On optimal taxes on fossil fuels to deal with global warming

[Mr. G]

For those interested in the handling of global warming problem there is this nice paper that came out in Econometrica in 2014:

http://hassler-j.iies.su.se/PAPERS/ECTA.pdf


"OPTIMAL TAXES ON FOSSIL FUEL IN GENERAL EQUILIBRIUM"

We analyze a dynamic stochastic general-equilibrium (DSGE) model with an
externality—through climate change—from using fossil energy. Our central result is a
simple formula for the marginal externality damage of emissions (or, equivalently, for
the optimal carbon tax). This formula, which holds under quite plausible assumptions,
reveals that the damage is proportional to current GDP, with the proportion depending
only on three factors: (i) discounting, (ii) the expected damage elasticity (how many
percent of the output flow is lost from an extra unit of carbon in the atmosphere), and
(iii) the structure of carbon depreciation in the atmosphere. Thus, the stochastic values
of future output, consumption, and the atmospheric CO2 concentration, as well as the
paths of technology (whether endogenous or exogenous) and population, and so on,
all disappear from the formula. We find that the optimal tax should be a bit higher
than the median, or most well-known, estimates in the literature. We also formulate a
parsimonious yet comprehensive and easily solved model allowing us to compute the
optimal and market paths for the use of different sources of energy and the corresponding
climate change. We find coal—rather than oil—to be the main threat to economic
welfare, largely due to its abundance. We also find that the costs of inaction are particularly
sensitive to the assumptions regarding the substitutability of different energy
sources and technological progress.

This paper is extremely successful in it's implementation of it's model, really simple and clear, like a classic paper from 60 years ago. Really an impressive achievement these days.

[Mr. G]

Some nice assumptions on global energy stocks used in the model:

Another key parameter is the size of the oil reserve. BP (2010) reported that proven global reserves of oil amount to 181.7 gigaton. However, these figures only aggregate reserves that are economically profitable to extract at current economic and technical conditions. Thus, they are not aimed at measuring the total resource base taking into account, in particular, technical progress, and they do not take into account the chance that new profitable oil reserves will be discovered. Rogner (1997) instead estimated global reserves taking into account technical progress, ending up at an estimate of over 5,000 gigaton of oil equivalents. Of this, around 16% is oil, that is, 800 gigaton. We take as a benchmark that the existing stock of oil is 300 gigaton, that is, somewhere well within the range of these two estimates.
To express fossil fuel in units of carbon content, we set the carbon content in crude oil to 846 KgC/ton oil. For coal, we set it to the carbon content of anthracite at 716 KgC/ton coal.
We have assumed that the scarcity rent for coal is negligible. This appears reasonable because, as noted, the reserves of coal are very large compared to those for oil. Rogner (1997) estimated that the coal supply is enough for several hundreds of years of consumption at current levels.

Some results of numerical simulations:

Similarly, by using the relation between carbon concentration in the atmosphere and the temperature—using the functional forms above, where T depends logarithmically on S—we can also compute the climate outcomes under the optimal and the market allocations. The results are summarized in Figure 7. Under laissez-faire, temperatures will have increased by 4.4 degrees Celsius 100 years from now, while the optimal use of fossil fuels leads to a heating of 2.6 degrees, that is, about half. At the end of the simulation period, the climate on earth is almost 10 degrees Celsius warmer without policy intervention, while the optimal tax limits heating to about 3 degrees. Note, however, that these temperature increases are measured relative to the pre-industrial climate; relative to the model’s prediction for the current temperature, the increases are about 11/2 degrees smaller.
Finally, we show the evolution of relative (net-of-damage) production of final-good output (GDP) in Figure 8. The optimal allocation involves negligible short-run losses in GDP. Output net of damages in the optimal allocation exceeds that in laissez-faire already from 2020. To understand this finding, recall (i) that using less coal implies less labor used in coal energy production and (ii) that oil consumption is not much affected by the optimal tax. After 100 years, GDP net of damages is 2.5% higher in the optimal allocation, and in year 2200, the difference is almost 15%.

Using an optimal policy on taxing carbon emissions will show a substantial beneficial effect only by the end of the 22nd century apparently. Though the model is full of strong assumptions used in these numerical exercises, assumptions that are not required to derive the optimal carbon tax rates.

[madd0ct0r]

Our estimate, for a discount rate of 1.5% per annum, is that the marginal externality
damage cost is a little under $60 per ton of carbon; for a discount rate
of 0.1%, it is about $500 per ton. We also argue that the optimal-tax computation
relying on our closed form is likely robust to a number of extensions. Put
in terms of projections for future taxes, our optimal-tax computation robustly
implies a declining value-added tax on fossil energy use.
...
We may also relate our findings to the price of emission rights in the European
Union Emission Trading System, in operation since 2005 and covering
large CO2 emitters in the EU. After collapsing during the great recession of
2008–2009, the price has hovered around 15 Euro per ton CO2, at an exchange
rate of 1.4 dollar per Euro corresponding to US$77 per ton carbon.43,44 This
price is more in line with the optimal tax rates we find for standard discount
rates.

they note that 'standard' discount rates in this context are much lower then the one they've used. It basically depends how long you think the carbon will be in the atmosphere and how much damage it'll do. The longer it hangs around, the more % of that damage is shifted into the future and costs less in the present.
They also note that this tax rate on carbon emissions means that absolute negative emissions should be subsided, which is good news for carbon capture ventures

[madd0ct0r]

Which is not to say I don't get your point G - that the method in the paper is more interesting then their exact number result. But I'm not an economist, and while I can just about follow waht they've written I sure as hell wouldn't want to develop it further.

The numbers on the other hand - i can plug that into my own work.