We consider a large class of semi-parametric models for recurrent events based on virtual ages. Modeling recurrent events lifetime data using virtual age models has a long history. This rich class of model contains standard model families as non-homogeneous Poisson processes and renewal processes and may include covariates or random effects (see for instance Pena (2006, Statistical Science) for a large overview on these models). In many non- or semi-parametric works the virtual age function is supposed to be known, this weakness can be overcome by parameterizing the virtual age function (see for instance Doyen and Gaudoin, 2004, Reliability Engineering and System Safety). Then the model consists of an unknown hazard rate function, the infinite-dimensional parameter of the model, and a parametrically specified virtual age (or effective) function. Recently Beutner, Bordes and Doyen (2017, Bernoulli) derived conditions on the family of effective age functions under which the profile likelihood inference method for the finite-dimensional parameter of the model leads to inconsistent estimates. Here we show how to overcome the failure of the profile likelihood method by smoothing the pseudo-estimator of the infinite-dimensional parameter of the model, by adapting a method proposed by Zeng and Lin (2007, Journal of the American Statistical Association) for the accelerated failure time model.