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Defining and Modeling State-Dependent Dynamic Systems

Published online by Cambridge University Press:  04 January 2017

Justin Esarey*
Department of Political Science, Rice University, 105 Herzstein Hall, 6100 Main Street, Houston, TX 77005
Jacqueline H. R. DeMeritt
Department of Political Science, University of North Texas, 1155 Union Circle #305340, Denton, TX 76203
e-mail: (corresponding author)


A state-dependent dynamic system is one in which (1) the marginal effect of x on y at time t () depends on the prior value of the dependent variable , and (2) the persistence of the dependent variable () depends on xt. We present a methodological strategy for dealing with state-dependent dynamic systems and demonstrate the consequences of ignoring state-dependence. As an applied example, we find evidence of state-dependence in the relationship between presidential approval and economic performance: high unemployment rates are most damaging to presidential approval among presidents with the highest initial approval ratings.

Research Article
Copyright © The Author 2013. Published by Oxford University Press on behalf of the Society for Political Methodology 

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Authors' note: The authors thank Matt Lebo, Ashley Leeds, Ric Stoll, Cliff Morgan, Randy Stevenson, two anonymous reviewers, and participants at the 2011 Annual Meeting of the Society for Political Methodology for helpful comments and suggestions about our paper. Supplementary materials for this article are available on the Political Analysis Web site.


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