Skip to main content Accessibility help
×
Home

Geographic Boundaries as Regression Discontinuities

  • Luke J. Keele (a1) and Rocío Titiunik (a2)

Abstract

Political scientists often turn to natural experiments to draw causal inferences with observational data. Recently, the regression discontinuity design (RD) has become a popular type of natural experiment due to its relatively weak assumptions. We study a special type of regression discontinuity design where the discontinuity in treatment assignment is geographic. In this design, which we call the Geographic Regression Discontinuity (GRD) design, a geographic or administrative boundary splits units into treated and control areas, and analysts make the case that the division into treated and control areas occurs in an as-if random fashion. We show how this design is equivalent to a standard RD with two running variables, but we also clarify several methodological differences that arise in geographical contexts. We also offer a method for estimation of geographically located treatment effects that can also be used to validate the identification assumptions using observable pretreatment characteristics. We illustrate our methodological framework with a re-examination of the effects of political advertisements on voter turnout during a presidential campaign, exploiting the exogenous variation in the volume of presidential ads that is created by media market boundaries.

Copyright

Corresponding author

Footnotes

Hide All

Authors' note: Authors are in alphabetical order. We thank the Associate Editor Betsy Sinclair, two anonymous referees, Lisa Blaydes, Matias Cattaneo, Thad Dunning, Don Green, Justin Grimmer, Danny Hidalgo, Simon Jackman, Marc Meredith, Clayton Nall, Ellie Powell, Randy Stevenson, Wendy Tam Cho, Jonathan Wand, Teppei Yamamoto, and seminar participants at the University of Michigan, Stanford University, Yale University, Duke University, the London School of Hygiene and Tropical Medicine, and Penn State University for valuable comments and discussion. Titiunik gratefully acknowledges financial support from the National Science Foundation (SES 1357561). An earlier version of this article was the winner of a 2010 Atlantic Causal Inference Conference Thomas R. Ten Have Citation for “exceptionally creative or skillful research on causal inference.” Parts of this manuscript were previously circulated in a working paper entitled “Geography as a Causal Variable.” Replication files available at Political Analysis Dataverse (Keele, Luke, and Titiunik, Rocio, 2014, Replication data for: Geographic boundaries as regression discontinuities, http://dx.doi.org/10.7910/DVN/26453 IQSS Dataverse Network [Distributor] V1 [Version]).

Footnotes

References

Hide All
Anderson, Michael L. 2008. Multiple inference and gender differences in the effects of early intervention: A reevaluation of the abecedarian, Perry preschool, and early training projects. Journal of the American Statistical Association 103(484): 1481–95.
Ansolabehere, Stephen D., and Hersh, Eitan. 2012. What big data reveal about survey misreporting and the real electorate. Political Analysis 20(4): 437–59.
Asiwaju, A.I. 1985. Partitioned Africa: Ethnic relations an Africa's international boundaries, 1884–1984. London: C. Hurst.
Banerjee, Sudipto. 2005. On geodetic distance computations in spatial modeling. Biometrics 61(2): 617–25.
Benjamini, Yoav, and Hochberg, Yosef. 1995. Controlling the false discovery rate: A practical and powerful approach to multiple testing. Journal of the Royal Statistical Society Series B 57(1): 289300.
Berger, Daniel. 2009. Taxes, institutions and local governance: Evidence from a natural experiment in colonial Nigeria. Unpublished manuscript.
Berk, Richard A. 2006. Regression analysis: A constructive critique. Thousand Oaks, CA: Sage Publications.
Black, Sandra E. 1999. Do better schools matter? Parental valuation of elementary education. Quarterly Journal of Economics 114(2): 577–99.
Broockman, David E. 2009. Do congressional candidates have reverse coattails? Evidence from a regression discontinuity design. Political Analysis 17(4): 418–34.
Calonico, Sebastian, Cattaneo, Matias D., and Titiunik, Rocío. 2014a. Robust data-driven inference in the regression-discontinuity design. Stata Journal.
Calonico, Sebastian, Cattaneo, Matias D., and Titiunik, Rocío. Forthcoming 2014b. Robust nonparametric confidence intervals for regression-discontinuity designs. Econometrica. https://www.econometricsociety.org/publications/econometrica/journal-materials/forthcoming-papers.
Calonico, Sebastian, Cattaneo, Matias D., and Titiunik, Rocío. 2014c, Rdrobust: An R package for robust inference in regression-discontinuity designs. Working Paper.
Card, David, and Krueger, Alan B. 1994. Minimum wages and employment: A case study of the fast-food industry in New Jersey and Pennsylvania. American Economic Review 84(4): 772–93.
Cattaneo, Matias D., Frandsen, Brigham, and Titiunik, Rocío. 2014. Randomization inference in the regression discontinuity design: An application to party advantages in the U.S. Senate. Journal of Causal Inference. DOI: 10.1515/jci-2013-0010.
Caughey, Devin, and Sekhon, Jasjeet S. 2011. Elections and the regression discontinuity design: Lessons from close U.S. House races, 1942–2008. Political Analysis 19(4): 385408.
Cohn, Molly J., and Jackman, Saul P. 2011. A comparison of aspatial and spatial measures of segregation. Transactions in GIS 14(1): 4766.
Cook, Thomas D., Shadish, William R., and Wong, Vivian C. 2008. Three conditions under which experiments and observational studies produce comparable causal estimates: New findings from within-study comparisons. Journal of Policy Analysis and Management 27(4): 724–50.
Cox, David R. 1958. Planning of experiments. New York: Wiley.
Dell, Melissa. 2010. The persistent effects of Peru's mining Mita. Ecometrica 78(6): 1863–903.
Eggers, Andrew C., and Hainmueller, Jens. 2009. MPs for sale? Returns to office in postwar British politics. American Political Science Review 103(4): 513–33.
Eggers, Andrew C., Fowler, Anthony, Hainmueller, Jens, Hall, Andrew B., and Snyder, James M. 2014. On the validity of the regression discontinuity design for estimating electoral effects: New evidence from over 40,000 close races. American Journal of Political Science, doi: 10.1111/ajps.12127.
Fan, J., and Gijbels, I. 1996. Local polynomial modelling and its applications: Monographs on statistics and applied probability, Vol 66. Boca Raton, FL: Chapman & Hall/CRC.
Fotheringham, A. Stewart, Brundson, Chris, and Charlton, Martin. 1998. Geographically weighted regression: A natural evolution of the expansion method for spatial data analysis. Environment and Planning 30:1905–27.
Fotheringham, A. Stewart, Brundson, Chris, and Charlton, Martin. 2002. Geographically weighted regression: The analysis of spatially varying relationships. Hoboken, NJ: Wiley and Sons.
Fotheringham, A. Stewart, and Wong, D. 1991. The modifiable areal unit problem in multivariate statistical analysis. Environment and Planning 23(4): 1025–44.
Gerber, Alan S., Kessler, Daniel P., and Meredith, Marc. 2011. The persuasive effects of direct mail: A regression-discontinuity-based approach. Journal of Politics 73(1): 140–55.
Gerber, Elisabeth R., and Hopkins, Daniel J. 2011. When mayors matter: Estimating the impact of mayoral partisanship on city policy. American Journal of Political Science 55(2): 326–39.
Gill, Jeff. 2002. Bayesian methods: A social and behavioral sciences approach. Boca Raton, FL: Chapman & Hall/CRC.
Goldstein, Kenneth, Franz, Michael, and Ridout, Travis. 2008. Political advertising in 2008. Combined file [dataset], final release.
Green, Donald P., Leong, Terence Y., Kern, Holger, Gerber, Alan S., and Larimer, Christopher W. 2009. Testing the accuracy of regression discontinuity analysis using experimental benchmarks. Political Analysis 17(4): 400–17.
Hahn, Jinyong, Todd, Petra, and van der Klaauw, Wilbert. 2001. Identification and estimation of treatments effects with a regression-discontinuity design. Econometrica 69(1): 201–09.
Hansen, Ben B., and Bowers, Jake. 2008. Covariate balance in simple, stratified, and clustered comparative studies. Statistical Science 23(2): 219–36.
Hernán, Miguel A., and VanderWeele, Tyler J. 2011. Compound treatments and transportability of causal inference. Epidemiology 22(3): 368–77.
Huber, Gregory A., and Arceneaux, Kevin. 2007. Identifying the persuasive effects of presidential advertising. American Journal of Political Science 51(4): 957–77.
Imbens, Guido W., and Kalyanaraman, Karthik. 2012. Optimal bandwidth choice for the regression discontinuity estimator. Review of Economic Studies 79(3): 933–59.
Imbens, Guido W., and Lemieux, Thomas. 2008. Regression discontinuity designs: A guide to practice. Journal of Econometrics 142(2): 615–35.
Imbens, Guido W., and Zajonc, Tristan. 2011. Regression discontinuity design with multiple forcing variables. Working Paper.
Keele, Luke J., Titiunik, Rocío, and Zubizarreta, José. 2014. Enhancing a geographic regression discontinuity design through matching to estimate the effect of ballot initiatives on voter turnout. Journal of the Royal Statistical Society: Series A (Statistics in Society). doi: 10.1111/rssa.12056.
Keele, Luke J., and Titiunik, Rocío. 2014a. Bounding treatment effects under interference in geographic natural experiments: An application to all-mail voting in Colorado. Working Paper.
Keele, Luke J., and Titiunik, Rocío. Forthcoming 2014b. Natural experiments based on geography. Political Science Research and Methods. Working Paper.
Kern, Holger L., and Hainmueller, Jens. 2008. Opium for the masses: How foreign media can stabilize authoritarian regimes. Political Analysis 17(2): 377–99.
Krasno, Jonathan S., and Green, Donald P. 2008. Do televised presidential ads increase voter turnout? Evidence from a natural experiment. Journal of Politics 70(1): 245–61.
Laitin, David D. 1986. Hegemony and culture: Politics and religious change among the Yoruba. Chicago: University of Chicago Press.
Lee, David S. 2008. Randomized experiments from non-random selection in U.S. House elections. Journal of Econometrics 142(2): 675–97.
Lee, David S., and Lemieux, Thomas. 2010. Regression discontiuity designs in economics. Journal of Economic Literature 48(2): 281355.
Malpezzi, Stephen. 2002. Hedonic pricing models and house price indexes: A select review. In Housing economics and public policy: Essays in honour of Duncan Maclennan, eds. Gibb, Kenneth and O’Sullivan, Anthony, 6789. Oxford: Blackwell Publishing.
Matzkin, Rosa L. 2007. Nonparametric identification. Handbook of Econometrics 6:5307–68.
Middleton, Joel A., and Green, Donald P. 2008. Do community-based voter mobilization campaigns work even in battleground states? Evaluating the effectiveness of Move On's 2004 outreach campaign. Quarterly Journal of Political Science 3(1): 6382.
Miguel, Edward. 2004. Tribe or nation? Nation building and public goods in Kenya versus Tanzania. World Politics 56(3): 327–62.
Miles, William F.S. 1994. Hausaland divided: Colonialism and independence in Nigeria and Niger. Ithaca, NY: Cornell University Press.
Miles, William F.S., and Rochefort, David. 1991. Nationalism versus ethnic identity in sub-Saharan Africa. American Political Science Review 85(2): 393403.
Nall, Clayton. 2012. The road to division: Interstate highways and geographic polarization. Unpublished manuscript.
Openshaw, S. 1984. The modifiable areal unit problem. Norwich, CT: Geo Books.
Papay, John P., Willett, John B., and Murnane, Richard J. 2011. Extending the regression-discontinuity approach to multiple assignment variables. Journal of Econometrics 161(2): 203–07.
Porter, Jack. 2003. Estimation in the regression discontinuity model. Unpublished manuscript.
Posner, Daniel N. 2004. The political salience of cultural difference: Why Chewas and Tumbukas are allies in Zambia and adversaries in Malawi. American Political Science Review 98(4): 529–45.
Reardon, Sean F., and O'Sullivan, John. 2004. Measures of spatial segregation. Sociological Methodology 34(1): 121–62.
Rosenbaum, Paul R. 2002. Observational studies. 2nd ed. New York: Springer.
Rubin, Donald B. 1986. Which ifs have causal answers. Journal of the American Statistical Association 81(396): 961–62.
Sheppard, Stephen. 1999. Hedonic analysis of housing markets. In Applied urban economics: Handbook of regional and urban economics, volume 3, chapter 41, eds. Cheshire, Paul and Mills, S., 1595–635. Amsterdam, The Netherlands: Elsevier.
Sinclair, Betsy, McConnell, Margaret, and Green, Donald P. 2012. Detecting spillover in social networks: Design and analysis of multilevel experiments. American Journal of Political Science 56(4): 1055–69.
Cho, Tam, Wendy, K., and Nicely, Erinn P. 2008. Geographic proximity versus institutions: Evaluating borders as real political boundaries. American Politics Research 36(6): 803–23.
Trounstine, Jessica. 2011. Evidence of a local incumbency advantage. Legislative Studies Quarterly 36(2): 255–80.
VanderWeele, Tyler J. 2009. Concerning the consistency assumption in causal inference. Epidemiology 20(6): 880–83.
Wong, D. 2008. A local multidimensional approach to evaluate changes in segregation. Urban Geography 29(3): 455–72.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Geographic Boundaries as Regression Discontinuities

  • Luke J. Keele (a1) and Rocío Titiunik (a2)

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed