Interpreting nonlinear semi-elasticities in reduced-form climate damage estimation


Observed changes in weather can reveal marginal impacts of climate change on economic outcomes and the potential for adaptation. When modeling the nonlinear relationship between weather and changes in economic outcomes empirically, model choice can confound the interpretation of marginal and percentage effects and their respective confidence intervals. I present a simple solution for better characterizing semi-elasticities of nonlinear climate damages, and evaluate its relevance in interpreting empirical climate damages. For small marginal effects, the implications of this interpretation error is small; for larger effects, however, the misinterpretation error can be substantial.

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  1. 1.

    This framework extends to models with any logarithmic dependent variable.

  2. 2.

    Alternatively, this equation could represent the effect of growing degree days on log agricultural yields, or the number of days above 90 °F on the log mortality rate.

  3. 3.

    Formally, g = [Y (D i t = 1) − Y (D i t = 0)] /Y (D i t = 0).

  4. 4.

    Note that \(\hat {g}\) and \(\hat {\beta }\) need not be equivalent at \(\hat {\beta }= 0\) because of the variance estimate that scales \(\hat {g}\). For the purpose of this figure, I set \(\hat {V}(\hat {\beta })= 0\) for \(\hat {\beta }= 0\) (see van Garderen and Shah (2002) for further discussion).

  5. 5.

    For details on the specification of BHM main regression results, see their supplementary information section B.1.

  6. 6.

    See Burke et al. (2015) for details. Replication code and data was accessed from: (Last accessed: Feb. 7, 2017).


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Wichman, C.J. Interpreting nonlinear semi-elasticities in reduced-form climate damage estimation. Climatic Change 148, 641–648 (2018).

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