The purpose of this paper is to propose a new empirical model capable of highlighting some aspects of cross-economy convergence which cannot be caught by the popular beta-convergence and sigma-convergence models. The idea is to analyse the growth of the economies as a function of the distance between the observed output per capita and the average output per capita within the sample, separating the behaviour of poorest and richest economies. After its specification, I applied the model to the case of the Russian regions over the period 1995-2015 using the fixed-effect estimator. The results show that, although the existence of a significant beta-convergence process, there is a lack of convergence in differences. When the differences between regional and national output per capita are negative, a positive and significant relationship between growth and levels emerges. Such a relationship turns to be negative and non-significant when the differences are positive, therefore denoting weak non-linearity between growth rate and level of output per capita. Similar findings have been found for labor productivity.