Erdem and Tybout (2003) deal with these limitations, albeit using artificial data. Their analysis is

J. Tybout Economic Development 570B Lecture 25 December 4, 2003 A number of studies have found that plant sizes tend to shrink in the face of heightened foreign competition, just as the Melitz model predicts. Nonetheless, the effects on scale efficiency are quite modest. The reason is that most of the adjustment in total domestic output comes from large firms that are operating in the flat portion of their average cost curves. exp: Mexico Using plant-level panel data and econometrically estimated cost or production functions, It is possible to decompose industry-wide growth in average cost or total factor productivity into the effects of better scale economy exploitation, reallocation of market shares toward more efficient firms, and a residual, which reflects intra-plant improvements in efficiency. (In the case of cost functions the residual also reflects changes in relative prices.) (graphs of scale economies here) Decomposition of Average Cost and Productivity Growth in Mexico, 1984 – 1990 Average Cost Growth (Percentages) Scale Effect Share Effect Residual Effect Total Growth -0.79 -0.98 -5.07 -6.84 Productivity Growth (percentages) Scale Effect Share Effect Residual Effect Total Growth 0.55 1.02 9.60 11.17 source: Tybout, James and M. Daniel Westbrook. "Trade Liberalization and Dimensions of Efficiency Change in Mexican Manufacturing Industries," Journal of International Economics, August 1995, 39(1/2), pp. 53-78. ...