We provide a nonlinear characterization of the macroeconomic impact of microeconomic TFP shocks in terms of reduced-form non-parametric elasticities for efficient economies. We also provide the mapping from structural parameters to these reduced- form elasticities, under general equilibrium. In this sense, the paper extends the foundational theorem of Hulten (1978) beyond first-order terms to capture nonlinearities. Key features ignored by first-order approximations that play a crucial role are: structural elasticities of substitution, network linkages, structural returns to scale, and the degree to which factors can be reallocated. Higher-order terms are large and economically interesting: they magnify negative shocks and attenuate positive shocks, resulting in an output distribution that is asymmetric (negative skewness), fat-tailed (excess kurtosis), and has a lower mean. They explain how small microeconomic shocks to critical sectors can have a large macroeconomic impact. To give a sense of magnitudes: in our benchmark calibration, output losses due to business cycle fluctuations are 0:6% of GDP, an order of magnitude larger than the cost of business cycles calculated by Lucas (1987), and are entirely due to a reduction in the mean of GDP because of nonlinearities in production; and accounting for second-order terms increases the estimated impact of the price shock to the critical sector of oil in the 1970s from 0:7% to 2:4% of world GDP.
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