Skip to main content Accessibility help

What To Do About Atheoretic Lags*

  • Skyler J. Cranmer, Douglas R. Rice and Randolph M. Siverson


We examine a problem that is confronted frequently by political science researchers seeking to model longitudinal data: what to do when one suspects a lag between the realization of a regressor and its effect on the outcome variable, but one has no theoretical reason to suspect a particular lag length. We examine the theoretical challenges posed by atheoretic lags, review existing methods for atheoretic lag analysis—most notably distributed lag specifications—and their shortcomings, and present an alternative approach for atheoretic lag analysis based on Bayesian model averaging (BMA). We demonstrate the use and utility of our approach with two examples: the litigant signal model in American politics and modernization theory in political economy. Our examples show the increasing difficulty of analyzing models with atheoretic lags as the set of possible specifications increases, and demonstrate the effectiveness of BMA for the modal type of specification in time-series cross-sectional applications.



Hide All

Skyler Cranmer, Carter Phillips and Sue Henry Associate Professor, Department of Political Science, The Ohio State University, 154 North Oval Mall, Derby Hall 2032, Columbus, OH 43210 ( Douglas Rice, Assistant Professor, Department of Political Science, University of Mississippi, P.O. Box 1848, 228 Deupree Hall University, MS 38677-1848 ( Randolph Siverson, Distinguished Professor Emeritus, Department of Political Science, University of California, Davis 578 Kerr Hall, One Shields Ave. Davis, CA 95616 ( Thanks are due to Janet Box-Steffensmeier, James Fowler, Jeff Gill, Domonik Hangartner, Gary King, Lee Walker, and Chris Zorn for their helpful comments. SJC gratefully acknowledges the support of the National Science Foundation (SES-1461493 and SES-1357622) and the Alexander von Humboldt Foundation.



Hide All
Akaike, Hirotugu. 1974. ‘A New Look at the Statistical Model Identification’. IEEE Transactions on Automatic Control 19(6):716723.
Almon, Shirley. 1965. ‘The Distributed Lag Between Capital Appropriations and Expenditures’. Econometrica 33(1):178196.
Amemiya, Takeshi, and Fuller, Wayne. 1967. ‘A Comparative Study of Alternative Estimators in a Distributed Lag Model’. Econometrica 35(3/4):509529.
Baird, Vanessa. 2004. ‘The Effect of Politically Salient Decisions on the U.S. Supreme Court’s Agenda’. The Journal of Politics 66(3):755772.
Baird, Vanessa. 2007. Answering the Call of the Court: How Justices and Litigants Set the Supreme Court Agenda. Charlottesville, VA: University of Virginia Press.
Baird, Vanessa, and Jacobi, Tonja. 2009. ‘Judicial Agenda-Setting Through Signaling and Strategic Litigant Responses’. Washington University Journal of Law and Policy 29:215239.
Barnard, George A. 1963. ‘New Methods of Quality Control’. Journal of the Royal Statistical Society, Series A 126(2):255258.
Bartels, Larry M. 1997. ‘Specification Uncertainty and Model Averaging’. American Journal of Political Science 41(2):641674.
Bartels, Larry M., and Zaller, John. 2001. ‘Presidential Vote Models: A Recount’. PS: Political Science and Politics 34(1):820.
Beck, Nathaniel. 1985. ‘Estimating Dynamic Models is Not Merely a Matter of Technique’. Political Methodology 11:7189.
Beck, Nathaniel. 1991. ‘Comparing Dynamic Specification: The Case of Presidential Approval’. Political Analysis 3:2750.
Beck, Neal, and Katz, Jonathan N.. 1996. ‘Nuisance Versus Substance: Specifying and Estimating Time-Series-Cross-Section Models’. Political Analysis 15:182195.
Black, Ryan C., and Owens, Ryan J.. 2009. ‘Agenda Setting in the Supreme Court: The Collision of Policy and Jurisprudence’. The Journal of Politics 71(3):10621075.
Boix, Carles. 2003. Democracy and Redistribution. New York, NY: Cambridge University Press.
Boix, Carles, and Stokes, Susan. 2003. ‘Endogenous Democratization’. World Politics 55(4):517549.
Brenner, Saul, and Krol, John F.. 1989. ‘Strategies in Certiorari Voting on the United States Supreme Court’. The Journal of Politics 51(4):828840.
Burkhart, Ross E., and Lewis-Beck, Michael S.. 1994. ‘The Economic Development Thesis’. American Political Science Review 88:903910.
Caldeira, Gregory A. 1981. ‘The United States Supreme Court and Criminal Cases, 1935–1976: Alternative Models of Agenda Building’. British Journal of Political Science 11(4):449470.
Caldeira, Gregory A., and Wright, John R.. 1988. ‘Organized Interests and Agenda Setting in the U.S. Supreme Court’. American Political Science Review 82(4):11091127.
Caldeira, Gregory A., Wright, John R., and Zorn, Christopher J.W.. 1999. ‘Strategic Voting and Gatekeeping in the Supreme Court’. Journal of Law, Economics and Organization 15(3):549572.
Chenery, Hollis B., and Taylor, Lance. 1968. ‘Development Patters: Among Countries and Over Time’. Review of Economic Statistics 50(4):391416.
Clemen, Robert T. 1989. ‘Combining Forecasts: A Review and Annotated Bibliography’. International Journal of Forecasting 5(4):559583.
Cranmer, Skyler J., and Siverson, Randolph M.. 2008. ‘Demography, Democracy and Disputes: The Search for the Elusive Relationship Between Population Growth and International Conflict’. Journal of Politics 70(3):794806.
Cutright, Phillips. 1963. ‘National Political Development: Social and Economic Correlates’. In Nelson W. Polsby, Robert A. Dentler and Paul A. Smith (eds), Politics and Social Life: An Introduction to Political Behavior. 569581. Boston, MA: Houghton Mifflin.
Dahl, Robert A. 1971. Polyarchy: Participation and Opposition. New Haven, CT: Yale University Press.
DeBoef, Suzanna, and Keele, Luke. 2008. ‘Taking Time Seriously’. American Journal of Political Science 52(1):184200.
Deutsch, Karl W. 1961. ‘Social Mobilization and Political Development’. American Political Science Review 55(3):493510.
Draper, David. 1995. ‘Assessment and Propagation of Model Uncertainty’. Journal of the Royal Statistical Society, Series B 57(1):4597.
Dufour, Jean-Marie, and Kiviet, Jan F.. 1998. ‘Exact Inference Methods for First-Order Autoregressive Distributed Lag Models’. Econometrica 66(1):79104.
Epp, Charles. 1998. The Rights Revolution: Lawyers, Activists, and Supreme Courts in Comparative Perspective. Chicago, IL: University of Chicago.
Epstein, David L., Bates, Robert, Goldstone, Jack, Kristensen, Ida, and O’Halloran, Sharyn. 2006. ‘Democratic Transitions’. American Journal of Political Science 50(3):551569.
Epstein, Lee, and Rowland, C.K.. 1991. ‘Debunking the Myth of Interest Group Invincibility in the Courts’. American Political Science Review 85(1):205217.
Epstein, Lee, and Segal, Jeffrey A.. 2000. ‘Measuring Issue Salience’. American Journal of Political Science 44(1):6683.
Epstein, Lee, and Kobylka, Joseph F.. 1992. The Supreme Court and Legal Change: Abortion and the Death Penalty. Chapel Hill, NC: University of North Carolina Press.
Erikson, Robert S., Bafumi, Joseph, and Wilson, Bret. 2001. ‘Was the 2000 Presidential Election Predictable’. PS: Political Science and Politics 34(4):815819.
Fearon, James D., and Latin, David D.. 2003. ‘Ethnicity, Insurgency, and Civil War’. American Political Science Review 97(1):7590.
Flemming, Roy, Dan Wood, B., and Bohte, John. 1999. ‘Attention to Issues in a System of Separated Powers: The Macrodynamics of American Policy Agendas’. Journal of Politics 61(1):76108.
Freund, Yoav, and Schapire, Robert. 1996. ‘Experiments With a New Boosting Algorithm’. In Machine Learning: Proceedings of the Thirteenth International Conference, Bari, Italy. 148–156.
Freund, Yoav, and Schapire, Robert. 1997. ‘A Decision-Theoretic Generalization of On-Line Learning and an Application to Boosting’. Journal of Computer and System Sciences 55(1):119139.
Geer, John, and Lau, Richard R.. 2006. ‘Filling in the Blanks: A New Method for Estimating Campaign Effects’. British Journal of Political Science 36(2):269290.
Gerber, Alan, Malhotra, Neil, Dowling, Conor, and Doherty, David. 2010. ‘Publication Bias in Two Political Behavior Literatures’. American Politics Research 38(4):591613.
Geweke, John. 1978. ‘Temporal Aggregation in the Multiple Regression Model’. Econometrica 46(3):643661.
Ghobarah, Hazem A., Huth, Paul, and Russett, Bruce. 2003. ‘Civil Wars Kill and Maim People-Long after the Shooting Stops’. American Political Science Review 97(2):189202.
Gill, Jeff. 2007. Bayesian Methods. Boca Raton, FL: Chapman & Hall/CRC.
Green, Donald, Kim, Soo Yeon, and Yoon, David. 2001. ‘Dirty Pool’. International Organization 55(2):441468.
Hoeting, Jennifer A., Madigan, David, Raftery, Adrian E., and Volinsky, Chris T.. 1999. ‘Bayesian Model Averaging: A Tutorial’. Statistical Science 14(4):382417.
Imai, Kosuke, and King, Gary. 2004. ‘Did Illegal Overseas Absentee Ballots Decide the 2000 U.S. Presidential Election?Perspectives on Politics 2(3):537549.
Jackman, Simon. 2009. Bayesian Analysis for the Social Sciences. New York, NY: Wiley.
Koyck, Leendert M. 1954. Distributed Lags and Investment Analysis. Amsterdam: North-Holland.
Kuznets, Simon. 1966. Modern Economic Growth: Rate, Structure, and Spread. New Haven, CT: Yale University Press.
Leamer, Edward E. 1978. Specification Searches. New York, NY: Wiley.
Lerner, Daniel. 1958. The Passing of Traditional Society. New York, NY: Free Press of Glencoe.
Lipset, Seymour M. 1959. ‘Some Social Requisites of Democracy: Economic Development and Political Legitimacy’. American Political Science Review 53(1):69105.
Londregan, John B., and Poole, Keith T.. 1996. ‘Does High Income Promote Democracy’. World Politics 49(1):130.
Lütkepohl, Helmut. 1980. ‘Approximation of Arbitrary Distributed Lag Structures by a Modified Polynomial Lag: An Extension’. Journal of the American Statistical Association 75(370):428430.
Madigan, David, and Raftery, Adrian E.. 1994. ‘Model Selection and Accounting for Model Uncertainty in Graphical Models Using Occam’s Window’. Journal of the American Statistical Association 89(428):15351546.
Martin, Andrew D., and Quinn, Kevin M.. 2002. ‘Dynamic Ideal Point Estimation Via Markov Chain Monte Carlo for the U.S. Supreme Court’. Political Analysis 10(2):134153.
Martin, James E. 1967. ‘Isolation of Lagged Economic Responses’. Journal of Farm Economics 49(1):160168.
McGuire, Kevin T., and Caldeira, Gregory A.. 1993. ‘Lawyers, Organized Interests, and the Law of Obscenity: Agenda-Setting in the Supreme Court’. American Political Science Review 87(3):715726.
Montgomery, Jacob M., and Nyhan, Brendan. 2010. ‘Bayesian Model Averaging: Theoretical Developments and Practical Applications’. Political Analysis 18(2):245270.
Moore, Barrington. 1966. Social Origins of Dictatorship and Democracy: Lord and Peasant in the Making of the Modern World. Boston, MA: Beacon Press.
Nelson, Charles R., and Schwert, G. William. 1974. ‘Estimating the Parameters of a Distributed Lag Model from Cross-Section Data: The Case of Hospital Admissions and Discharges’. Journal of the American Statistical Association 69(347):627633.
Nicholson, Chris, and Collins, Paul. 2008. ‘The Solicitor General’s Amicus Curiae Strategies in the Supreme Court’. American Politics Research 36:382415.
Perry, H.W. 1991. Deciding to Decide: Agenda Setting in the United States Supreme Court. Cambridge: Harvard University Press.
Peters, C. Scott. 2007. ‘Getting Attention: The Effect of Legal Mobilization on the U.S. Supreme Court’s Attention to Issues’. Political Research Quarterly 60(3):561572.
Prezeworski, Adam. 1990. Democracy and the Market: Political and Economic Reforms in Eastern Europe and Latin America. New York, NY: Cambridge University Press.
Przeworski, Adam, and Limongi, Fernando. 1993. ‘Political Regimes and Economic Growth’. Journal of Economic Perspectives 7(3):5169.
Przeworski, Adam, and Limongi, Fernando. 1997. ‘Modernization: Theories and Facts’. World Politics 49(2):155183.
Przeworski, Adam, Alvarez, Michael E., Cheibub, Jose A., and Limongi, Fernando. 1996. ‘What Makes Democracies Endure?Journal of Democracy 7(1):3955.
Przeworski, Adam, Alvarez, Michael E., Cheibub, Jose A., and Limongi, Fernando. 2000. Democracy and Development: Political Institutions and Well-Being in the World, 1950–1990. New York, NY: Cambridge University Press.
Raftery, Adrian E. 1995. ‘Bayesian Model Selection in Social Research’. Sociological Methodology 25:111163.
Rostow, Walt W. 1960. The Stages of Economic Growth: A Non-Communist Manifesto. Cambridge: Cambridge University Press.
Rueschemeyer, Dietrich, Stephens, Evelyne H., and Stephens, John D.. 1992. Capitalist Development and Democracy. Chicago, IL: University of Chicago Press.
Simonsohn, Uri, Nelson, Leif, and Simmons, Joseph. 2014. ‘P-Curve: A Key to the File Drawer’. Journal of Experimental Psychology 143(2):534547.
Solow, Robert M. 1960. ‘On a Family of Lag Distributions’. Econometrica 28(2):393406.
Tibshirani, Robert. 1996. ‘Regression Shrinkage and Selection Via the Lasso’. Journal of the Royal Statistical Society, Series B 58:267288.
Tibshirani, Robert. 1997. ‘The Lasso Method for Variable Selection in the Cox Model’. Statistics in Medicine 16:385395.
Trivedi, Pravin K. 1985. ‘Distributed Lags, Aggregation and Compounding: Some Econometric Implications’. The Review of Economic Studies 52(1):1935.
Ulmer, S. Sidney. 1984. ‘The Supreme Court’s Certiorari Decisions: Conflict as a Predictive Variable’. American Political Science Review 78(4):901911.
Valentino, Nicholas, Brader, Ted, and Jardina, Ashley. 2013. ‘Immigration Opposition Among U.S. Whites: General Ethnocentrism or Media Priming of Attitudes About Latinos?’. Political Psychology 34(2):149166.
Warren, T. Camber. 2014. ‘Not by the Sword Alone: Soft Power, Mass Media, and the Production of State Sovereignty’. International Organization 68(1):111141.
Zaller, John R. 2004. ‘Floating Voters in U.S. Presidential Elections, 1948–2000’. In Willem Saris and Paul M. Sniderman (eds), Studies in Public Opinion: Attitudes, Nonattitudes, Measurement Error, and Change. 166:214. Princeton, NJ: Princeton University Press.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Political Science Research and Methods
  • ISSN: 2049-8470
  • EISSN: 2049-8489
  • URL: /core/journals/political-science-research-and-methods
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


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