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On the identification of joint distributions using marginals and aggregates

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  • Felt, Marie-Hélène

Abstract

A data combination approach is proposed to identify variables’ joint distribution when only their marginals and the distribution of their sum are known. Nonparametric identification is achieved by modelling dependence using a latent common-factor structure. A variation of the well-known Lemma of Kotlarski (Kotlarski,1967) is established. Potential applications are proposed where aggregated data help identify within-household or longitudinal distributions in the absence of intra-household or panel data, respectively.

Suggested Citation

  • Felt, Marie-Hélène, 2020. "On the identification of joint distributions using marginals and aggregates," Economics Letters, Elsevier, vol. 194(C).
    • Handle: RePEc:eee:ecolet:v:194:y:2020:i:c:s016517652030269x
    DOI: 10.1016/j.econlet.2020.109431
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    References listed on IDEAS

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    1. Linton, Oliver & Whang, Yoon-Jae, 2002. "Nonparametric Estimation With Aggregated Data," Econometric Theory, Cambridge University Press, vol. 18(2), pages 420-468, April.
    2. Manuel Arellano & Stéphane Bonhomme, 2016. "Nonlinear panel data estimation via quantile regressions," Econometrics Journal, Royal Economic Society, vol. 19(3), pages 61-94, October.
    3. Marie-Hélène Felt, 2018. "A Look Inside the Box: Combining Aggregate and Marginal Distributions to Identify Joint Distributions," Staff Working Papers 18-29, Bank of Canada.
    4. Stéphane Bonhomme & Jean-Marc Robin, 2010. "Generalized Non-Parametric Deconvolution with an Application to Earnings Dynamics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(2), pages 491-533.
    5. Hu, Yingyao & Sasaki, Yuya, 2015. "Closed-form estimation of nonparametric models with non-classical measurement errors," Journal of Econometrics, Elsevier, vol. 185(2), pages 392-408.
    6. Evdokimov, Kirill & White, Halbert, 2012. "Some Extensions Of A Lemma Of Kotlarski," Econometric Theory, Cambridge University Press, vol. 28(4), pages 925-932, August.
    7. Schennach, Susanne M., 2019. "Convolution without independence," Journal of Econometrics, Elsevier, vol. 211(1), pages 308-318.
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    Cited by:

    1. Li, Jiaqi, 2023. "Predicting the demand for central bank digital currency: A structural analysis with survey data," Journal of Monetary Economics, Elsevier, vol. 134(C), pages 73-85.

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