Title:      Path, Phat, and State Dependence in
Observation-driven Markov 

Authors:    Robert Walker

Entrydate:  2007-07-17 23:04:11

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.

http://polmeth.wustl.edu/retrieve.php?id=712