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Modeling Duration Dependence

Published online by Cambridge University Press:  04 January 2017

Christopher J. W. Zorn
Christopher J. W. Zorn*
Affiliation:
Department of Political Science, Emory University, Atlanta, GA 30322. e-mail: czorn@emory.edu., http://www.emory.edu/POLS/zorn/
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Abstract

As applications of duration analysis have burgeoned in political science, scholars have become increasingly aware of the potential substantive importance of duration dependence: the extent to which the conditional hazards of the events of interest are rising or falling over time. Here I discuss the issue of duration dependence, focusing on the distinction between “spurious” dependence due to unobserved heterogeneity and “true” duration dependence due to state dependence in the process of interest. I present a simple extension of a commonly used parametric duration model—the Weibull model—which allows researchers to assess the influence of causal variables on the nature and extent of duration dependence in their data. I then illustrate the application of this “generalized Weibull” model using data on the duration of international alliances.

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Type
Research Article
Information
Political Analysis , Volume 8 , Issue 4 , 18 July 2000 , pp. 367 - 380
Copyright
Copyright © 2000 by the Society for Political Methodology 

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References

Alt, James, and King, Gary. 1994. “Transfers of Governmental Power: The Meaning of Time Dependence.” Comparative Political Studies 27(2): 190–210.CrossRefGoogle Scholar
Alvarez, R. Michael, and Brehm, John. 1995. “American Ambivalence Towards Abortion Policy: Development of a Heteroskedastic Probit Model of Competing Values.” American Journal of Political Science 39 (Nov.): 1055–1082.CrossRefGoogle Scholar
Beck, Nathaniel. 1998. “Modelling Space and Time: The Event History Approach.” In Research Strategies in the Social Sciences, eds. Scarbrough, E. and Tanenbaum, E. London: Oxford University Press.Google Scholar
Beck, Nathaniel, Katz, Jonathan N., and Tucker, Richard. 1998. “Taking Time Seriously: Time-Series-Cross-Section Analysis with a Binary Dependent Variable.” American Journal of Political Science 42 (Oct.): 1260–1288.CrossRefGoogle Scholar
Bennett, D. Scott. 1997. “Testing Alternative Models of Alliance Duration, 1816–1984.” American Journal of Political Science 41 (July): 846–878.CrossRefGoogle Scholar
Bennett, D. Scott. 1998. “Integrating and Testing Models of Rivalry Termination.” American Journal of Political Science 42 (Oct.): 1200–1232.CrossRefGoogle Scholar
Bennett, D. Scott. 1999. “Parametric Models, Duration Dependence, and Time-Varying Data Revisited.” American Journal of Political Science 43 (Jan.): 256–270.CrossRefGoogle Scholar
Bennett, D. Scott, and Stam, Allan C. III. 1996. “The Duration of Interstate Wars.” American Political Science Review 90 (June): 239–257.CrossRefGoogle Scholar
Bennett, D. Scott, and Stam, Allan. 1998. “The Declining Advantages of Democracy: A Combined Model of War Outcomes and Duration.” Journal of Conflict Resolution 42 (June): 344–366.Google Scholar
Blossfeld, Hans-Peter, and Rohwer, Götz. 1995. Techniques of Event History Modeling. Mahwah, NJ: Lawrence Erlbaum.Google Scholar
Box-Steffensmeier, Janet M., and Zorn, Christopher J. W. 1998. “Duration Models and Proportional Hazards in Political Science.” Paper presented at the Annual Meeting of the Midwest Political Science Association, April 23–25, Chicago, IL.Google Scholar
Box-Steffensmeier, Janet M., and Zorn, Christopher J. W. 1999. “Modeling Heterogeneity in Duration Analysis.” Paper presented at the 16th Annual Meeting of the Society for Political Methodology, July 15–18, College Station, TX.Google Scholar
Bueno de Mesquita, Bruce, and Siverson, Randolph M. 1995. “War and the Survival of Political Leaders: A Comparative Study of Regime Types and Political Accountability.” American Political Science Review 89 (June): 841–855.CrossRefGoogle Scholar
Butler, Richard J., and Worrall, John D. 1991. “Gamma Duration Models with Heterogeneity.” The Review of Economics and Statistics 73: 161–166.Google Scholar
Clark, David H., and Hart, Robert A. Jr. 1998. “Controlling Duration Dependence in Conflict Analyses: A Replication and Extension of ‘Regime Types and Status Quo Evaluations’.” American Journal of Political Science 42 (Oct.): 1335–1342.CrossRefGoogle Scholar
Cox, D. R. 1972. “Regression Models and Life Tables.” Journal of the Royal Statistical Society, Series B 34(2): 187–220.Google Scholar
Davidian, M., and Carroll, R. J. 1987. “Variance Function Estimation.” Journal of the American Statistical Association 82: 1079–1091.CrossRefGoogle Scholar
Elbers, Chris, and Ridder, Geert. 1982. “True and Spurious Duration Dependence: The Identifiability of the Proportional Hazard Model.” Review of Economic Studies 49: 403–409.CrossRefGoogle Scholar
Felmlee, Diane, Sprecher, Susan, and Bassin, Edward. 1990. “The Dissolution of Intimate Relationships: A Hazard Model.” Social Psychology Quarterly 53(1): 13–30.CrossRefGoogle Scholar
Fleming, Thomas R., and Harrington, David P. 1991. Counting Processes and Survival Analysis. New York: Wiley.Google Scholar
Gaubatz, Kurt Taylor. 1996. “Democratic States and Commitment in International Relations.” International Organization 50 (Jan.): 109–130.Google Scholar
Goemans, Hein. 1999. “The Termination of the First World War.” Manuscript. Durham, NC: Duke University.Google Scholar
Gönül, Füsan, and Srinivasan, Kannan. 1993. “Consumer Purchase Behavior in a Frequently Bought Product Category: Estimation Issues and Managerial Insights from a Hazard Function Model with Heterogeneity.” Journal of the American Statistical Association 88 (Dec.): 1219–1227.Google Scholar
Greene, William. 1997. LIMDEP Version 7.0: User's Manual. Bellport, NY: Econometric Software, Inc.Google Scholar
Harvey, A. C. 1976. “Estimating Regression Models with Multiplicative Heteroscedasticity.” Econometrica 44 (May): 461–465.CrossRefGoogle Scholar
Heckman, James J. 1991. “Identifying the Hand of Past: Distinguishing State Dependence from Heterogeneity.” American Economic Review 81 (May): 75–79.Google Scholar
Heckman, James J. and Singer, Burton. 1984a. “A Method for Minimizing the Impact of Distributional Assumptions in Econometric Models for Duration Data.” Econometrica 52 (Mar.): 271–320.CrossRefGoogle Scholar
Heckman, James J. and Singer, Burton. 1984b. “The Identifiability of the Proportional Hazards Model.” Review of Economic Studies 51: 231–241.CrossRefGoogle Scholar
Honoré, Bo E. 1990. “Simple Estimation of a Duration Model with Unobserved Heterogeneity.” Econometrica 58 (Mar.): 453–473.CrossRefGoogle Scholar
Hougaard, Philip. 1986. “Survival Models for Heterogeneous Populations Derived from Stable Distributions.” Biometrika 73 (Aug.): 387–396.CrossRefGoogle Scholar
Jorgensen, Bent. 1997. The Theory of Dispersion Models. London: Chapman and Hall.Google Scholar
Kalbfleisch, J. D. and Prentice, Ross L. 1980. The Statistical Analysis of Failure Time Data. New York: Wiley.Google Scholar
King, Gary. 1989. “Event Count Models for International Relations: Generalizations and Applications.” International Studies Quarterly 33: 123–147.CrossRefGoogle Scholar
Laird, Nan, and Oliver, Donald. 1981. “Covariance Analysis of Censored Survival Data Using Log-Linear Analysis Techniques.” Journal of the American Statistical Association 96 (June): 231–240.CrossRefGoogle Scholar
Lancaster, Tony. 1979. “Econometric Methods for Duration of Unemployment.” Econometrica 47: 939–955.CrossRefGoogle Scholar
Lancaster, Tony. 1985. “Generalized Residuals and Heterogenous Duration Models, with Application to the Weibull Model.” Journal of Econometrics 28: 155–169.CrossRefGoogle Scholar
Lancaster, Tony. 1990. The Econometric Analysis of Transition Data. New York: Cambridge University Press.CrossRefGoogle Scholar
Lancaster, Tony, and Nickell, Stephen J. 1980. “The Analysis of Re-Employment Probabilities for the Unemployed (with Discussion).” Journal of the Royal Statistical Society, Series A 143(2): 141–165.CrossRefGoogle Scholar
Larsen, Ulla, and Vaupel, James W. 1993. “Hutterite Fecundability by Age and Parity: Strategies for Frailty Modeling of Event Histories.” Demography 30 (Feb.): 81–102.CrossRefGoogle ScholarPubMed
Manton, Kenneth G., Stallard, Eric, and Vaupel, James W. 1986. “Alternative Models for the Heterogeneity of Mortality Risks Among the Aged.” Journal of the American Statistical Association 81 (Sept.): 635–644.CrossRefGoogle ScholarPubMed
McCarty, Nolan, and Razaghian, Rose. 1999. “Advice and Consent: Senate Responses to Executive Branch Nominations.” American Journal of Political Science 43 (Oct.): 1122–1143.CrossRefGoogle Scholar
McDonald, James B., and Butler, Richard J. 1987. “Some Generalized Mixture Distributions with an Application to Unemployment Duration.” The Review of Economics and Statistics 69 (May): 232–240.CrossRefGoogle Scholar
McQueen, Grant, and Thorley, Steven. 1994. “Bubbles, Stock Returns, and Duration Dependence.” Journal of Financial and Quantitative Analysis 29 (Sept.): 379–401.CrossRefGoogle Scholar
Morrow, James D. 1991. “Alliances and Asymmetry: An Alternative to the Capability Aggregation Model of Alliances.” American Journal of Political Science 35 (Nov.): 904–933.CrossRefGoogle Scholar
Mudambi, Ram, and Taylor, Larry W. 1991. “A Nonparametric Investigation of Duration Dependence in the American Business Cycle: A Note.” Journal of Political Economy 99(3): 654–656.CrossRefGoogle Scholar
Omori, Yasuhiro, and Johnson, Richard A. 1993. “The Influence of Random Effects on the Unconditional Hazard Rate and Survival Functions.” Biometrika 80(4): 910–914.CrossRefGoogle Scholar
Petersen, Trond. 1993. “Recent Advances in Longitudinal Methodology.” Annual Review of Sociology 19: 425–454.CrossRefGoogle Scholar
Reiter, Dan, and Stam, Alan C. III. 1998. “Democracy, War Initiation and Victory.” American Political Science Review 92 (June): 377–389.CrossRefGoogle Scholar
Ridder, Geert. 1990. “The Nonparametric Identification of Generalized Accelerated Failure-Time Models.” Review of Economic Studies 57: 167–182.CrossRefGoogle Scholar
Russett, Bruce. 1993. Grasping the Democratic Peace: Principles for a Post Cold War World. Princeton, NJ: Princeton University Press.Google Scholar
Schemper, Michael. 1992. “Cox Analysis of Survival Data with Non-Proportional Hazard Functions.” The Statistician 41: 455–465.CrossRefGoogle Scholar
Sichel, Daniel E. 1991. “Business Cycle Duration Dependence: A Parametric Approach.” The Review of Economics and Statistics 73 (May): 254–260.CrossRefGoogle Scholar
Silcock, Herbert. 1954. “The Phenomenon of Labor Turnover.” Journal of the Royal Statistical Society, Series A 117 (4): 429–440.CrossRefGoogle Scholar
Vaupel, James W., Manton, Kenneth G., and Stallard, Eric. 1979. “The Impact of Heterogeneity in Individual Frailty on the Dynamics of Mortality.” Demography 16 (Aug.): 439–454.CrossRefGoogle ScholarPubMed
Vermunt, Jeroen K. 1997. Log-Linear Models for Event Histories. Thousand Oaks, CA: Sage.Google Scholar
Vuchinich, Samuel, and Teachman, Jay. 1993. “Influences on the Duration of Wars, Strikes, Riots and Family Arguments.” Journal of Conflict Resolution 37 (Sept.): 544–568.CrossRefGoogle Scholar
Walt, Stephen M. 1987. The Origins of Alliances. Ithaca, NY: Cornell University Press.Google Scholar
Warwick, Paul. 1992. “Rising Hazards: An Underlying Dynamic of Parliamentary Government.” American Journal of Political Science 36 (Nov.): 857–876.CrossRefGoogle Scholar
Warwick, Paul. 1994. Government Survival in Parliamentary Democracies. Cambridge: Cambridge University Press.Google Scholar
Warwick, Paul, and Easton, Stephen T. 1992. “The Cabinet Stability Controversy: New Perspectives on a Classic Problem.” American Journal of Political Science 36 (Feb.): 122–146.CrossRefGoogle Scholar
Werner, Suzanne. 1999. “The Precarious Nature of Peace: Resolving the Issues, Enforcing the Settlement, and Renegotiating the Terms.” American Journal of Political Science 43 (July): 912–934.CrossRefGoogle Scholar
Yamaguchi, Kazuo. 1986. “Alternative Approaches to Unobserved Heterogeneity in the Analysis of Repeatable Events.” In Sociological Methodology 1986, ed. Brandon Tuma, Nancy. Washington, DC: American Sociological Association.Google Scholar
Zuehlke, Thomas W. 1987. “Duration Dependence in the Housing Market.” The Review of Economics and Statistics 69: 701–709.CrossRefGoogle Scholar