This paper suggests that the main (and possibly unique) source of beta- and sigma-convergence in GDP per worker (i.e. labor productivity) across Italian regions over the 1980-2004 period is the change in technical and allocative efficiency, i.e. convergence in relative TFP levels. To obtain this result, I construct an approximation of the production frontier at different points in time using Data Envelope Analysis (DEA), and measure efficiency as the output-based distance from the frontier. This method is entirely data-driven, and does not require the specification of any particular functional form for technology. Changes in GDP per worker can be decomposed into changes in relative efficiency, changes due to overall technological progress, and changes due to capital deepening. My results suggest that: (i) differences in relative TFP are quantitatively important; (ii) while technological progress and capital deepening are the main, and equally important, forces behind the rightward shift in the distribution of GDP per worker, convergence in relative TFP is the main determinant of the change in its shape.