Exploring reallocation’s apparent weak contribution to growth

Two recent meta-analyses use variants of the Baily et al. (Brookings Papers Econ Act Microecon 1:187–267, 1992) (BHC) decompositions to ask whether recent robust growth in aggregate labor productivity (ALP) across 25 countries is due to lower barriers to input reallocation. They find weak gains from measured reallocation and strong within-plant productivity gains. We show these findings may be because BHC indices decompose ALP growth using plant-level output-per-labor (OL) as a proxy for the marginal product of labor and changes in OL as a proxy for changes in plant-level productivity. We provide simple examples to show that (1) reallocation growth from labor should track marginal changes in labor weighted by the marginal product of labor, (2) BHC reallocation growth can be positively correlated, negatively correlated, or uncorrelated with actual growth arising from the reallocation of inputs, and that (3) BHC indices can mistake growth from reallocation as growth from productivity, principally because OL is neither a perfect index of marginal products nor plant-level productivity. We then turn to micro-level data from Chile, Colombia, and Slovenia, and we find for the first two that BHC indices report weak or negative growth from labor reallocation. Using the reallocation definition based on marginal products we find a positive and robust role for labor reallocation in all three countries and a reduced role of plant-level technical efficiency in growth. We close by exploring potential corrections to the BHC decompositions but here we have limited success.