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Abstract The paper considers formally the mapping from distortions in the allocations of resources across firms to aggregate productivity. TFP gaps are characterized as the integral of a strictly concave function with respect to an employment-weighted measure of distortions. Size related distortions are shown to correspond to a mean preserving spread of this measure, explaining the stronger effects on TFP found in the literature. In general, the effect of correlation between distortions and productivity is shown to be ambiguous; conditions are given to determine its sign. An empirical lower bound on distortions based on size distribution of firms is derived and analyzed, revealing that substantial rank reversals in firm size are necessary for distortions to explain large TFP gaps. The effect of curvature on the impact and measurement of distortions is also considered.

On the Measure of Distortions