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A Look Inside the Box: Combining Aggregate and Marginal Distributions to Identify Joint Distributions

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  • Marie-Hélène Felt

Abstract

This paper proposes a method for estimating the joint distribution of two or more variables when only their marginal distributions and the distribution of their aggregates are observed. Nonparametric identification is achieved by modelling dependence using a latent common-factor structure. Multiple examples are given of data settings where multivariate samples from the joint distribution of interest are not readily available, but some aggregate measures are observed. In the application, intra-household distributions are recovered by combining individual-level and household-level survey data. I show that, for individuals living in couple relationships, personal cash-management practices are significantly influenced by the partner's use of cash and stored-value cards. This finding implies that, for some methods of payment at least, ignoring the partner's impact might lead to spurious regression results due to an omitted variable bias.

Suggested Citation

  • 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.
    • Handle: RePEc:bca:bocawp:18-29
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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.
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    3. Carlos Arango & Angelika Welte, 2012. "The Bank of Canada’s 2009 Methods-of-Payment Survey: Methodology and Key Results," Discussion Papers 12-6, Bank of Canada.
    4. Heng Chen & Marie-Hélène Felt & Kim P. Huynh, 2017. "Retail payment innovations and cash usage: accounting for attrition by using refreshment samples," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(2), pages 503-530, February.
    5. Carlos Arango & Kim Huynh & Ben Fung & Gerald Stuber, 2012. "The Changing Landscape for Retail Payments in Canada and the Implications for the Demand for Cash," Bank of Canada Review, Bank of Canada, vol. 2012(Autumn), pages 31-40.
    6. William J. Baumol, 1952. "The Transactions Demand for Cash: An Inventory Theoretic Approach," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 66(4), pages 545-556.
    7. Evdokimov, Kirill & White, Halbert, 2012. "Some Extensions Of A Lemma Of Kotlarski," Econometric Theory, Cambridge University Press, vol. 28(4), pages 925-932, August.
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    9. Ben Fung & Kim Huynh & Gerald Stuber, 2015. "The Use of Cash in Canada," Bank of Canada Review, Bank of Canada, vol. 2015(Spring), pages 45-56.
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    12. Ben Fung & Kim Huynh & Leonard Sabetti, 2012. "The Impact of Retail Payment Innovations on Cash Usage," Staff Working Papers 12-14, Bank of Canada.
    13. Christopher Henry & Kim Huynh & Rallye Shen, 2015. "2013 Methods-of-Payment Survey Results," Discussion Papers 15-4, Bank of Canada.
    14. Li, Tong & Vuong, Quang, 1998. "Nonparametric Estimation of the Measurement Error Model Using Multiple Indicators," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 139-165, May.
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    Cited by:

    1. Marie-Hélène Felt & David Laferrière, 2020. "Sample Calibration of the Online CFM Survey," Technical Reports 118, Bank of Canada.
    2. Felt, Marie-Hélène, 2020. "On the identification of joint distributions using marginals and aggregates," Economics Letters, Elsevier, vol. 194(C).

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    More about this item

    Keywords

    Bank notes; Digital Currencies; Econometric and statistical methods;
    All these keywords.

    JEL classification:

    • C - Mathematical and Quantitative Methods
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • D14 - Microeconomics - - Household Behavior - - - Household Saving; Personal Finance
    • E41 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Demand for Money

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