Semiparametric estimation of Markov decision processeswith continuous state space

Oliver Linton and Sorawoot Srisuma

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: We propose a general two-step estimation method for the structural parameters of popular semiparametric Markovian discrete choice models that include a class of Markovian Games and allow for continuous observable state space. The estimation procedure is simple as it directly generalizes the computationally attractive methodology of Pesendorfer and Schmidt-Dengler (2008) that assumed finite observable states. This extension is non-trivial as the value functions, to be estimated nonparametrically in the first stage, are defined recursively in a non-linear functional equation. Utilizing structural assumptions, we show how to consistently estimate the infinite dimensional parameters as the solution to some type II integral equations, the solving of which is a well-posed problem. We provide sufficient set of primitives to obtain root-T consistent estimators for the finite dimensional structural parameters and the distribution theory for the value functions in a time series framework.

Keywords: discrete Markov decision models; kernel smoothing; Markovian games; semi-parametric estimation; well-posed inverse problem.D (search for similar items in EconPapers)
JEL-codes: J1 (search for similar items in EconPapers)
Pages: 59 pages
Date: 2010-08
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http://eprints.lse.ac.uk/58187/ Open access version. (application/pdf)

Related works:
Journal Article: Semiparametric estimation of Markov decision processes with continuous state space (2012)
Working Paper: Semiparametric Estimation of Markov Decision Processeswith Continuous State Space (2010)
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