Statistical tests of a simple energy balance equation in a synthetic model of cotrending and cointegration

Josep Lluís Carrion-i-Silvestre, Dukpa Kim

Research output: Contribution to journalArticlepeer-review


We develop new tests for the linear relationship between temperature and forcing, which is one of the most studied implications from a simple energy balance model. We consider a bivariate system of temperature and forcing where the time path of well-mixed-greenhouse-gases forcing is included as a potential common trend function in addition to a stochastic trend and a broken linear trend. Our test statistics are first devised as the likelihood ratio and then are modified to remove nuisance parameters in the asymptotic null distribution. The asymptotic null distribution and the required modification differ as to the existence of a stochastic trend. Thus, the test statistics are modified in two different ways and then are combined using the super-efficient estimator of the sum of autoregressive coefficients. The asymptotic critical values from the two cases remain close and we use the bigger one to control size for both cases. The proposed tests are applied to four temperature series and a forcing series. The null hypothesis of the linear relationship is not rejected with conventional sizes.

Original languageEnglish
Pages (from-to)22-38
Number of pages17
JournalJournal of Econometrics
Issue number1
Publication statusPublished - 2021 Sept

Bibliographical note

Funding Information:
We thank the editor and anonymous referees for their helpful comments. We also thank the participants at the Pi-day econometrics conference held at Boston University in March 2019 and the econometric models of climate change conference (EMCC-IV) held at University of Milano-Bicocca in August 2019. Carrion-i-Silvestre gratefully acknowledges the financial support from the Spanish Ministerio de Ciencia y Tecnología, Agencia Española de Investigación (AEI) and European Regional Development Fund (ERDF, EU) under grants ECO2017-83255-C3-1-P (AEI/ERDF, EU) and ECO2016-81901-REDT . Kim’s work was supported by the Korea University Future Research Grants ( K1822291 ).

Publisher Copyright:
© 2020 Elsevier B.V.


  • Global mean temperature
  • Radiative forcing

ASJC Scopus subject areas

  • Economics and Econometrics


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