Grouped Variation in Factor Shares: An Application to Misallocation

A striking feature of micro-level plant data is the presence of significant variation in factor cost shares across plants within an industry. We develop a methodology to decompose this variation into idiosyncratic and group-specific components and to use cluster analysis to recover the number and membership of groups using breaks in the dispersion of factor cost shares across firms. We apply our methodology to Chilean plant-level data and find that group-specific variation accounts for approximately one-third of the variation in factor shares across firms. We motivate our results with an economic model in which group-specific variation can arise from differences in production technologies or through distortions that affect different groups of firms. We evaluate several potential explanations for our results and argue that our findings are most consistent with the interpretation of group-specific variation arising from the presence of multiple production technologies. Under this interpretation, ignoring groups overstates the gains from eliminating mis-allocation by roughly one-third.