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Copulas in Econometrics


  • Yanqin Fan

    () (Department of Economics, University of Washington, Seattle, Washington 98195)

  • Andrew J. Patton

    (Department of Economics, Duke University, Durham, North Carolina 27708-0097)


Copulas are functions that describe the dependence between two or more random variables. This article provides a brief review of copula theory and two areas of economics in which copulas have played important roles: multivariate modeling and partial identification of parameters that depend on the joint distribution of two random variables with fixed or known marginal distributions. We focus on bivariate copulas but provide references on recent advances in constructing higher-dimensional copulas.

Suggested Citation

  • Yanqin Fan & Andrew J. Patton, 2014. "Copulas in Econometrics," Annual Review of Economics, Annual Reviews, vol. 6(1), pages 179-200, August.
  • Handle: RePEc:anr:reveco:v:6:y:2014:p:179-200

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    3. Anne Opschoor & André Lucas & Istvan Barra & Dick van Dijk, "undated". "Closed-Form Multi-Factor Copula Models with Observation-Driven Dynamic Factor Loadings," Tinbergen Institute Discussion Papers 19-013/IV, Tinbergen Institute.
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    8. Diego Caballero & André Lucas & Bernd Schwaab & Xin Zhang, 2019. "Risk endogeneity at the lender/investor-of-last-resort," BIS Working Papers 766, Bank for International Settlements.
    9. Jozef Barun'ik & Tobias Kley, 2015. "Quantile Coherency: A General Measure for Dependence between Cyclical Economic Variables," Papers 1510.06946,, revised Dec 2018.
    10. Martyna Kobus & Radoslaw Kurek, 2017. "Copula-based measurement of interdependence for discrete distributions," Working Papers 431, ECINEQ, Society for the Study of Economic Inequality.
    11. Souhaib Ben Taieb & James W. Taylor & Rob J. Hyndman, 2017. "Coherent Probabilistic Forecasts for Hierarchical Time Series," Monash Econometrics and Business Statistics Working Papers 3/17, Monash University, Department of Econometrics and Business Statistics.

    More about this item


    Sklar’s theorem; multivariate models; Fréchet-Hoeffding inequality; bounds;

    JEL classification:

    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation


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