Bad math from the critics of CAFE reform

Critics are using some howlingly bad math to poke holes in Bush’s proposed reforms to the CAFE standards.

The CAFE standards have been enormously effective in raising fuel efficiency by requiring automakers to meet certain averages across their entire fleets. Bush has proposed dropping the fleet-wide standards, and instead requiring automakers to raise efficiency for each vehicle type within its fleet.

Economist Dean Baker doesn’t like it:

Thus, each car maker would have to gradually and steadily improve the mileage of each type of car, instead of improving the fuel efficiency of their entire fleet. According to EPA estimates, the 2006 Toyota Prius gets 55 miles per gallon (mpg), and the 2007 Ford Explorer gets 16 mpg. Under the new standards, both cars must improve their mileage. Which means that if, a few years from now, the Prius is still at 55 mpg and the Ford Explorer is at 20 mpg, Toyota will be penalized, while Ford will be a model corporate citizen….But what good does relative fuel efficiency do us? If a huge SUV is slightly more fuel efficient, so what?

I’ll tell you what: under typical driving conditions, raising the fuel efficiency of a Ford Explorer from 16 to 20 mpg saves as much gas as raising the fuel efficiency of a Prius from 55 to 175 mpg. (Here’s a spreadsheet with the math, if you want to play with the numbers yourself.) From an engineering standpoint, which do you suppose is easier to build: a 20-mpg SUV or a 175-mpg hybrid?

And this analysis doesn’t even take into account the fact that many more people drive SUVs than drive hybrids. In short, raising the efficiency of gas guzzlers has a vastly greater environmental benefit than raising the efficiency of already-efficient cars. Baker surely know this.

Of course, the devil is the details with this sort of thing. The real loophole would be allowing automakers to shift cars between vehicle types to escape stricter standards. A report in AutoWeek makes this sound like all-too-real a possibility.

Which is why we still favor a regime of tradeable fuel economy credits. An environmental policy nerd can dream, can’t he?

(Via Kevin Drum.)

Update: A commenter suggests that current CAFE standards at least indirectly push automakers to bias their fleet to more fuel-efficient cars. On the contrary, CAFE sets up some perverse incentives for automakers that can actually allow them to pollute more heavily by selling hybrids. Because CAFE looks at fleetwide averages rather than at individual vehicle classes, automakers can use the sale of hybrids to balance the sale of gas guzzlers. And, as we’ve already noted, a gas guzzler is much more bad than a hybrid is good.

To demonstrate this, I updated the spreadsheet with three hypothetical fleets. All three consist of 5,000 cars, and all three have an average fuel economy of 29 mpg. Superficially, these fleets look identical. The difference comes from the mix of vehicle classes in each fleet.

Fleet 1 provides a baseline. An equal number of cars are sold in each vehicle class.

Fleet 2 shows what happens when the automakers sell hybrids more heavily, which also also allows them to sell additional gas guzzlers without dropping their fleetwide average fuel economy. The net result? A 6% increase in the amount of gasoline used.

Fleet 3 has the same mix of vehicles as Fleet 1. But in Fleet 3, the fuel economy of the hybrids increases, allowing for a corresponding drop in the fuel economy of the gas guzzlers. Here the results are even more dramatic: a whopping 22% increase in gasoline used.

This is a toy example, but it does demonstrate the flaws in the current design of CAFE. Theoretically, requiring vehicle class-specific efficiency improvements could make a lot of sense. Please note, however, that this is not an endorsement of the Bush proposal. Nor is it a criticism. I’m not familiar with the particulars of the bill, and thus will remain judiciously silent. (Tradeable fuel economy credits! Woo-hoo! Sorry.)

Update 2: The “toy example” of different fleet models is so different from how CAFE actually works that I no longer think it’s particularly useful. (The math around the hypothetical Prius and Explorer, on the other hand, is perfectly valid, so far as I know.) So the points in this post still stand, but the spreadsheet model of the fleets is not particularly relevant to the current set of CAFE laws.

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  1. BCC - May 25, 2006

    I’m afraid that I agree with Dean Baker.

    I noticed in your spreadsheet is that moving someone from an explorer to a Prius saves 554 gallons, versus the 156 saved due to Explorer efficiency improvements.

    Current CAFE standards indirectly encourage vehicle makers to bias their fleet to more fuel-efficient cars (at least, this is what they would choose to do if CAFE standards were raised significantly).

    The proposed standards provide no incentive for automakers to push high-efficiency (and typically lower-margin) vehicles, and opens up lots of other loopholes that automakers could manipulate.

    Current CAFE standards may very well be an example of a poorly designed government regulation. The proposed standards, however, are an example of really badly designed regulations.

    They will make life easier for automakers, but will not have much of an effective on total gasoline consumption in this country.

    Me? I’d scrap the cumbersome and marginally effective CAFE program and push for tradeable credits, or failing that, an increased gas tax. Regulations work best when the details of how to meet their objectives are left to the producers and consumers.

  2. Adam - May 25, 2006

    Yes, moving a person from a guzzler to a hybrid is obviously the best scenario, but CAFE isn’t really set up to address this problem.
    Although it did a great job in the 70’s, current CAFE is pretty messed up, and I’m less confident than you are that it encourages good behavior on the part of automakers. See the updated math above.
    And any way you slice it, Dean Baker’s comments are silly. There might be a very good case to make against the proposed CAFE reform, but he isn’t making it.

  3. Jenn - May 31, 2006

    Implication that Dean’s case is “silly” without pointing to a basis for the opinion is simply unsupported criticism – which by the way is unhelpful.

    I however do agree with Dean. He points to at least one of the conceptual problems with the proposed plan. I’ll take a shot at explaining what I believe to be the goal of this plan.

    This is another display of how Washington bows to Big Oil. As the previous poster notes: The CAFE standards of the 70s worked. Look at any chart of US oil consumer over the 8 year window – Post President Carter. For those of you that remember TV Commercials of that era, do you recall just how hard the auto companies pushed fuel-efficient models? This was because they had to. Let’s face it, if you walk into a dealership and that dealership is under pressure to move 100 Ford Escorts/month, many more buyers will walk out with an Escort than without the mandate in place. That was the reality, and that’s what Ford did and GM did. Truth be told, they were selling those vehicles a very small profit just to move them fast and hard – Everyone was winning.

    Again, in reply to the previous post – You have in fact converted more drivers to fuel-efficient models.

    Toyota and Honda, at present, are crushing the US auto industry with their innovation in high MPG automobiles. The American Auto Company is, as usual, dragging their feet. (It’s the reason the Ford Hybrid SUV is powered with Toyota Hybrid technology. I believe that President Bush’s CAFE reform is designed to penalize Honda & Toyota’s behavior. I personally would like to know just what the penalty is? I’ll bet it’s designed to actually get them to drop the vehicle from the line up.

    Think about this. Under this new plan, if you were an auto company with a hot new fuel-efficient model, how would you introduce it? You’d probably introduce the initial model to yield a fraction its potential mileage just to give you head room. However, seeing that Honda and Toyota have already gone the distance they have nowhere to hide. This plan is indicative of the typical US Red-Tape Dinosaur business model – Move slow and heavy – Give the lobbyist time to think – Don’t give anyone the opportunity to catapult themselves to the top.

    You know, everyone dances around this issue, but there is a deep connection between our dependence on oil and our government leaders. Remember; it was under George Bush Senior that the CAFE Standards of the 70’s were dismantled, which in turn led to the return of the volume of gas-guzzlers we have on the road today.

  4. Adam - May 31, 2006

    Unsupported criticism? I supplied a spreadsheet with the actual math. How many blog posts do you know that are dorkily earnest enough to come with their own spreadsheets?
    I suspect that I’m running into some sort of “CAFE is good, changing CAFE is evil” orthodoxy here, so let me restate: this post is not about the merits or failings of the proposed legislation, whose details are unknown to me. This post is about the misconception that putting more hybrids on the road is the only or even the best way to restrain fuel usage in the U.S.
    (Note: this is very different than saying hybrids aren’t the best way for individual drivers to restrain fuel usage. In most cases, they are. But at the aggregate, national level, we have to acknowledge certain realities about what people are choosing to drive.)
    Dean Baker very explicitly uses this misconception to build a case against a type of reform that could, if done correctly, be beneficial. I don’t think it’s the type of argument anyone should be making.

  5. Xta - May 31, 2006

    Your final spreadsheet does have an error in it – you only displayed the average fuel economy out to zero decimal places. When I displayed it to just one decimal place I found that in your example 3 the average economy was only 28.6, vs 29.0 in the other examples. But displaying it to zero decimal places caused it to be rounded up. I had to raise the fuel economy of the SUV from 8 to 10 mpg in order the get the numbers to match up. That makes the increased fuel usage in that example only 13% higher. Your point still stands but you might want to fix the spreadsheet.

    Ed. note — I’d rather keep the numbers rough. The spreadsheet is a toy example that is just meant to illustrate a general point about how the design of a fuel economy standard can have unintended consequences. The general direction of the percentages is more important than the exact magnitude.

  6. Dan - May 31, 2006

    Good post and good spreadsheet to show the math.

  7. Jenn - May 31, 2006

    Yes, I saw your spreadsheet, and it is a good example, but here is the error I see in your journalistic approach.

    1) Dean Baker is commenting on the “Newly” Proposed changes. – His comment simply points out that these changes are detrimental to the goal and will result in the most successful designs being throttled due to the almost certain nature of them being penalized in the future. We need results fast. The technology is ready. Vehicles capable of 75MPG are availble now, and 150+MPG designs are sitting on the shelves waiting to be implimented. But, under the new CAFE plan these technologies will be unnecessarily strangled. (Do you agree?)

    2) Your spreadsheet articulates why the” Current” CAFE model is not working. I think we all agree there.

    So, given 1 & 2 above I don’t see where you and Dean disagree? If fact, I don’t see any indication in this thread regarding Dean Baker’s comment on the current CAFE model?
    Therefore, I must ask, why you would accuse Dean’s argument as silly as you articulate nothing opposing his position.

    The problem here is that a fleet plan does work. In fact, it worked when first enacted in the late 70s, but, it was broken by Big Oil. (P.S. – It was broken for just the reason you point to in your spreadsheet)

  8. James - May 31, 2006

    Seems to me a better calculation is to use total gas consumed (cell e23) and divide sumproduct(c18:21,D18:21) by that. For a weighted averaged “effective” fuel economy. Because the problem with fleet fuel economy as calculated is that it assumes (to be an effective measure) that a lower mpg car will be driven less than a high mpg car. And it just ain’t so. So the best way to fix it is to measure the total predicted gas usage and divide by total assumed milage, and that gives you a real number.
    measuring it this way, the example fleets get 19.49 mpg, 16.43 mpg, and 15.28 mpg. Highlighting that in ALL cases they work out worse than the CAFE calculation *and* the measure successfully captures the change for the different mixes. Allowing for meaningful penalty/incentives to automakers.

  9. Tony - May 31, 2006

    I agree with James. Here in Canada we don’t use mpg, but a fuel consumption measure (litres/100 km, equivalent in concept to the gallons per mile James calculated). Fuel consumption values CAN be properly averaged, but the inverse (mpg) cannot, as Adam shows.
    To see this more clearly, imagine two cars – one with poor fuel economy (say 20 litres/100 km) and one with amazing fuel economy (say 1 litre/100 km). If each vehicle is driven 100 km, an average 100 km driven consumes 10.5 litres. However, it’s certainly not true that we can average the inverses (5 km/litre and 100 km/litre, respectively) to get 52.5 km/litre, because that suggests that on average it only took about 2 litres per 100 km, which we just showed was completely untrue. The CAFE fleet approach therefore significantly understates the average fleet fuel consumption per mile.
    It seems to me that the best approach (consistent with both Baker and Adam) would be to require a specified fleet average fuel consumption per mile (30 mpg ~ equivalent to 3.3 gallons per 100 miles).

  10. wayward - June 1, 2006

    CAFE doesn’t encourage companies to build more efficient cars, as much it encourages them to build smaller cars. Smaller cars are often less safe than larger cars. Larger cars also tend to stay on the road longer. (I see 20 year old Caprices every day. I rarely see 20 year old Cavaliers.) More importantly, they often don’t fit consumer’s needs. As a recent Chevy Suburban commercial implied, the massive Suburban isn’t so inefficient if you can fit everyone into one vehicle, as opposed to several compacts.
    For some people, a large vehicle is the most efficient way of meeting their transportation needs. Any new regulation should take this into consideration.
    I do want be clear in that I believe Government regulation IS necessary because in the US, the market won’t solve the problem. Those who can afford a new car can also afford the gas. Cost conscious consumers buy used, which means the automakers don’t care about them. However, a bad regulation can be worse than no regulation.

  11. Jenn - June 1, 2006

    Interesting comments Wayward and a very self-fulfilling attitude. If you look beyond yourself you might notice this predicament we have all been dragged into is not just about the price of gas. If it were, I would totally agree. What is it about?

    1) A sustainable earth – Have you heard of globalwarming? I wonder how the two Bush brothers discus this at the dinner table: Florida’s governor cautiously entered the debate

    2) It’s about pollutant byproducts that are mounting carcinogens level in everything we touch and eat.

    3) And lastly, but extremely important, it’s about our young men and women who are now fighting to keep the price at pump down so that all our “I want more for less” Americans, and I want more in my paycheck BigOil CEOs, can support them driving their behemoth vehicles, which I’m near certain they could do without.

    No I haven’t seen the commercial, but have you ever heard of a mini-van? (I’m sure you going to say something like; Along with the 6 kids and parents they was a 22ft boat in tow. And you know, your right, almost every SUV I’ve seen on the road is loaded with people and pulling a house-trailer.

    Now, regarding your safety argument. If you look at the stats – statistically you are safer in the larger vehicle because the stats are generated to show total numbers of deaths, and consequently when someone is killed in a two vehicle collision between truck and passenger car the truck does win. (If you call that a win?)

    What you are not mentioning is this:

    1) FWD SUVs and Trucks do not handle nearly as well as passenger cars and are therefore multiple times more likely to cause a highway traffic accent due to poor maneuverability. I’m sure you heard of the Ford Explorer catastrophe. (And don’t blame that on the tires, I know someone that works for Fire Stone, I’m completely aware of the cause of that problem – and it was not the tires. Talk about backroom deals – Fire Stone was just the fall guy.) Don’t believe me? Do a Google search for : firestone AND explorer AND tires AND pressure. You’ll find that it was the published inflation pressures that were causing the tires to overheat. Why were the inflation pressures low? Because, FORD needed a cheap and dirty way to make an poor handling vehicle almost adequate.

    2) Traffic fatalities in Europe are less than America and Traffic injuries are far less.

  12. Adam - June 2, 2006

    Hi guys,
    Great discussion. Some comments:
    Jenn, your point 1 about penalizing promising technologies is interesting. I don’t actually see Dean making this same point in his piece (except maybe very obliquely), but it is a good point. So, no, I still don’t agree with Dean, and I stand by the notion that it is just as important to remove gas guzzlers from the road as it is to promote highly-efficient vehicles. But your comment is definitely thought-provoking. I think where we most strongly agree is that, whatever the specific design of CAFE, the really important thing is to raise the standard more aggressively. After, whatever its flaws, CAFE was very successful for a time.
    James and Tony — the system you’re describing is actually very close to how CAFE actually works. I was striving for simplicity in my toy example, but I think it’s pretty clear now that I overreached — the fleet models in the spreadsheet are so simplified as to be misleading. I’m going to leave the spreadsheet as is, but update the post.
    The stuff in the spreadsheet about individual car models is still valid though.

  13. Paul Nickerson - June 7, 2006

    The CAFE debate is certainly very interesting, but we all need to remember that the first responders to climate change related to auto emissions must be us as individuals. Everyone needs to take an honest look at his/her driving habits and figure out how best to reduce carbon and other pollutants coming out of the pipe. My solution, which I realize is not for everyone, was to buy another vehicle. Let me explain. Until last July I drove a full-size Chevy pickup full time. It gets 15-18 mpg. In July, I acquired an older Mazda which gets 36-40. The best part is that I kept the truck, but drive it 90% less, and mainly for hauling firewood, mulch, rocks etc; for towing a boat, hunting trips and hazardous winter driving. And the Mazda, as old as it is, still passes California emission stds. I guess the other satisfying aspect is reduced oil consumption which does go hand in hand with fewer emissions

  14. Adrienne - November 13, 2008

    Your math is WRONG. In your toy example you incorrectly calculated the average fleet efficiency. The equation used to calculate it is found on the NHTSA CAFE overview website.
    It is impossible to increase the number of gallons of gas consumed by changing the fleet makeup, while leaving the average fuel efficiency constant.
    The point: An increase in CAFE will ALWAYS decrease gallons of gas used (assuming the same number of cars and miles traveled). No matter what the fleet makeup is.