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Nonparametric identification of dynamic models with unobserved state variables

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  • Yingyao Hu
  • Matthew Shum

Abstract

We consider the identification of a Markov process {W t, X t*} for t=1,2,...,T when only {W t} for t=1, 2,..,T is observed. In structural dynamic models, W t denotes the sequence of choice variables and observed state variables of an optimizing agent, while X t* denotes the sequence of serially correlated state variables. The Markov setting allows the distribution of the unobserved state variable X t* to depend on W t-1 and X t-1 *. We show that the joint distribution of (W t, X t*, W t-1 , X t-1 *) is identified from the observed distribution of (W t+1 , W t, W t-1 , W t-2 , W t-3 ) under reasonable assumptions. Identification of the joint distribution of (W t, X t*, W t-1 , X t-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 Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP13/08.

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Date of creation: May 2008
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Handle: RePEc:ifs:cemmap:13/08

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Cited by:
  1. Jason R. Blevins, 2011. "Sequential Monte Carlo Methods for Estimating Dynamic Microeconomic Models," Working Papers 11-01, Ohio State University, Department of Economics.
  2. Yingyao Hu & Matthew Shum, 2008. "Nonparametric Identification of Dynamic Models with Unobserved State Variables," Economics Working Paper Archive 543, The Johns Hopkins University,Department of Economics.
  3. Yingyao Hu & Yutaka Kayaba & Matt Shum, 2010. "Nonparametric learning rules from bandit experiments: the eyes have it!," CeMMAP working papers CWP15/10, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. Susanne Schennach, 2012. "Measurement error in nonlinear models- a review," CeMMAP working papers CWP41/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  5. Hanming Fang & Edward Kung, 2012. "Why Do Life Insurance Policyholders Lapse? The Roles of Income, Health and Bequest Motive Shocks," PIER Working Paper Archive 12-006, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  6. Shiu, Ji-Liang, 2014. "An alternative identification of nonlinear dynamic panel data models with unobserved covariates," Economics Letters, Elsevier, vol. 122(2), pages 338-342.
  7. Patrick Bajari & Chenghuan Sean Chu & Denis Nekipelov & Minjung Park, 2013. "A Dynamic Model of Subprime Mortgage Default: Estimation and Policy Implications," NBER Working Papers 18850, National Bureau of Economic Research, Inc.
  8. Zhou, Yiyi, 2012. "Failure to Launch in Two-Sided Markets: A Study of the U.S. Video Game Market," MPRA Paper 42002, University Library of Munich, Germany.
  9. Yingyao Hu & Matthew Shum & Wei Tan, 2010. "A Simple Estimator for Dynamic Models with Serially Correlated Unobservables," Economics Working Paper Archive 558, The Johns Hopkins University,Department of Economics.
  10. Yingyao Hu & Matthew Shum, 2008. "Identifying Dynamic Games with Serially-Correlated Unobservables," Economics Working Paper Archive 546, The Johns Hopkins University,Department of Economics.

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