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Their goal, it seems, isn't political.
However, that's obvious from the description of the two sets of households.
The first set wasn't "Democrats, environmental-minded people, and renewable-energy users". It was or, and that makes a difference. These are arguably three overlapping groups.
The problem is that you can't non-invasively identify a group of "Republicans that haven't donated to environmental causes and who don't subscribe to renewable energy sources." For just the latter you'd have to get the addresses of all renewable energy subscribers and pick addresses not on it; that's a much tougher call than just picking addresses from a specific energy company's renewable-electricity subscriber list. You'd have to get an exhaustive list of environmental causes--leaving aside the question of what is included in that category--and pick addresses on none of them, instead of getting one or two NGO's lists and picking addresses from it. And in both cases there's the question of whether it was a conscious choice to not donate or subscribe.
It's easy to pick addresses from voter registration lists. So the set is based on exclusive or, and two of the three alternatives are just <+> versus undefined. Yet we're trying to read it as <+> versus <->, which is true only for dem/repub. I know repubs that donate to environmental causes, believe it or not, and who subscribe to electricity from renewable sources. I'd argue there's a difference between dems and repubs, to be sure, but it's not as large as "repub" versus a set of people who are "environmentalists, green-energy users, or dems". I suspect there's a very large thumb on the scale--a scale that I doubt the researchers were focusing on.
I can't get to the paper. I don't think it's worth paying $5 for it at the NBER site. So I don't know if they controlled for historical energy use, house size and age, occupancy rate, etc., etc. In fact, I think for their purposes these don't really much matter--they weren't saying much about dems versus repubs themselves, from what the article says, but on the need for a multiplicity of messages. Kahn, one of the authors, is in public policy. I suspect the 4-5% point spread is generally valid for the variation resulting from merely pointing out energy usage rates, but without looking at the factors in the analysis of variation, the value of n, or the calculated error it's hard to take the 1% number seriously.
I suspect the conclusion is that instead of just using meters that report energy consumption they'd like to see meters that could also display price or that were accompanied by information on other consequences of high energy consumption. I know I look at the bottom line before looking at energy usage, but at any given moment know that consumption is closely related to bottom line.
For additional examples, my father thought the price and quantity of electricity wasn't a big deal, but my brother's mantra is "Every time you turn something on, every hour it runs, that's one time less it'll turn on and one hour closer replacement is." My father accepted that his AC unit's lifespan wasn't just the number of years it had been installed but was at least as much determined by the number of times it was operated and by hours of operation--and a few degrees higher would mean the AC unit turned on less often and ran for less time overall. He pondered the sticker shock of a new AC unit, not monthly expenses. My mother, on the other hand, didn't look at the numbers of kilowatt hours the household used, instead she obsessed over every cent spent every month--so she ironed, did laundry, baked, and even listened to the radio based on the electricity rates for a given time of day. I'd visit and she'd shoo me to the porch to read during the day, she'd turn off the radio and say I could listen to it later. (Now, with Alzheimer's, she does the wash at 5:45 pm every day, even if it's just the clothes she wore that day, and dries it at 9 a.m. the next morning.)
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