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On the Identification of Nonparametric Structural Models

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Latent Variable Modeling and Applications to Causality

Part of the book series: Lecture Notes in Statistics ((LNS,volume 120))

Abstract

In this paper we study the identification of nonparametric models, that is, models in which both the functional forms of the equations and the probability distributions of the disturbances remain unspecified. Identifiability in such models does not mean uniqueness of structural parameters but rather uniqueness of policy-related predictions that such parameters would normally support.

We provide sufficient and necessary conditions for identifying predictions of the type “Find the distribution of Y, assuming thatXis controlled by external intervention,” where Y andXare arbitrary variables of interest. Whenever identifiable, such predictions can be expressed in closed algebraic form, in terms of observed distributions. We also show how the identifying criteria can be tested qualitatively using the graphical representation of the structural model, thus simplifying and generalizing the standard identifiability tests of linear models (e.g., rank and order). Finally, we provide meaningful and precise definitions of effect decomposition for both parametric and nonparametric models.

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Author information

Authors and Affiliations

  1. Cognitive Systems Laboratory, Computer Science Department University of California, Los Angeles, 90024, USA

    Judea Pearl

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  1. Judea Pearl
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Editors and Affiliations

  1. Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA

    Maia Berkane

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© 1997 Springer-Verlag New York, Inc.

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Pearl, J. (1997). On the Identification of Nonparametric Structural Models. In: Berkane, M. (eds) Latent Variable Modeling and Applications to Causality. Lecture Notes in Statistics, vol 120. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1842-5_3

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  • DOI: https://doi.org/10.1007/978-1-4612-1842-5_3

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-94917-8

  • Online ISBN: 978-1-4612-1842-5

  • eBook Packages: Springer Book Archive

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