The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd


  • Pravin K. Trivedi
Reference work entry


Copulas are functional forms that parameterize the joint distribution of random variables based on their stated marginal distributions and a dependence parameter. The approach is based on Sklar’s theorem. Copulas provide a general method for modelling dependence between random variables that may exhibit asymmetric dependence, which is often inadequately captured by measures of linear dependence. Copulas are often generated by using mixtures and convex sums. Although a bivariate distribution is the most commonly encountered specification, higher dimensional joint distributions can also be generated.


Clayton copula Copulas Cumulative distribution functions GARCH effects Gaussian copula Gumbel copula Marginal distributions Selection models Sklar, A. Sklar’s theorem Tail dependence 

JEL Classifications

C1; C51 
This is a preview of subscription content, log in to check access.


  1. Cherubini, U., E. Luciano, and W. Vecchiato. 2004. Copula methods in finance. New York: John Wiley.CrossRefGoogle Scholar
  2. Joe, H. 1997. Multivariate models and dependence concepts. London: Chapman and Hall.CrossRefGoogle Scholar
  3. Nelsen, R. 1999. An introduction to copulas. New York: Springer.CrossRefGoogle Scholar
  4. Patton, A. 2006. Estimation of multivariate models for time series of possibly different lengths. Journal of Applied Econometrics 21: 147–173.CrossRefGoogle Scholar
  5. Sklar, A. 1973. Random variables, joint distributions, and copulas. Kybernetica 9: 449–460.Google Scholar
  6. Sklar, A. 1996. Random variables, distribution functions, and copulas – a personal look backward and forward. In Distributions with fixed marginals and related topics, ed. L. Ruschendorf, B. Schweizer, and M. Taylor. Hayward: Institute of Mathematic Statistics.Google Scholar
  7. Smith, M. 2003. Modeling selectivity using Archimedean copulas. Econometrics Journal 6: 99–123.CrossRefGoogle Scholar
  8. Zimmer, D., and P. Trivedi. 2006. Using trivariate copulas to model sample selection and treatment effects: Application to family health care demand. Journal of Business and Economic Statistics 24: 63–76.CrossRefGoogle Scholar

Copyright information

© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Pravin K. Trivedi
    • 1
  1. 1.