This article deals with heterogeneity and spatial dependence in economic growth analysis by developing a two‐stage strategy that identifies clubs by a mapping analysis and estimates a club convergence model with spatial dependence. Since estimation of this class of convergence models in the presence of regional heterogeneity poses both identification and collinearity problems, we develop an entropy‐based estimation procedure that simultaneously takes account of ill‐posed and ill‐conditioned inference problems. The two‐step strategy is applied to assess the existence of club convergence and to estimate a two‐club spatial convergence model across Italian regions over the period 1970 to 2000.