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Path, Phat, and State Dependence in Observation-driven Markov Walker, Robert Uploaded 07-17-2007 Keywords Markov models qualitative time series ergodic theorem Abstract Many social science theories posit dynamics that depend in important ways on the present state and focus on a reasonably small number of states. Despite the importance of theoretical notions of path dependence, empirical models, with a few exceptions (Alvarez, Cheibub, Limongi and Przewroski 2000; Epstein, Bates, Goldstein, O'Halloryn, and Kristensen 2006; Beck. Jackman, Epstein, and O'Halloryn 2001), have paid little attention to the implications of state dependence for empirical studies. This despite the fact that there are many possible ways in which history might matter -- we focus on the categorization given by Page (2006) -- and these different ways that history might matter manifest themselves in sets of models that can be tested and compared. This paper considers the basic properties of observation-driven Markov chains [stationarity/time homogeneity, communication, transience, periodicity, irreducibility, and ergodicity] and the issues that arise in their implementation as likelihood estimators to provide a window into methods for the study of path dependence. Application of these concepts to longitudinal data on human rights abuses and exchange rate regime transitions provides evidence that history may also not exert uniform effects. The empirical examples highlight the subtle substantive assumptions that manifest in different modeling choices. The human rights example calls for an important qualification in the widely studied relationship between democracy and human rights abuses. The exchange rate regime example highlights the usefulness of Markov models for multinomial processes.