The Marginal Product of Climate

We develop an empirical approach to value changes to a climate in terms of total market output given optimal factor allocations in general equilibrium. Our approach accounts for unobservable heterogeneity across locations as well as the costs and benefits of adaptation in climates of arbitrary dimension. Importantly, we demonstrate that the Envelope Theorem implies the marginal product of a long-run climate can be exactly identified using only idiosyncratic weather variation. We apply this method to the temperature climate of the modern United States and find that, despite evidence that populations adapt, the marginal product of temperature has remained unchanged during 1970-2010, with high temperatures having low net value. Integrating marginal products recovers a value function for temperature, describing the causal effect of non-marginal climate changes net of adaptive re-optimization. We use this value function to consider the influence of temperature in the current cross-section and a future climate change scenario.