Sample Bias in Decompositions of Economic Dynamics

Decompositions are a common method for quantifying within- and across-agent contributions to aggregate economic dynamics. We show that the standard practice of applying decompositions to sample data yields biased estimates of these contributions, and for common sample designs, these biases can be addressed by reformulating the decomposition as an estimation problem and applying standard statistical techniques. An application to India suggests sample bias meaningfully changes our understanding of how firm dynamics contribute to productivity growth. We also demonstrate our method enables the study of settings traditionally impeded by data limitations, such as productivity and firm dynamics in Sub-Saharan Africa.