This paper develops a general theory of aggregation in inefficient economies. We provide nonparametric formulas for aggregating microeconomic shocks in economies with distortions such as taxes, markups, frictions to resource reallocation, financial frictions, and nominal rigidities. We allow for arbitrary elasticities of substitution, returns to scale, factor mobility, and input-output network linkages. We show how to separately measure changes in technical and allocative efficiency. We also show how to compute the social cost of distortions. We pursue applications focusing on firm-level markups in the United States. We find that improvement in allocative efficiency, due to the reallocation over time of market share to high-markup firms, accounts for about half of aggregate TFP growth over the period 1997–2015. We also find that eliminating the misallocation resulting from the large and dispersed markups estimated in the data would raise aggregate TFP by about 15%, increasing the economy-wide cost of monopoly distortions by two orders of magnitude compared with the famous 0.1% estimate by Harberger (1954). These exact numbers should be interpreted with care because the data are imperfect and require substantial imputation.

We study a flexible class of trade models with international production networks and arbitrary wedge‐like distortions like markups, tariffs, or nominal rigidities. We characterize the general equilibrium response of variables to shocks in terms of microeconomic statistics. Our results are useful for decomposing the sources of real GDP and welfare growth, and for computing counterfactuals. Using the same set of microeconomic sufficient statistics, we also characterize societal losses from increases in tariffs and iceberg trade costs and dissect the qualitative and quantitative importance of accounting for disaggregated details. Our results, which can be used to compute approximate and exact counterfactuals, provide an analytical toolbox for studying large‐scale trade models and help to bridge the gap between computation and theory.