Dependence Measures in Bivariate Gamma Frailty Models

36 Pages Posted: 12 Apr 2014

See all articles by Gerard J. van den Berg

Gerard J. van den Berg

VU University Amsterdam - Department of Economics; Centre for Economic Policy Research (CEPR); IZA Institute of Labor Economics; Tinbergen Institute

Georgios Effraimidis

Qualcomm, Inc.


Bivariate duration data frequently arise in economics, biostatistics and other areas. In "bivariate frailty models", dependence between the frailties (i.e., unobserved determinants) induces dependence between the durations. Using notions of quadrant dependence, we study restrictions that this imposes on the implied dependence of the durations, if the frailty terms act multiplicatively on the corresponding hazard rates. Marginal frailty distributions are often taken to be gamma distributions. For such cases we calculate general bounds for two association measures, Pearson's correlation coefficient and Kendall's tau. The results are employed to compare the flexibility of specific families of bivariate gamma frailty distributions.

Keywords: bivariate gamma distribution, duration models, competing risks, Kendall's tau, negative and positive quadrant dependence, Pearson's correlation coefficient, unobserved heterogeneity, survival analysis

JEL Classification: C41, C51, C34, C33, C32, J64

Suggested Citation

van den Berg, Gerard J. and Effraimidis, Georgios, Dependence Measures in Bivariate Gamma Frailty Models. IZA Discussion Paper No. 8083. Available at SSRN:

Gerard J. Van den Berg (Contact Author)

VU University Amsterdam - Department of Economics ( email )

De Boelelaan 1105
1081 HV Amsterdam
+31 20 444 6132 (Phone)
+32 20 444 6020 (Fax)

Centre for Economic Policy Research (CEPR)

United Kingdom

IZA Institute of Labor Economics

P.O. Box 7240
Bonn, D-53072

Tinbergen Institute

Burg. Oudlaan 50
Rotterdam, 3062 PA

Georgios Effraimidis

Qualcomm, Inc. ( email )

5775 Morehouse Dr
San Diego, CA 92121
United States

Register to save articles to
your library


Paper statistics

Abstract Views
PlumX Metrics