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Entropic Latent Variable Integration via Simulation

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  • Susanne M. Schennach

Abstract

This paper introduces a general method to convert a model defined by moment conditions that involve both observed and unobserved variables into equivalent moment conditions that involve only observable variables. This task can be accomplished without introducing infinite‐dimensional nuisance parameters using a least favorable entropy‐maximizing distribution. We demonstrate, through examples and simulations, that this approach covers a wide class of latent variables models, including some game‐theoretic models and models with limited dependent variables, interval‐valued data, errors‐in‐variables, or combinations thereof. Both point‐ and set‐identified models are transparently covered. In the latter case, the method also complements the recent literature on generic set‐inference methods by providing the moment conditions needed to construct a generalized method of moments‐type objective function for a wide class of models. Extensions of the method that cover conditional moments, independence restrictions, and some state‐space models are also given.

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File URL: http://hdl.handle.net/10.3982/ECTA9748
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Bibliographic Info

Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 82 (2014)
Issue (Month): 1 (01)
Pages: 345-385

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Handle: RePEc:wly:emetrp:v:82:y:2014:i:1:p:345-385

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  1. Yuichi Kitamura, 2001. "Asymptotic Optimality of Empirical Likelihood for Testing Moment Restrictions," Econometrica, Econometric Society, vol. 69(6), pages 1661-1672, November.
  2. Charles F. Manski & Elie Tamer, 2002. "Inference on Regressions with Interval Data on a Regressor or Outcome," Econometrica, Econometric Society, vol. 70(2), pages 519-546, March.
  3. Susanne M Schennach, 2007. "Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models," Econometrica, Econometric Society, vol. 75(1), pages 201-239, 01.
  4. Gerda Claeskens, 2004. "Restricted likelihood ratio lack-of-fit tests using mixed spline models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(4), pages 909-926.
  5. Canay, Ivan A., 2010. "EL inference for partially identified models: Large deviations optimality and bootstrap validity," Journal of Econometrics, Elsevier, vol. 156(2), pages 408-425, June.
  6. Golan, Amos & Judge, George G. & Miller, Douglas, 1996. "Maximum Entropy Econometrics," Staff General Research Papers 1488, Iowa State University, Department of Economics.
  7. Susanne Schennach & Yingyao Hu, 2012. "Nonparametric identification and semiparametric estimation of classical measurement error models without side information," CeMMAP working papers CWP40/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  8. repec:cup:cbooks:9780521496032 is not listed on IDEAS
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Cited by:
  1. Susanne Schennach, 2013. "Convolution without independence," CeMMAP working papers CWP46/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  2. 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.

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