Statistics as a Liberal Art

I recently came across this 11-year-old lecture (PDF) by David Moore which argues that statistics, as a mode of thinking, should be considered as a liberal art: That is, something that all educated people should understand, even if they never become professional statisticians:

That statistics is so often a guide to policy is testimony to the unusual prevalence of statistical issues in policy discussions. It is easy to think of policy questions to which (say) chemistry is relevant, and also easy to think of issues to which chemistry has nothing to contribute. I find it hard to think of policy questions, at least in domestic policy, that have no statistical component. The reason is of course that reasoning about data, variation, and chance is a flexible and broadly applicable mode of thinking. That is just what we most often mean by a liberal art.

Moore then goes on to discuss the nature of the liberal arts, which he divides into "philosophical" and "oratorical" traditions (one seeks the truth come what may, the other seeks to instill virtues that are valuable for citizenship); and he suggests that the liberal arts should be thought of as a sort of add-on to our evolutionary heritage. We can instinctively make out the features of a darkened room, say, but we need training to determine if the data in a scatterplot is strongly or weakly correlated.

I thought this was an interesting thesis, in that it's a kind of modern update of the medieval quadrivium: arithmetic, geometry, music, and astronomy. Paired with the trivium (grammar, rhetoric, and logic), it helped prepare students for the more difficult studies of philosophy and theology. (A style of education that, in turn, seems to derive from Socrates' curriculum for the guardians in the Republic.) We live in a post-metaphysical age, of course, so studying mathematical subjects is no longer about training the mind for understanding God, the Good, or Being. But having at least some background in quantitative methods is essential for understanding the modern world: To be able to answer questions about crime, health care, global warming, etc., means, in part, pulling oneself out of the realm of the anecdotal and personal, and knowing how to manipulate data responsibly. Perhaps a modern version of Plato's Academy would have inscribed on its gate, not "ἀγεωμέτρητος μηδεὶς εἰσίτω" (Let no one ignorant of geometry enter), but "ἀστατίστικος μηδεὶς εἰσίτω" (Let no one ignorant of statistics enter).

The Political Tipping Point for Cap-and-Trade

So a recent poll found that about 60% of Americans support a cap-and-trade program to reduce global warming, even if it meant that their monthly electric bills went up by $10; but if they went up by $25, then about 60% of Americans would oppose cap-and-trade. This naturally raises the question: What would the price of carbon emissions have to be in order to raise the average American's electric bill by those amounts -- that is, what is the effective ceiling for the price of carbon emissions, after which support collapses?

First, let's lay out some facts. According to the Energy Information Administration, in 2007 the average American household consumed 936 kWh (3.19 million BTU) of electricity per month, which, at an average retail price of ¢10.65/kWh, translates to an average monthly bill of $99.70. Now, of the sources of electricity that come from fossil fuels, about 49.9% comes from coal, 20.3% from natural gas, 1.2% from petroleum liquids (e.g., fuel oil and kerosene), 0.4% from petroleum coke, and 0.1% from other sources (e.g., propane).¹ Let's assume, for the sake of this exercise, that our average American household receives electricity from all possible sources, and in exactly the proportions listed here. (I'm not listing other sources like nuclear and hydro, as they obviously have no carbon emissions.)

We also have to consider the specific carbon content of each of these fuels; some are dirtier than others. EIA provides a handy table for this, from which I present the emission coefficients for the five types of fossil fuels just mentioned:

Coal:² 215.2 lbs_CO2/MBTU
Natural Gas: 117.08
Petroleum Liquids:³ 162.77
Petroleum Coke: 225.13
Other Gases:⁴ 132.98

Now, with all that laid out, let's do some number crunching. Factoring the consumption proportions above into our hypothetical average American's monthly electricity consumption, we get this:

Coal: 0.499 * 3.19 = 1.59 MBTU
Natural Gas: 0.203 * 3.19 = 0.65
Petroleum Liquids: 0.012 * 3.19 = 0.04
Petroleum Coke: 0.004 * 3.19 = 0.013
Other Gases: 0.001 * 3.19 = 0.003

That divvies up the fossil fuel portion of our hypothetical average American's electricity consumption. Now we find out how many carbon emissions that produces:

Coal: 215.2 * 1.55 = 342.17 lbs
Natural Gas: 117.08 * 0.65 = 76.1
Petroleum Liquids: 162.77 * 0.04 = 6.51
Petroleum Coke: 225.13 * 0.013 = 2.93
Other Gases: 132.98 * 0.001 = 0.13

All told, that's about 428 lbs of CO₂. Next, we do the same thing we did before with consumption, only now with the money spent on electricity:

Coal: 0.499 * $99.70 = $49.75
Natural Gas: 0.203 * $99.70 = $20.24
Petroleum Liquids: 0.012 * $99.70 = $1.20
Petroleum Coke: 0.004 * $99.70 = $0.40
Other Gases: 0.001 * $99.70 = $0.10

That totals $71.69. If we divide this set of numbers by the last set, we get ratios which, when multiplied by 2,000 lbs, gives us the price per ton of CO₂ for each of these fuels. Now we can attempt to answer our original question, so let us ask what would happen if we set a surcharge on carbon emissions in the following amounts (note that these figures are the portions of our hypothetical average American household's bill spent on the various fuels):

	$25/tCO2	$50	$75	$100	$125
Coal	$54.03	$58.30	$62.58	$66.86	$71.14
Natural Gas	$21.19	$22.14	$23.09	$24.05	$25.00
Petroleum Liquids	$1.28	$1.36	$1.44	$1.53	$1.61
Petroleum Coke	$0.44	$0.51	$0.47	$0.55	$0.58
Other Gases	$0.10	$0.10	$0.10	$0.11	$0.11
Total	$77.04	$82.39	$87.73	$93.08	$98.43
Addition to Bill	$5.35	$10.70	$16.04	$21.39	$26.74

I'll have to go back to get the exact prices that correspond with the increases cited in the poll, but the results seem pretty clear: It seems the price of carbon emissions could go up to $50/tCO₂, and a strong majority of Americans, according to the poll, would still support a cap-and-trade plan; it would have to go over $75/tCO₂ to raise bills by $17.50, where we might expect opinion to flip from support to opposition; and it would have to go well over $100/tCO₂ in order for Americans to turn firmly against cap-and-trade. To put things in perspective, the initial price of carbon emissions under the Waxman-Markey bill is expected to be around $15/tCO₂.

Keep in mind, however, that there are a lot of heroic assumptions being made here: For one, the proportions for fossil fuel consumption are going to vary significantly for actual households, rather than hypothetical ones, based on where one lives; some places are going to be more carbon-intensive than others. I'm also assuming that the introduction of a price on carbon emissions will result in no transition from fossil fuels to alternatives: Were the price to go permanently from $0 to $25/tCO₂, say, or $25 to $50, it would be ridiculous to believe that that wouldn't spur more investment in nuclear, hydro, efficiency measures, or renewables, or fuel-switching from coal to natural gas. And of course, one should never invest too much in a single poll.

I welcome any comments or corrections to my analysis here; I'm pretty sure someone has done this already for an older version of this poll, but I couldn't find it on the web.

¹ Sources: here and here, data from 2007 -- I'm basically subtracting out the commercial and industrial sectors in calculating these proportions.
² Average of carbon content for Anthracite, Bituminous, Sub-Bituminous, and Lignite.
³ Average of carbon content for kerosene, distillate fuel oil, residual fuel oil, and jet fuel. Not sure how the latter is used to make electricity, though. It may just be the way EIA classifies it: Jet fuel may be a petroleum liquid, and petroleum liquids are used to make electricity, but that doesn't mean jet fuel is used to make electricity -- not to my knowledge, anyway. I considered leaving it out, but I doubt doing that would change the final analysis much.
⁴ Average of propane, flare gas, and LPG. Again, I may have screwed up here in calculating an average carbon content -- this is the Other category, after all. But again, any adjustments would likely have no effect on the final analysis.

The Course of Climate Legislation, in Graphs

Generally, it's wise to take prediction markets with a few grains of salt. But I think the Intrade graph of the probability of a cap-and-trade program being enacted by the end of 2010 tracks fairly well how climate legislation has fared thus far:


As you can see, it dips sharply in May, when it looked like Waxman-Markey might not get out of Energy and Commerce, then gets better and better, until it passes in late June and briefly crosses 50. Then nothing for a while, then the Senate delays until September, and just recently delays indefinitely -- and it tumbles.

For comparison's sake, here's the graph for the contract saying cap-and-trade will be enacted by the end of 2009:


Its activity isn't terribly different from the 2010 contract, though note that it starts to decline in mid-July, rather than mid-August. A sign, perhaps, that the health care debate was crowding out any chance of climate change legislation being acted upon this year?