The paper aims at providing a suitable measure of total factor productivity levels by introducing a mapping structure within the regional conditional convergence framework. Our goal is twofold. First, we introduce an endogenous spatial representation of unobserved fixed effects in the conditional convergence process. Second, we develop a generalized maximum entropy estimation procedure in order to improve the efficiency of the estimates and to account for ill-posed and ill-conditioned inference problems. The proposed approach is applied to assess the existence of catching-up across Italian regions over the period 1960-1996 and to identify the effects of technology and geographic spillovers on the determination of TFP levels.