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 cost shares into idiosyncratic and group-specific components. In particular, we carry out a cluster analysis to recover the number and membership of groups using breaks in the dispersion of factor cost shares across plants. 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 also study the implications ofthese groups in cost shares on the gains from eliminating misallocation. We place bounds on their importance and find that ignoring them can overstate the gains from eliminating misallocation by up to one-third.