princeton University Press.Google Scholar
Klein, Stephen P., Sacks, Jerome, and Freedman, David A. 1991. “Ecological Regression versus the Secret Ballot.” Jurimetrics 31: 393–413.Google Scholar
Kmenta, Jan. 1986. Elements of Econometrics, 2nd ed. New York: MacMillan.Google Scholar
Land, Kenneth C. 1993. “Discriminatory Electoral Practices, Contextual Effects, and a New Double Regression Method for the Courts.” Social Science Quarterly 74: 469–470.Google Scholar
Lichtman, Allan J. 1991. “Passing the Test: Ecological Regression Analysis in the Los Angeles County Case and Beyond.” Evaluation Review 15: 770–799.CrossRefGoogle Scholar
Loewen, James W., and Grofman, Bernard. 1989. “Comment: Recent Developments in Methods Used in Vote Dilution Litigation.” Urban Lawyer 21: 589–604.Google Scholar
Ramanathan, Ramu. 2002. Introductory Econometrics with Applications. Fort Worth, TX: Harcourt College.Google Scholar
Rao, J. N. K. 1986. “Ratio Estimators.” In Encyclopedia of Statistical Sciences, Vol. 7. New York: John Wiley & Sons, pp. 639–646.Google Scholar
Shaw, Daron R. 1997. “Estimating Racially Polarized Voting: A View from the States.” Political Research Quarterly 50: 49–74.CrossRefGoogle Scholar
Studenmund, A. H. 1997. Using Econometrics: A Practical Guide, 3rd ed. Reading, PA: Addison-Wesley.Google Scholar
Wooldridge, Jeffrey M. 2003. Introductory Econometrics: A Modern Approach, 2nd ed. Mason: South-Western.Google Scholar
Zax, Jeffrey S. 2002. “Comment on” Estimating the Extent of Racially Polarized Voting in Multicandidate Contests’ by Bernard Grofman and Michael Migalski.” Sociological Methods and Research 31: 73–84.CrossRefGoogle Scholar
Zax, Jeffrey S. 2004. “Goodman's Identity after 50 Years: Its Implications for Regression-Based Inference.” Working paper. Boulder: University of Colorado.Google Scholar