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Entropic Latent Variable Integration via Simulation

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  • Susanne M. Schennach

    () (Institute for Fiscal Studies and Brown University)

Abstract

This paper introduces a general method to convert a model defined by moment conditions involving both observed and unobserved variables into equivalent moment conditions involving only observable variables. This task can be accomplished without introducing infinite-dimensional nuisance parameters using a least-favourable entropy-maximising 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 GMM-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.

Suggested Citation

  • Susanne M. Schennach, 2013. "Entropic Latent Variable Integration via Simulation," CeMMAP working papers CWP32/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:32/13
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    File URL: http://www.cemmap.ac.uk/wps/cwp321313.pdf
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    References listed on IDEAS

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    1. 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.
    2. S. M. Schennach & Yingyao Hu, 2013. "Nonparametric Identification and Semiparametric Estimation of Classical Measurement Error Models Without Side Information," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 177-186, March.
    3. 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.
    4. Golan, Amos & Judge, George G. & Miller, Douglas, 1996. "Maximum Entropy Econometrics," Staff General Research Papers Archive 1488, Iowa State University, Department of Economics.
    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. Yuichi Kitamura, 2001. "Asymptotic Optimality of Empirical Likelihood for Testing Moment Restrictions," Econometrica, Econometric Society, vol. 69(6), pages 1661-1672, November.
    7. Susanne M Schennach, 2007. "Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models," Econometrica, Econometric Society, vol. 75(1), pages 201-239, January.
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    Cited by:

    1. Isaiah Andrews & Anna Mikusheva, 2016. "Conditional Inference With a Functional Nuisance Parameter," Econometrica, Econometric Society, vol. 84, pages 1571-1612, July.
    2. Manuel Arellano & St├ęphane Bonhomme, 2015. "Nonlinear Panel Data Estimation via Quantile Regression," Working Papers wp2015_1505, CEMFI.
    3. Komunjer, Ivana & Ragusa, Giuseppe, 2016. "Existence And Characterization Of Conditional Density Projections," Econometric Theory, Cambridge University Press, vol. 32(04), pages 947-987, August.
    4. Firpo, Sergio & Galvao, Antonio F. & Song, Suyong, 2017. "Measurement errors in quantile regression models," Journal of Econometrics, Elsevier, vol. 198(1), pages 146-164.
    5. Susanne M. Schennach, 2012. "Measurement error in nonlinear models - a review," CeMMAP working papers CWP41/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. Susanne M. Schennach, 2013. "Convolution without independence," CeMMAP working papers CWP46/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

    More about this item

    Keywords

    method of moments; latent variables; unobservables; partial indentification; entropy; simulations; least-favourable family;

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