Skip to main content

Advertisement

Log in

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

  • Letter
  • Published:
Climatic Change Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Notes

  1. This framework extends to models with any logarithmic dependent variable.

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

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

  6. See Burke et al. (2015) for details. Replication code and data was accessed from: https://purl.stanford.edu/wb587wt4560https://purl.stanford.edu/wb587wt4560 (Last accessed: Feb. 7, 2017).

References

  • Barreca A, Clay K, Deschênes O, Greenstone M, Shapiro JS (2015) Convergence in adaptation to climate change: evidence from high temperatures and mortality, 1900–2004. Am Econ Rev 105(5):247–251

    Article  Google Scholar 

  • Barreca A, Clay K, Deschenes O, Greenstone M, Shapiro JS (2016) Adapting to climate change: the remarkable decline in the US temperature-mortality relationship over the twentieth century. J Polit Econ 124(1):105–159

    Article  Google Scholar 

  • Burke M, Emerick K (2016) Adaptation to climate change: evidence from US agriculture. Am Econ J Econ Pol 8(3):106–40

    Article  Google Scholar 

  • Burke M, Hsiang SM, Miguel E (2015) Global non-linear effect of temperature on economic production. Nature 527(7577):235–239

    Article  Google Scholar 

  • Carleton TA, Hsiang SM (2016) Social and economic impacts of climate. Science 353(6304)

  • Chan NW, Wichman CJ (2017) The effects of climate on leisure demand: evidence from North America. Working Paper Version: December 5

  • Dell M, Jones BF, Olken BA (2012) Temperature shocks and economic growth: evidence from the last half century. Am Econ J Macroecon 4(3):66–95

    Article  Google Scholar 

  • Dell M, Jones BF, Olken BA (2014) What do we learn from the weather? The new climate–economy literature. J Econ Lit 52(3):740–798

    Article  Google Scholar 

  • Deryugina T, Hsiang SM (2014) Does the environment still matter? Daily temperature and income in the United States. Technical Report, National Bureau of Economic Research

  • Halvorsen R, Palmquist R (1980) The interpretation of dummy variables in semilogarithmic equations. Am Econ Rev 70(3):474–75

    Google Scholar 

  • Kennedy PE (1981) Estimation with correctly interpreted dummy variables in semilogarithmic equations. Am Econ Rev 71(4)

  • Schlenker W, Roberts MJ (2006) Nonlinear effects of weather on corn yields. Appl Econ Perspect Policy 28(3):391–398

    Google Scholar 

  • Schlenker W, Roberts MJ (2009) Nonlinear temperature effects indicate severe damages to US crop yields under climate change. Proc Natl Acad Sci 106(37):15594–15598

    Article  Google Scholar 

  • van Garderen KJ, Shah C (2002) Exact interpretation of dummy variables in semilogarithmic equations. Econ J 5(1):149–159

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Casey J. Wichman.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wichman, C.J. Interpreting nonlinear semi-elasticities in reduced-form climate damage estimation. Climatic Change 148, 641–648 (2018). https://doi.org/10.1007/s10584-018-2197-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10584-018-2197-z

Navigation