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Most of contemporary macroeconomics is predicated on aggregate production functions, which postulate reduced-form aggregate relationships between factors of production and aggregate output. Despite previous attempts, a general theory of the microeconomic foundations of aggregate production functions is still wanting. The need for an aggregation framework is more pressing given the increased availability of high-quality microeconomic datasets. Our goal in this lecture is to propose such a theory and to gear it explicitly towards empirical applications. We characterize the properties of aggregate production functions as intuitive functions of structural microeconomic parameters: network of input-output linkages, microeconomic elasticities of substitution, returns to scale, and degree of factor market reallocation.

We also propose an alternative to aggregate production functions in the form of propagation equations, which are more robust to the introduction of frictions and imperfectly-competitive market structures. We offer two concrete applications: a quantitative exploration of capital-skill complementarities and the skill premium; and a re-interpretation of the Cambridge capital controversy as a manifestation of broader and empirically more relevant properties of aggregation.