Modelling the dependence between the times to international adoption of two related technologies

The structure of the dependence between the times to adoption by a country of two related innovations, the fax and the cellular telephone, is modelled in two stages. The first stage is the choice of density function for the time to adoption. The second stage is describing the dependence relation. For the first stage, a Weibull density function is used with its scale factor adapted to account for the economic and technological environments in different countries. Environmental data are collected from several sources. Copulas are used to model the dependence relation, three single parameter copulas are considered, those due to Farlie-Gumbel-Morgenstern (FGM), Frank and Plackett. Their properties are described and a combined estimation of the copula and density function parameters carried out. The limitations of the FGM copula rule it out from further consideration. The other copulas coupled with the Weibull, using eight environmental variables, are shown to provide valuable insights into the effects of environmental variables on adoption times. Given that a country has adopted one technology, the model of the dependence relation is used to provide the conditional density of the time to adoption of the other technology.