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Nonparametric Identification of Dynamic Models with Unobserved State Variables

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Yingyao Hu
Matthew Shum

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Abstract

We consider the identification of a Markov process {Wt,Xt*} for t = 1, 2, ... , T when only {Wt} for t = 1, 2, ... , T is observed. In structural dynamic models, Wt denotes the sequence of choice variables and observed state variables of an optimizing agent, while Xt* denotes the sequence of serially correlated unobserved state variables. The Markov setting allows the distribution of the unobserved state variable Xt* to depend on Wt-1 and Xt-1*. We show that the joint distribution f Wt, Xt*, Wt-1, Xt-1* is identified from the observed distribution f Wt+1, Wt, Wt-1, Wt-2, Wt-3 under reasonable assumptions. Identification of f Wt, Xt*, Wt-1, Xt-1* is a crucial input in methodologies for estimating dynamic models based on the "conditional-choice-probability (CCP)" approach pioneered by Hotz and Miller.

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Paper provided by The Johns Hopkins University,Department of Economics in its series Economics Working Paper Archive with number 543.

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Date of creation: Apr 2008
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Handle: RePEc:jhu:papers:543

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  1. Yingyao Hu & Matthew Shum, 2008. "Identifying Dynamic Games with Serially-Correlated Unobservables," Economics Working Paper Archive 546, The Johns Hopkins University,Department of Economics. [Downloadable!]
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