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Beyond Correlation: Measuring Interdependence Through Complementarities

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  • Margaret Meyer
  • Bruno Strulovici

Abstract

Given two sets of random variables, how can one determine whether the former variables are more interdependent than the latter? This question is of major importance to economists, for example, in comparing how various policies affect systemic risk or income inequality. Moreover,correlation is ill-suited to this task as it is typically not justified by any economic objective. Economists' interest in interdependence often stems from complementarities (or substitutabilities) in the environment they analyze. This paper studies interdependence using supermodular objective functions: these functions treat their variables as complements, and their expectation increases as the realizations of the variables become more aligned. The supermodular ordering has a linear structure, which we exploit to obtain tractable characterizations and methods for comparing multivariate distributions, and extend when objective functions are also monotonic or symmetric. We also provide suffcient conditions for comparing random variables generated by common and idiosyncratic shocks or by heterogeneous lotteries, and illustrate our methods with several applications. Revised August 2015

Suggested Citation

  • Margaret Meyer & Bruno Strulovici, 2013. "Beyond Correlation: Measuring Interdependence Through Complementarities," Economics Series Working Papers 655, University of Oxford, Department of Economics.
  • Handle: RePEc:oxf:wpaper:655
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    Cited by:

    1. Veli Safak, 2020. "Matching Multidimensional Types: Theory and Application," Papers 2006.14243, arXiv.org.
    2. Kızıldemir, Bünyamin & Privault, Nicolas, 2015. "Supermodular ordering of Poisson arrays," Statistics & Probability Letters, Elsevier, vol. 98(C), pages 136-143.

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    More about this item

    Keywords

    Interdependence; Supermodularity; Correlation; Copula; Mixture; Majorization; Tournament;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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