WYPR Midday with Dan Rodricks: Cash for Clunkers and GPHM

Dan Rodricks of WYPR in Baltimore reviewed the details and merits of the Cash for Clunkers program on his July 27 broadcast. He invited me to join him to talk about the implications of "Gallons per Mile" for Cash for Clunkers. Here's the link to the broadcast.

In a nutshell:

1) Gallons per mile makes clear that national policy should focus on improving the fuel efficiency of the most inefficient cars, suvs, and trucks. The following table shows the gas consumption (per 100 miles) for different levels of mpg:

10 mpg = 10 gallons per 100 miles (gphm)
11 mpg = 9 gphm
12.5 mpg = 8 gphm
14 mpg = 7 gphm
16.5 mpg= 6 gphm
20 mpg = 5 gphm
25 mpg = 4 gphm
33 mpg = 3 gphm
50 mpg = 2 gphm

Thus, improvements of even 1 or 2 mpg in the "teens" can save about a gallon every 100 miles. That translates to 100 gallons every 10,000 miles, or one ton of carbon. That is the same amount of gas (and carbon) saved by replacing a 33 mpg car with a 50 mpg car. In fact, replacing a 14 mpg car with a 25 mpg car saves more gas (3 gallons per 100 miles) than any possible improvement on a 33 mpg car.

Cash for Clunkers makes sense because it focuses on cars in the "teens".

2) GPM helps car buyers see the true value of a Cash for Clunkers trade in. The voucher is only half the story; the other half is the value of the gas savings. Thus, GPM tools, like the GPM calculator at www.gpmcalculator.com, are essential for car dealers and car buyers during the trade in process: Know your gas savings!

3) And, in the long term, any number of policy decisions would be easier if the country adopted "gallons per hundred miles" (GPHM) to talk about fuel economy. Why? The things we care about as a country--carbon emissions, gas consumption, and personal gas costs--are a direct function of "GPHM", but not of MPG. It's as simple as: GPM can be subtracted to know gas savings; MPG cannot.

The CAFE increases in the spring were misinterpreted at times because major news outlets translated "mileage increases" directly to carbon reduction.

If you are interested in trading in a car in the Cash for Clunkers program, be sure to check the size and value of your gas savings at this post. The gas savings can be worth as much as the voucher.

Popular Mechanics Adds GPHM

Popular Mechanics has joined USA Today in offering gallons per hundred miles (GPHM) in its car reviews. Popular Mechanics included g/100m as one of "25 Bold Ideas" in their July issue.

The July 16 post ends, "The difference in the mpg ratings doesn't reflect the actual difference in fuel consumption the way that gallons/100 miles does, pure and simple. And that's why PM is starting to report fuel economy this way on its recent test drives. Pointedly, the EPA should promote this system too. Sure, it's trivial to calculate the difference, but with the current emphasis that car manufacturers, government agencies and consumers are placing on fuel economy, we need to change our way of thinking from high mileage to low consumption. "

If you are interested in learning more about gas savings from a trade in, please go to this May 29 post.

The Final Cash for Clunkers Bill, June 2009

The Final Bill

A final bill has passed both houses. Here is the official government site for details (from the NHTSA): http://www.cars.gov

[Updated: Here's an analysis of how the program is doing as of August 6.]

If you are considering trading in a car, carefully examine the gas cost savings as well as the voucher. Gas savings are better seen using "Gallons per Hundred Miles" (GPHM) than using MPG. In the table below, note that a 14 to 25 MPG trade in saves 3 gallons of gas every 100 miles, or 300 gallons every 10,000 miles. That's about $3,500 in savings in just 40,000 miles of driving. This post gives you multiple tools for calculating the gas savings of a trade in. The value of the gas savings can be as large as the value of the voucher.

MPG	GPHM
10	10
11	9
12.5	8
14	7
16.5	6
20	5
25	4
33	3
50	2
100	1

Thoughts on the Final Bill

The final bill has decent MPG improvements for cars (4 MPG and 10 MPG)--enough to "payback" the carbon released in producing the car--but not for large light duty trucks. We believe a tiered system based on GPM and requiring larger gas savings would have been better for reducing CO2 emissions.

However, if people go beyond the minimum MPG improvements when they make a trade in, that will make the program effective in reducing CO2 emissions.

25 Bold Ideas in Popular Mechanics July 2009 (the EPA waits.....)

G/100M is one of the 25 Bold Ideas.

Here is a post explaining why PM will use "GPHM" as a standard part of their car reviews in the future.

The idea has been adopted by USA Today but only partially by the EPA. The fueleconomy.gov site (run by the EPA and DOE) offers g/100m... if you know to look for it. Unfortunately, most of the site dances around gas consumption and never lands on it squarely. For example, the site has a good gas payback calculator here:

http://www.fueleconomy.gov/feg/savemoney.shtml

But, the calculator doesn't tell you your gas consumption.

You have the option to pick gallons per 100 miles when selecting and comparing specific cars here: http://www.fueleconomy.gov/feg/sbs.htm ....if you know where to look (it moves around across different pages). However, nothing on the site explains why you'd want to switch to g/100m.

The site does provide one GPM measure with every car description: Gallons per 25 miles. But this is a poor measure because all cars look pretty much the same on the scale. Larger scales make differences clearer (see Burson, Larrick, & Lynch, 2009, Psychological Science). We encourage the EPA and DOE to make g/100m more available to car buyers.

GPHM Table to see Gas Savings on Trade Ins (Including Cash for Clunkers)

[Update June 10: There are two personal benefits from Cash for Clunkers. One is the voucher. That one's clear. But the other benefit is the dollar value of the gas savings that result from a trade in. That one is less obvious because gas savings are a not a one-to-one function of MPG increases.

In many cases--especially for very inefficient cars--the savings in gas costs will be larger than the rebate. In that sense, the gas savings can be thought of as a kind of "matching" program for the voucher. It doubles the value of the voucher.]

The table below shows how different levels of Miles per Gallon (MPG) translate to Gallons per Hundred Miles (GPHM). You can easily calculate the gas savings from a trade in by subtracting the new GPHM from the old one. For example, trading in a 17 MPG car for a 28 MPG car saves 5.9 minus 3.6 = 2.3 gallons per hundred miles. That saves more than 200 gallons of gas (and $500) over 10,000 miles of driving. It also saves 2 tons of CO2 emissions over that distance. The gas cost calculations below assume that gas costs $2.50 per gallon.

Here is a downloadable version of the table below.

These tables directly caclulate the gas and cost savings of trading in a car that gets 18 MPG or less for different combinations of cars with higher MPG.

Finally, this online calculator will let you compare gas consumption and gas costs for any combination of MPG, driving distance, and gas price. It also allows you to calculate gas consumption and cost information on 2009 cars.

MPG	Gallons per 100 Miles	Gas Costs to Drive 10,000 Miles
10	10.0	$2,500
11	9.1	$2,273
12	8.3	$2,083
13	7.7	$1,923
14	7.1	$1,786
15	6.7	$1,667
16	6.3	$1,563
17	5.9	$1,471
18	5.6	$1,389
19	5.3	$1,316
20	5.0	$1,250
21	4.8	$1,190
22	4.5	$1,136
23	4.3	$1,087
24	4.2	$1,042
25	4.0	$1,000
26	3.8	$962
27	3.7	$926
28	3.6	$893
29	3.4	$862
30	3.3	$833
31	3.2	$806
32	3.1	$781
33	3.0	$758
34	2.9	$735
35	2.9	$714
36	2.8	$694
37	2.7	$676
38	2.6	$658
39	2.6	$641
40	2.5	$625
41	2.4	$610
42	2.4	$595
43	2.3	$581
44	2.3	$568
45	2.2	$556
46	2.2	$543
47	2.1	$532
48	2.1	$521
49	2.0	$510
50	2.0	$500

A Tiered Cash For Clunkers System Using GPM

Because CO2 reductions are not a linear function of MPG increases, it is very difficult to craft a sensible Cash for Clunkers bill using MPG.

Relying on MPG forces policy makers to set many different tiers and increments for trucks and cars. And, even then, not all MPG increments have the same implication. A 10 MPG increase has different CO2 implications depending on whether you’re starting with an original vehicle that gets 12 MPG or 18 MPG (the first starting point would save over 70 pounds of CO2 every 100 miles; the second starting point would save only 40 pounds of CO2). (See this post for details on the final June 18 Cash for Clunkers billl.)

In terms of CO2 reduction, however, all GPM decreases are created equal: Saving 1 gallon of gas every 100 miles saves 20 pounds of CO2.

A Tiered System based on GPHM (Gallons per 100 Miles)

As we’ve argued in many previous posts, the ideal Cash for Clunkers would be a tiered voucher system tied to GPM decreases. In this post, we’ll illustrate a simple tiered system using “gallons per 100 miles” (GPHM).

First, we need to set a minimum GPHM savings. In previous posts we’ve argued that a trade-in that saves 1 gallon per 100 miles would offset the CO2 emissions that are released when manufacturing the new car in a reasonable period of driving. Specifically, 7 tons of CO2 are produced in manufacture, so the new car requires saving 700 gallons of gas to offset its production. A 1 GPHM decrease would offset the CO2 emissions from the new car in 70,000 miles of driving. Other proposals would require a 2.5 gallon increase per 100 miles to achieve this offset with less driving. We’ll work with a 2 GPHM principle: The minimum trade in that qualifies for a voucher must save 2 gallons per 100 miles.

Let’s start by rewarding the minimum trade-in $3,000. Then reward each additional gallon per 100 miles saved with a $1,000 voucher. Car buyers could receive larger vouchers by saving up to 3 more gallons per 100 miles. Here is the policy in a chart:

A decrease of....
2 gallons per 100 miles (GPHM) = $3,000 voucher
3 gallons per 100 miles (GPHM) = $4,000 voucher
4 gallons per 100 miles (GPHM) = $5,000 voucher
5 gallons per 100 miles (GPHM) = $6,000 voucher

A trade in that saves the minimum 2 gallons per 100 miles would offset the CO2 from manufacturing the new car in 35,000 miles of driving. A trade in that saves a full 5 gallons per 100 miles (or more) would offset the CO2 from manufacturing the new car in 14,000 miles of driving (or less).

Also, note that personal gas costs drop as a direct function of GPHM decreases. Assuming gas is $2.50 per gallon and you drive 10,000 miles in a year, the cost savings from saving 1 gallon per 100 miles is $250. Saving 4 gallons per 100 miles is worth $1,000 per year in cost savings.

This tiered GPM system is simple.

• It ensures covering the CO2 emissions from production of the new car.
• Each level of GPHM decrease saves 1 ton of CO2 every 10,000 miles
• There doesn’t need to be a maximum efficiency for the original car
• There doesn’t need to be a minimum efficiency for the new car

Why no maximum or minimum? Because all GPHMs are created equal. We don’t care where the reductions come from. Any time a gallon is saved in 100 miles of driving it reduces CO2 emissions by about a ton in a year’s worth of driving.

Realistically, however, efficient cars will not be able to qualify for a large voucher. Someone who currently owns a 25 MPG car (which consumes 4 gallons per 100 miles) can qualify for a voucher by trading it in for a 50 MPG car (which uses 2 gallons per 100 miles). This yields a 2 GPHM decrease and the $3,000 voucher.

However, someone who currently owns a 12 MPG car (which consumes more than 8 gallons per 100 miles) has many trade in options. The person could trade it in for a 16 MPG car (6.25 gallons per 100 miles) to qualify for the $3,000 voucher. Alternatively, the person could earn the $5,000 voucher by switching to a 25 MPG vehicle (which consumes 4 gallons per 100 miles--and save $1,000 per year in gas costs).

The Limits of a Tiered Voucher System based on GPHM

The only limit, of course, is that people are not familiar with gallons per 100 miles. Yet.

The USA Today’s automobile writer, James Healey, has started adding GPHM to his automobile reviews. We need the EPA, DOE, and Consumer Reports to follow suit.

GPHM is an easy number to understand.

And, from a policy perspective, it is differences in gallons per 100 miles that are directly connected to CO2 reduction.

There are no "differences in MPG" that we can use to make clear, simple policy.

The MPG Illusion and the need for GPM

The MPG Illusion

Test your understanding of fuel efficiency with this interactive quiz.

Go here for the original Science article.

This March 2009 post offers a current overview.

The Problem with MPG

What is the problem with MPG? Consider a decision between two cars--a current vehicle and a new vehicle that is more efficient. Which improvement will save the most gas over 10,000 miles?
A) An improvement from 10 to 11 MPG
B) An improvement from 16.5 to 20 MPG
C) An improvement from 33 to 50 MPG

Surprisingly, all save about the same amount of gas over 10,000 miles: About 100 gallons.

The way to calculate the amount of gas used is to divide distance by MPG. A quick check of the numbers above will confirm the following gas usage over 10,000 miles:

10 MPG = 1000 gallons
11 MPG = 900 gallons
16.5 MPG = 600 gallons
20 MPG = 500 gallons
33 MPG = 300 gallons
50 MPG = 200 gallons

We want to emphasize that a higher MPG car is always more efficient than a lower MPG car for a given distance. We are not saying that a car that getst 11 MPG is somehow better than a car that gets 50 MPG -- to the contrary, we encourage all drivers to buy the most efficient vehicle they can. What we are saying is that MPG can be confusing when thinking about the benefits of improving MPG. The bottom line is that equal increases in MPG are not equal in gas savings.

As the examples above shows, small MPG improvements on inefficient cars can save a lot of gas. Of course, most people look at an improvement from 10 to 11, or 16 to 20, and think, why bother? But replacing an inefficient car with a car that is more efficient -- even by just a few miles per gallon -- is valuable in both gas savings and greenhouse gas reductions. Every 100 gallons saved reduces carbon dioxide emissions by 1 ton.

In short, you cannot simply look at an MPG increase from one vehicle to another to know the gas savings. Also, when a family thinks about its average fuel consumption, it cannot simply take an average MPG levels of two vehicles. Given two cars that are driven the same distance, the combination of 18 MPG and 50 MPG uses more gas than the combination of 28 MPG and 30 MPG. Direct comparisons of MPG is what leads to illusions. In each case, you have to convert MPG to know the amount of gas used.* We describe this step next.

The Solution

The solution to this illusion is thinking about gallons of gas used over some meaningful distance. We will use the term GPM (gallons per mile) as a general shorthand for expressing gas consumption over a given distance. We will focus specifically on Gallons Per 10,000 Miles.

We favor 10,000 miles for several reasons. First, 10,000 miles is close to the distance many people drive in a year. Second, it is a round number that is easy to adjust up or down. Third, it overcomes a natural tendency to minimize small gains: What appear to be small gas savings at 100 miles (6 vs. 5 gallons per 100 miles) are more obviously worthwhile when aggregated to a yearly number (600 vs. 500 gallons per 10,000 miles). The value of saving 100 gallons per year is clear. (The effect of scaling on "discriminability" is discussed in a paper that is available by request.)

Of course, because people do drive different distances in a year, final GPM numbers need to be tailored for each person's own circumstance. The tables and calculators below do the GPM math for you.

The Key is Amount of Gas Used

Another way of framing the basic issue is "Which is more useful to know: How far you can drive on a gallon of gas? Or, how much gas you will use while owning a car?" MPG answers the first question. GPM answers the second question.

We suspect that, when buying a car, most people want to know gas consumption. Gas consumption, as measured by GPM, can be directly translated to the cost of driving the car and to the amount of greenhouse gas emissions. MPG cannot.

Tools for GPM Calculations

Follow these links for tools for calculating GPM:

Tools for Calculating GPM from MPG

GPM Calculator Including All 2009 Automobiles

MPG vs. GPM - Which is more Useful?

Does using GPM imply that MPG should be scrapped? No. MPG is useful. Specifically, MPG tells you the range of your car's gas tank. For example, MPG can help you decide whether you can wait two more exits to refill your tank.

Both MPG and GPM have a useful role at different points in owning a car. MPG is useful when you're driving a car. GPM is useful when you're purchasing a car -- it better captures the fuel consumption, and fuel savings, when comparing a current car to a new car, or when comparing two new cars to each other.

Note that both measures serve equally well to tell you what is more efficient: 50 MPG is better than 20 MPG; 200 gallons per 10,000 miles is better than 500 gallons per 10,000 miles. They are not equal, however, in accurately conveying the gas savings from efficiency gains.

The two measures do not provide equal information. We would argue that GPM is better than MPG at helping people see the outcomes of their car decisions:

• GPM spells out in clear numbers how much gas one is going to use. 1,000 gallons per 10,000 miles is clearly dreadful. 200 gallons per 10,000 is clearly great.

• One can immediately tell how much a car will cost to fuel over 10,000 miles.


• One can see the actual magnitude of the gas savings when comparing a more efficient car to a less efficient car. Specifically, one can subtract one car's GPM from another to see the gas savings. MPG cannot be subtracted.
  

None of these outcomes is apparent with MPG until you do more math.

The Research Findings

Our main research finding is that the majority of people assume that equal increases in MPG are equal in gas savings; a minority thinks that gas savings are equivalent to percentage improvement. Both lines of reasoning lead to erroneous conclusions. In a final study we show that expressing fuel efficiency as GPM (in this case, gallons per 100 miles) leads the majority of people to identify the efficiency improvements that save the most gas. A brief summary of the three studies in Science appears at the Nudge blog. (and reposted here)

The Cause of the Illusion

For those mathematically inclined, the cause of the illusion is simple: MPG creates an illusion because it is a ratio. By necessity, MPG has a curvilinear relationship with its inverse (GPM). Because people do not spontaneously take the reciprocal, they incorrectly map changes in MPG to changes in amount of gas consumed. The formula for calculating GPM in this graph is 10,000 miles divided by MPG. Download a powerpoint copy of this graph here.














Percentage Improvement in MPG is Flawed

Some people expect that, although linear reasoning with MPG is incorrect, percentage increases in MPG captures amount of gas saved over a given distance. Even percentages, however, are prone to illusions with MPG. See this note for three examples of why percentage improvement fails.

For example, it is easy to see in the example given above that improving from 10 to 11 MPG is a 10% improvement; 16.5 to 20 MPG is a 20% improvement; and 33 to 50 MPG is a 50% improvement. Although they all represent different percentage improvements in MPG, they all save 100 gallons of gas over 10,000 miles. Although an improvement from 10 MPG to 13 MPG is only a 30% improvement, it saves more than twice the gas of the 50% improvement from 33 to 50 MPG. The problem with percentage reasoning is that it needs to be applied to a starting level of gas consumed; that amount differs over different levels of MPG. It is captured in GPM.

Imperial vs. Metric

The metric system does not solve the MPG illusion. India uses kilometers and liters but expresses efficiency as kilometers per liter. Because the ratio is distance over volume, it creates a parallel illusion to MPG. See this blog for a nice translation to the Indian context:

http://www.livemint.com/2008/06/19222458/Efficiency-measure-gives-wrong.html

Many countries currently use liters per 100 kilometers, which has the right numerator (volume) and denominator (distance) for judging efficiency gains. However, some people living in those countries have questioned how helpful it has been. We think that the base distance should be larger so that differences between efficiency levels are clearer and involve fewer decimal places.

Go here for more thoughts on the metric system.

*Technically speaking, GPM is an intermediate step in calculating the harmonic mean used to measure automaker compliance with CAFE standards. A family also needs to calculate a harmonic mean to understand their total fuel efficiency-the family can't simply weight the MPG of two vehicles by their respective driving distances.

My main webpage at Duke can be found here