Michael Greenstone in the NY Times:

Respondents were asked if they would support a fee on their monthly electricity bill to combat climate change, and they were offered fees at various levels: $1, $10, $20, $30, $40 and $50. (Each household was asked about only one of these levels.) The responses were that 57 percent would pay at least $1; 39 percent would pay at least $10; 29 percent would pay $20; 24 percent would pay $30; 17 percent would pay $40; and 20 percent would pay $50.

Let's check the math. When faced with this type of data, I prefer to make the most conservative approach possible. In my book with Ted McConnell on the Valuation of Environmental and Natural Resources (Available at bookstores near you on Amazon), we show that the most conservative estimate of willingness to pay from this type of data is something we call the Turnbull Lower Bound on Willingness to Pay. The story goes like this: If 57% of respondents say they are willing to pay at least $1, then 43% of respondents are willing to [pay less than $1. To be conservative, we are going to assume those 43% of respondents are willing to pay $0 (that's pretty conservative).

Now what about the 57% who are willing to pay more than $1? Based on the data provided, 39% of respondents are willing to pay at least $10. That means that 18% of respondents (57%-39%) are willing to pay somewhere between $1 and $10. Again to be conservative, we will assume that these 18% are willing to pay the lowest amount indicated for that group ($1).

So now we have 43% of respondents willing to pay $0 and 18% willing to pay $1. Following a similar method, if 39% are willing to pay at least $10 and 29% are willing to pay at least $20, then 10% (39%-29%) are willing to pay between $10 and $20. Conservatively we will say this group is willing to pay $10.

We can keep following this method and we will see that we can conservatively say that 5% of the respondents (29%-24%) are willing to pay $20, and 7% of respondents (24%-17%) are willing to pay $30.

When it comes to the last two groups we run in to a little bit of a problem. The survey revealed that 17% of respondents are willing to pay at least $40, but 20% of respondents are willing to pay at least $50. This seems to violate my economic senses. We would expect that as the price of combating climate change increases, the percentage of people willing to pay the price would go down. This is just the law of demand (higher prices, lower quantity demanded). But in this case the percentage willing to pay the higher price goes up. We can conclude one fo two things: either a) the law of demand is wrong, or b) because we are using a sample, we can sometimes get weird results. We're going to go with b).

So how do we handle the screwy results? Since we know that the 20% who say they would be willing to pay $50 should also say they are willing to pay $40 and we are going to combine the $40 and $50 group and say they are all conservatively willing to pay $40. But what percentage of respondents is that? Since we have 43% of our sample willing to pay $0, 18% willing to pay a minimum of $1, 10% willing to pay $10, 5% willing to pay $20, 7% willing to pay $30 that leaves 27% willing to pay $40.

Now combining our results, we can multiply the percentage of respondents (in decimal form) willing to pay each $ amount by the corresponding dollar amount to get a very conservative lower bound on the expected value of willingness to pay for the sample of respondents. Here's the math:

0.43*$0 + 0.18*$1 + 0.10*$10 + 0.05*$20 + 0.07*$30 + 0.27*40 =

$15.08

So being extra conservative, Greenstone finds that the lower bound on expected willingness to pay for this group of respondents to combat climate change is $15.08 in higher electricity bills per month.

In my book (Available at bookstores near you on Amazon), we show that the approach I just outlined is an absolute lowerbound on expected willingness to pay. Greenstone uses a slightly different approach (assigning the midpoint value to each group of respondents and then some generous rounding) and comes to a similar conclusion.

Specifically, these responses can be used to infer how much people value addressing climate change. To give you a flavor of the approach, take the 39 percent of households that are in favor of at least a $10 fee and the 29 percent that are in favor of at least a $20 fee. Doing some back-of-the-envelope calculations, I find that 10 percent (39 percent minus 29 percent) of households would favor a fee between $10 and $20. I then assign the midpoint — $15 — to this 10 percent of the population. I carry this approach through for the rest of the responses.

The net result is that, on average, American households are willing to pay $15 to $20 per month more on their electricity bill. The $15 is a lower bound because it assumes that the entire 20 percent of respondents who accept at least $50 are willing to pay $50, while the $20 figure assumes that this group is willing to pay $75 on average.

Buy my book (Available at bookstores near you on Amazon) to see why my approach is more defensible.