Abstract
Allen and Tett (1999, herein AT99) introduced a Generalized Least Squares (GLS) regression methodology for decomposing patterns of climate change for attribution purposes and proposed the “Residual Consistency Test” (RCT) to check the GLS specification. Their methodology has been widely used and highly influential ever since, in part because subsequent authors have relied upon their claim that their GLS model satisfies the conditions of the Gauss-Markov (GM) Theorem, thereby yielding unbiased and efficient estimators. But AT99 stated the GM Theorem incorrectly, omitting a critical condition altogether, their GLS method cannot satisfy the GM conditions, and their variance estimator is inconsistent by construction. Additionally, they did not formally state the null hypothesis of the RCT nor identify which of the GM conditions it tests, nor did they prove its distribution and critical values, rendering it uninformative as a specification test. The continuing influence of AT99 two decades later means these issues should be corrected. I identify 6 conditions needing to be shown for the AT99 method to be valid.
Highlights
In a highly influential paper published more than 20 years ago, Allen and Tett (1999, AT99) introduced a Generalized Least Squares (GLS) regression methodology for decomposing patterns of climate change across forcings for the purpose of making causal inferences about anthropogenic drivers of climate change, and proposed a “Residual Consistency Test” (RCT) to allow researchers to check the validity of the regression model
The methodology of AT99 is seminal to the optimal fingerprinting literature
The literature resting on AT99 figures prominently in the increasing confidence with which the Intergovernmental Panel on Climate Change (IPCC 2013) and others have attributed most modern climate change to anthropogenic influences, greenhouse gases, especially since 1950
Summary
In a highly influential paper published more than 20 years ago, Allen and Tett (1999, AT99) introduced a Generalized Least Squares (GLS) regression methodology for decomposing patterns of climate change across forcings for the purpose of making causal inferences about anthropogenic drivers of climate change, and proposed a “Residual Consistency Test” (RCT) to allow researchers to check the validity of the regression model They claimed their method satisfies the conditions of the Gauss-Markov (GM) theorem, thereby yielding best (as in minimum variance) linear unbiased coefficient estimates, commonly denoted “BLUE”, a claim that has been relied upon subsequently by other authors AT99 provided no formal null hypothesis of the RCT nor did they prove its asymptotic distribution, making non-rejection against 2 critical values uninformative for the purpose of model specification testing
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