Correct Specification and Identification of Nonparametric Transformation Models

Chiappori, Pierre‐André; Komunjer, Ivana

doi:10.2139/ssrn.1533512

Cited by 7 publications

(10 citation statements)

References 30 publications

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“…This expression shows that when ε ≡ 0, the model is mathematically identical to the well studied transformation model (Ekeland, Heckman, and Nesheim (2004), Chiappori and Komunjer (2008)). Appendix C.1 uses results from Chiappori and Komunjer (2008) to formally derive conditions under which any distribution F XZ can be rationalized.…”

Section: Limitations Of Sorting Patternsmentioning

confidence: 67%

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Latent indices in assortative matching models

Diamond

Agarwal

2017

Quantitative Economics

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A large class of two-sided matching models that include both transferable and non-transferable utility result in positive assortative matching along a latent index. Data from matching markets, however, may not exhibit perfect assortativity due to the presence of unobserved characteristics. This paper studies the identification and estimation of such models. We show that the distribution of the latent index is not identified when data from one-to-one matches are observed. Remarkably, the model is nonparametrically identified using data in a single large market when each agent on one side has at least two matched partners. The additional empirical content in many-to-one matches is demonstrated using simulations and stylized examples. We then derive asymptotic properties of a minimum distance estimator as the size of the market increases, allowing estimation using dependent data from a single large matching market. The nature of the dependence requires modification of existing empirical process techniques to obtain a limit theorem.

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Section: Limitations Of Sorting Patternsmentioning

confidence: 67%

“…Appendix C.1 uses results from Chiappori and Komunjer (2008) to formally derive conditions under which any distribution F XZ can be rationalized.…”

Section: Limitations Of Sorting Patternsmentioning

confidence: 99%

Latent indices in assortative matching models

Diamond

Agarwal

2017

Quantitative Economics

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“…Proof. The proof proceeds by re-writing the matching model with " 0 as a transformation model of Chiappori and Komunjer (2008), which they show is correctly speci…ed. See Appendix A.3 for details.…”

Section: Limitations Of Sorting Patterns: a Negative Resultsmentioning

confidence: 93%

Identification and Estimation in Two-Sided Matching Markets

Agarwal

Diamond

2013

SSRN Journal

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We study estimation and non-parametric identi…cation of preferences in two-sided matching markets using data from a single market with many agents. We consider a model in which preferences of each side of the market are vertical, utility is nontransferable and the observed matches are pairwise stable. We show that preferences are not identi…ed with data on one-to-one matches but are non-parametrically iden-ti…ed when data from many-to-one matches are observed. The additional empirical content in many-to-one matches is illustrated by comparing two simulated objective functions, one that does and the other that does not use information available in manyto-one matching. We also prove consistency of a method of moments estimator for a parametric model under a data generating process in which the size of the matching market increases, but data only on one market is observed. Since matches in a single market are interdependent, our proof of consistency cannot rely on observations of independent matches. Finally, we present Monte Carlo studies of a simulation based estimator.

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“…Horowitz (1996) and Chiappori and Komunjer (2009) analyzed the semiparametric and nonparametric identification of transformation models. They do not rely on tail conditions like our sufficient conditions, but instead assume continuous variation in the covariates.…”

Section: Conclusion and Extensionsmentioning

confidence: 99%

Regular Variation and the Identification of Generalized Accelerated Failure-Time Models

Abbring

Ridder

2011

SSRN Journal

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Ridder (1990) provides an identification result for the Generalized AcceleratedFailure-Time (GAFT) model. We point out that Ridder's proof of this result is incomplete, and provide an amended proof with an additional necessary and sufficient condition that requires that a function varies regularly at 0 and ∞. We also give more readily interpretable sufficient conditions on the tails of the error distribution or the asymptotic behavior of the transformation of the dependent variable. The sufficient conditions are shown to encompass all previous results on the identification of the Mixed Proportional Hazards (MPH) model. Thus, this paper not only clarifies, but also unifies the literature on the non-parametric identification of the GAFT and MPH models.

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Correct Specification and Identification of Nonparametric Transformation Models

Cited by 7 publications

References 30 publications

Latent indices in assortative matching models

Latent indices in assortative matching models

Identification and Estimation in Two-Sided Matching Markets

Regular Variation and the Identification of Generalized Accelerated Failure-Time Models

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