Third excerpt (previous excerpts):

Most studies of global climate change using econometric methods have ignored the role of the ocean. Though these studies sometimes produce plausible estimates of the climate sensitivity, they universally produce implausible estimates of the rate of adjustment of surface temperature to long-run equilibrium. For example, Kaufmann and Stern (2002) find that the rate of adjustment of temperature to changes in radiative forcing is around 50% per annum even though they estimate an average global climate sensitivity of 2.03K. Similarly, Kaufmann et al. (2006) estimate a climate sensitivity of 1.8K, while the adjustment coefficient implies that more than 50% of the disequilibrium between forcing and temperature is eliminated each year. Furthermore, the autoregressive coefficient in the carbon dioxide equation of 0.832 implies an unreasonably high rate of removal of CO2 from the atmosphere. The methane rate of removal is also very high.

Simple AR(1) I(1) autoregressive models of this type assume that temperature adjusts in an exponential fashion towards the long run equilibrium. The estimate of that adjustment rate tends to go towards that of the fastest adjusting process in the system, if, as is the case, that is the most obvious in the data. Schlesinger et al. (no date) illustrate these points with a very simple first order autoregressive model of global temperature and radiative forcing. They show that such a model approximates a model with a simple mixed layer ocean. Parameter estimates can be used to infer the depth of such an ocean. The models that they estimate have inferred ocean depths of 38.7-185.7 meters. Clearly, an improved time series model needs to simulate a deeper ocean component.

Stern (2006) used a state space model inspired by multicointegration. The estimated climate sensitivity for the preferred model is 4.4K, which is much higher than previous time series estimates and temperature responds much slower to increased forcing. However, this model only used data on the top 300m of the ocean and the estimated increase in heat content in the pre-observational period seems too large.

Pretis (2015) estimates an I(1) VAR for surface temperature and the heat content of the top 700m of the ocean for observed data for 1955-2011. The climate sensitivity is 1.67K for the preferred model but 2.16K for a model, which excludes the level of volcanic forcing from the radiative forcing aggregate, entering only as first differences. With two cointegrating vectors it is not possible to “read off” the rate of adjustment of surface temperature to increased forcing and Pretis does not simulate impulse or transient response functions.

Kaufmann, R. K., Kauppi, H., Stock, J. H., 2006. Emissions, concentrations, and temperature: a time series analysis. Climatic Change 77(3-4), 249-278.

Kaufmann, R. K., Stern, D. I., 2002. Cointegration analysis of hemispheric temperature relations. Journal of Geophysical Research 107(D2), Article No. 4012.

Pretis, F., 2015. Econometric models of climate systems: The equivalence of two-component energy balance models and cointegrated VARs. Oxford Department of Economics Discussion Paper 750.

Schlesinger, M. E., Andronova, N. G., Kolstad, C. D., Kelly, D. L., no date. On the use of autoregression models to estimate climate sensitivity. mimeo, Climate Research Group, Department of Atmospheric Sciences, University of Illinois at Urbana-Champaign, IL.

Stern, D. I., 2006. An atmosphere-ocean multicointegration model of global climate change. Computational Statistics and Data Analysis 51(2), 1330-1346.

Most studies of global climate change using econometric methods have ignored the role of the ocean. Though these studies sometimes produce plausible estimates of the climate sensitivity, they universally produce implausible estimates of the rate of adjustment of surface temperature to long-run equilibrium. For example, Kaufmann and Stern (2002) find that the rate of adjustment of temperature to changes in radiative forcing is around 50% per annum even though they estimate an average global climate sensitivity of 2.03K. Similarly, Kaufmann et al. (2006) estimate a climate sensitivity of 1.8K, while the adjustment coefficient implies that more than 50% of the disequilibrium between forcing and temperature is eliminated each year. Furthermore, the autoregressive coefficient in the carbon dioxide equation of 0.832 implies an unreasonably high rate of removal of CO2 from the atmosphere. The methane rate of removal is also very high.

Simple AR(1) I(1) autoregressive models of this type assume that temperature adjusts in an exponential fashion towards the long run equilibrium. The estimate of that adjustment rate tends to go towards that of the fastest adjusting process in the system, if, as is the case, that is the most obvious in the data. Schlesinger et al. (no date) illustrate these points with a very simple first order autoregressive model of global temperature and radiative forcing. They show that such a model approximates a model with a simple mixed layer ocean. Parameter estimates can be used to infer the depth of such an ocean. The models that they estimate have inferred ocean depths of 38.7-185.7 meters. Clearly, an improved time series model needs to simulate a deeper ocean component.

Stern (2006) used a state space model inspired by multicointegration. The estimated climate sensitivity for the preferred model is 4.4K, which is much higher than previous time series estimates and temperature responds much slower to increased forcing. However, this model only used data on the top 300m of the ocean and the estimated increase in heat content in the pre-observational period seems too large.

Pretis (2015) estimates an I(1) VAR for surface temperature and the heat content of the top 700m of the ocean for observed data for 1955-2011. The climate sensitivity is 1.67K for the preferred model but 2.16K for a model, which excludes the level of volcanic forcing from the radiative forcing aggregate, entering only as first differences. With two cointegrating vectors it is not possible to “read off” the rate of adjustment of surface temperature to increased forcing and Pretis does not simulate impulse or transient response functions.

**References**Kaufmann, R. K., Kauppi, H., Stock, J. H., 2006. Emissions, concentrations, and temperature: a time series analysis. Climatic Change 77(3-4), 249-278.

Kaufmann, R. K., Stern, D. I., 2002. Cointegration analysis of hemispheric temperature relations. Journal of Geophysical Research 107(D2), Article No. 4012.

Pretis, F., 2015. Econometric models of climate systems: The equivalence of two-component energy balance models and cointegrated VARs. Oxford Department of Economics Discussion Paper 750.

Schlesinger, M. E., Andronova, N. G., Kolstad, C. D., Kelly, D. L., no date. On the use of autoregression models to estimate climate sensitivity. mimeo, Climate Research Group, Department of Atmospheric Sciences, University of Illinois at Urbana-Champaign, IL.

Stern, D. I., 2006. An atmosphere-ocean multicointegration model of global climate change. Computational Statistics and Data Analysis 51(2), 1330-1346.

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