THIS POST IS A CRITICAL REVIEW OF THE RESEARCH FINDING THAT CLIMATE CHANGE HAS CAUSED A DECLINE IN LABOR PRODUCTIVITY PARTICULARLY SO IN THE AREAS MARKED BY CIRCLES IN THE MAP ABOVE

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1. On 9/23/2019, an open access research paper appeared on Nature on the impact of climate change on labor productivity. CITATION: Exposure to excessive heat and impacts on labour productivity linked to cumulative CO2 emissions, Yann Chavaillaz, Philippe Roy, Antti-Ilari Partanen, Laurent Da Silva, Émilie Bresson, Nadine Mengis, Diane Chaumont & H. Damon Matthews, Scientific Reports Volume 9, Article number: 13711 (2019). [LINK TO FULL TEXT] .
2. It finds that: ABSTRACT: Cumulative CO2 emissions are a robust predictor of mean temperature increase. However, many societal impacts are driven by exposure to extreme weather conditions. Here, we show that cumulative emissions can be robustly linked to regional changes of a heat exposure indicator, as well as the resulting socioeconomic impacts associated with labour productivity loss in vulnerable economic sectors. We estimate historical and future increases in heat exposure using simulations from eight Earth System Models. Both the global intensity and spatial pattern of heat exposure evolve linearly with cumulative emissions across scenarios (1% CO2, RCP4.5 and RCP8.5). The pattern of heat exposure at a given level of global temperature increase is strongly affected by non-CO2 forcing. Global non-CO2 greenhouse gas emissions amplify heat exposure, while high local emissions of aerosols could moderate exposure. Considering CO2 forcing only, we commit ourselves to an additional annual loss of labour productivity of about 2% of total GDP per unit of trillion tonne of carbon emitted. This loss doubles when adding non-CO2 forcing of the RCP8.5 scenario. This represents an additional economic loss of about 4,400 G$ every year (i.e. 0.59 $/tCO2), varying across countries with generally higher impact in lower-income countries.
3. The finding is  based on the observed correlation of heat exposure with cumulative emissions as described in this part of the paper where CCE = cumulative emissions. “At a global scale, the annual total heat exposure over land areas increases linearly as a function of CCE for the four lowest WBGT thresholds selected. In the 1% CO2 (CO2-only) scenario, heat exposure above the light threshold increases by 213.1±105.1K-days per trillion tonne of carbon (TtC) (see Fig. 1a–d and Supplementary Table S3). As current CCE are estimated at 555 PgC27, this represents an estimated increase in heat exposure of about 118.3±58.3K-days relative to the beginning of the pre-industrial period. Heat exposure above the extreme and deadly thresholds also increases with cumulative emissions, by 55.30±53.31 and 18.44±28.37K-days per TtC, respectively (see Fig. 1e,f); however, given the small signals and high inter-model spread, we were not able to demonstrate a statistically robust linear relationship with CCE. Across all WBGT thresholds, the RCP scenarios show a more rapid and more robust increase in heat exposure compared to the 1% CO2 scenario as a result of additional positive non-CO2 forcing.
4. The methodology is described by these charts that show the relationship between cumulative degree-days (measured in degrees Kelvin) and cumulative emissions. The high correlation between these two time series supports the statistical significance of the regression coefficient that describes the the effect of emissions on degree days of heat exposure as an increase of 118 degK-days relative to pre-industrial. The impact of AGW on labor productivity is thus established.

THE SPURIOUSNESS OF CORRELATIONS BETWEEN CUMULATIVE VALUES

1. It is noted here that emissions are always positive and the way degree days are defined in terms of degrees Kelvin, that series also consists of positive numbers. It is shown in related posts that a time series of the cumulative values of another time series has neither time scale nor degrees of freedom and that therefore their correlation has no interpretation; and that experiments with random numbers show that as long as the two time series being compared have a similar sign bias, i.e., mostly positive or mostly negative, their cumulative values will show a correlation by virtue only of the sign convention. Therefore such correlation cannot be interpreted in terms of the responsiveness of the object time series to changes in the explanatory time series. The statistical details of this argument may be found in these posts on this site: [LINK] [LINK] .
2. We conclude from these considerations that the use of the cumulative values of  time series data in a statistical test for the impact of emissions on labor productivity does not and cannot lead to a the conclusion that emissions since pre-industrial have caused a loss in labor productivity. The findings of the reference paper that loss in labor productivity can be attributed to AGW is thus found to be a spurious and a figment of the loss in degrees of freedom when cumulative values of time series are computed.
3. Below are four charts that demonstrate the spuriousness of correlations between cumulative values. The top two charts show that the cumulative values shown in the lower chart, of random numbers  shown in the upper chart, do not always contain a strong positive correlation but that their relationship is random. In the bottom two charts, a small bias is introduced in the first chart for the random number generator to generate mostly positive values; and here we see that this sign convention bias in and of itself can create a spurious correlation between the cumulative values. Such correlation does not serve as evidence that the object time series is responsive to the explanatory time series. The time series of the cumulative values of another time series contains neither time scale nor degrees of freedom and therefore no conclusions may be drawn from their apparent correlation that can only be taken to be illusory.
4. A more complete analysis of this result is provided in a related post [LINK]  where it is argued that: “The near perfect proportionality between cumulative warming and cumulative emissions described by Matthews and others in 2009 [LINK] is a creation of the transformation to cumulative values. That proportionality is also found in the cumulative values of random numbers. This correlation derives from a sign pattern wherein emissions are always positive, and in a time of global warming, changes in temperature have a positive bias. It is shown here that under the same conditions the same correlation is found in random numbers. Therefore although strong correlation and regression coefficients can be computed from the time series of cumulative values, these statistics have no interpretation because they are illusory. The presentation of climate action mathematics by climate science in the form of carbon budgets derived from the TCRE has no interpretation in the real world because the TCRE is a creation of a spurious correlation. The instability and unreliability of the TCRE demonstrated in this work, has been noted in climate science research [LINK], [LINK], and in other posts on this site [LINK] . This work provides further evidence of instability along with a statistical basis for instability in the TCRE.”
5. We conclude therefore that the correlation and regression analysis of cumulative degree days against cumulative emissions do not establish a causal relationship between them because of the spuriousness of correlations between cumulative values.