## Morning Must-Read: Kevin Bryan: “Aggregation in Production Functions: What Applied Economists Should Know,” J. Felipe & F. Fisher (2003)

**Kevin Bryan:** “Aggregation in Production Functions: What Applied Economists Should Know,” J. Felipe & F. Fisher (2003): "What conditions are required to construct an aggregated production function Y=F(K,L)...

...or more broadly to aggregate across firms an economy-wide production function Y=F(K,L)? Note that the question is not about the definition of capital per se, since defining 'labor' is equally problematic when man-hours are clearly heterogeneous, and this question is also not about the more general capital controversy worries, like reswitching.... The conditions under which factors can be aggregated are ridiculously stringent... that the marginal rate of substitution between different types of factors in one aggregation, e.g. capital, does not depend on the level of factors not in that aggregation, e.g. labor. Surely this is a condition that rarely holds: how much I want to use... different types of trucks will depend on how much labor I have at hand.... Why, then, do empirical exercises using, say, aggregate Cobb-Douglas seem to give such reasonable parameters, even though the above theoretical results suggest that parameters like 'aggregate elasticity of substitution between labor and capital' don’t even exist?.... Since ex-post production Y must equal the wage bill plus the capital payments plus profits, Felipe notes that this identity can be algebraically manipulated to Y=AF(K,L) where the form of F depends on the nature of the factor shares. That is, the good fit of Cobb-Douglas or CES can simply reflect an accounting identity.... It doesn’t strike me that aggregate production functions are measuring arbitrary things. However, if we are using parameters from these functions to do counterfactual analysis, we really ought know better exactly what approximations or assumptions are being baked into the cake...