THE ECONOMIST recently published an article about the costs and benefits of various kinds of zero- and low-carbon energy, “Sun, wind and drain”. The article was based on research by Charles Frank of the Brookings Institution (whose paper is here). Dr Frank, citing the work of Paul Joskow of the Massachusetts Institute of Technology, argued that the usual way of calculating energy costs—so-called “levelised costs”, or the total capital and operating cost of a generating unit over its lifetime—was flawed when applied to renewable-energy sources and therefore not a useful way of comparing different methods of generating power. He used a different method of calculating costs: a cost-benefit analysis in which the costs include the cost of supplying power when an energy source is not working (for example, solar panels at night) and the benefits include the value of carbon emissions avoided by zero- or low-carbon generation (ie, saved because a coal- or gas-fired plant would have produced a certain amount of carbon dioxide in generating the same amount of energy).

Dr Frank concluded that, using his cost-benefit figures, solar power is the most expensive way of reducing carbon emissions, followed by wind power. Then comes hydropower and nuclear plants. The most efficient way of cutting carbon, on his figures, is through a technology called gas combined cycle (gas CC, an especially efficient sort of gas-fuelled plant).

Dr Amory Lovins, the chairman and chief scientist of the Rocky Mountain Institute, a non-profit organisation in Colorado, took issue with Dr Frank’s study and with The Economist for having written an article about it. His letter to The Economist is here. Other criticisms by him are here. And here. And here.

Dr Lovins makes several points but perhaps the central one is that the statistics Dr Frank uses are wrong, misleading and out of date. He says the capital costs of solar and wind power are only about half what Dr Frank says they are. The proper figures, Dr Lovins argues, make solar and wind power look more efficient than other technologies, not less.

Dr Lovins cites figures for the capital cost of solar from the US Department of Energy. These show that the weighted average capital cost of 113 utility-scale solar projects completed in 2012 was $3,900 per kilowatt (KW). Dr Frank used figures from the US Energy Information Administration (EIA), also part of the Department of Energy. Their estimate was $3,873 per KW—very similar to Dr Lovins’s preferred figure.

On the capital cost of wind, Dr Lovins again cites the US Department of Energy, in this case its Wind Technologies Market Report, which calculated the weighted average capital cost of 118 wind projects in 2012 to be $1,940/KW. Dr Frank’s again uses the EIA, whose figure is $2,213/KW. That is 14% higher, not 100% higher.

Dr Lovins is correct about one thing: Dr Frank’s numbers are rather old. They come from the EIA’s Annual Power Report, published in December 2013. This report did not give actual figures for capacity factors for wind and solar power (the capacity factor of a power plant is the ratio of energy produced to the capacity of the plant). It merely estimated them, and Dr Frank used these estimates. Since then the EIA has published actual capacity factors for wind and solar—and these do indeed, make wind and solar look better, as Dr Lovins claims. But not all that much.

Dr Frank has recalculated his figures using actual, rather than estimated, numbers. In his original paper, he reckoned the overall costs of solar power were a whopping $188,800 per MW per year more than a similar-sized coal plant (ie, adding up all the costs and benefits, solar power was that much more expensive than coal). Using the new numbers, he finds that solar’s net cost is lower: $158,800 per MW per year, compared with coal. That is an improvement of $30,000 per MW per year, though it is still a net cost. In the original study, wind energy cost $25,300 per MW per year more than coal. With the new figures, the net costs become net benefits: $31,200 per MW per year cheaper than coal. Even so, wind and solar are still less beneficial than the alternatives which Dr Franks considers. Compared with coal, hydropower is $156,800 per MW per year cheaper using the new numbers (before, it had been $180,400 cheaper). Nuclear is $261,300 cheaper (previously $318,600). And gas CC is $476,600 cheaper (before, $535,400). In other words, the new figures reduce the benefits of the other technologies and improves the efficiency of renewables. But it does not alter the ranking: gas CC, nuclear and hydropower are still more cost effective at cutting emissions than wind and solar. And the gap between them and the others is still fairly large.

Readers may be forgiven for being baffled by these conflicting numbers, which also change all the time. The original Economist article conceded that “there are, of course, all sorts of reasons to choose one form of energy over another” and arguments will doubtless continue about the relative merits of different sorts of no- and low-carbon power generation. But so far nothing in the new calculations seems to provide a strong reason for changing the article’s main conclusion: “governments should target emissions reductions from any source, rather than focus on boosting certain kinds of renewable energy.”