Carbon from clunkers: A back of the envelope calculation

According to preliminary data from the Cash for Clunkers program, the average car clunked had MPG of 15.8 and these were replaced with cars with 25.4 MPG. Let's say a typical driver drives 15,000 miles/year. That amounts to nominal savings of 15000/15.8 - 15000/25.4 = 358.8 gals./year.

According to the EPA, each gallon of gas burned creates 19.4 pounds of CO2. So the nominal annual savings in carbon emissions is about 3.5 tons of CO2.

Approximating actual carbon savings is a lot more difficult. Among other things, we need to consider (a) how long the clunked car would have remained on the road were it not clunked; (b) the car the buyer would have bought had he/she not been enticed with subsidies into buying a higher-mileage vehicle; (c) when he/she would have bought that other car; (d) whether buying a new higher-MPG car causes the buyer to drive more.

These are difficult issues and I don't have hard data to answer them. So it goes--this is a back-of-the-envelope calculation.

The assumptions:

First I'm going to assume that the total fleet size does not change. Each car clunked is going to be replaced by a new car that can easily be produced using the excess car manufacturing capacity currently available.

Second, I'm going to assume that people are not generally going to drive more as a result of the Cash for Clunkers program. While I do expect the newly purchased vehicles will be driven more than the cars clunked, the difference will be made up by fewer miles driven on other less-used cars. I'm going to assume that these fewer miles will be evenly distributed across other cars in the fleet. Furthermore, I'm going to assume that other cars in the fleet have average 20 MPG, which lies about halfway between the clunkers and the new cars replacing the clunkers.

Third, I'm going to assume each car clunked would have remained in use for another five years. I don't have a good justification for this number. It just seems about right to me.

Fourth, I'm going to assume (b) and (c) are a wash. That is, I'm going to assume that the $3500-$4500 incentive to buy a higher mileage vehicle just offsets the general increase in MPG that occurs over time as CAFE standards rise and technology improves. So I'm assuming each car purchased under the Cash-for-Clunkers program has the same mileage as the car that would have bought at some future point in time.

Fifth, I'm going to assume that of the 15000 miles that is about the typical distance driven in a new car, about 10000 miles come from the car clunked and 5000 miles come from another 20 MPG cars that the buyer may have access to.

I think these assumptions imply that each car clunked saves about

5 x 19.4 x (5000/20 - 5000/25.4 + 10000/15.8 - 10000/25.4) = 28,359 lbs of carbon

So, each car clunked saves about 14 tons of CO2.

What's a ton of carbon worth? That's another hard question. The current offset price, which is probably a lot less than the social value, is in the ballpark of $4/ton. High-end estimates of the value appear to be around $100/ton, which would put the social value at about $1400 per car.

Of course, there are other kinds of pollution savings besides CO2 and I'm not counting those. The social vlaue could be larger.

And this is a rough calculation. Please write a comment about any assumptions or calculations that may be way off the mark.

But right now it looks to me like Cash for Clunkers wouldn't be an especially good deal in normal-economy times. But the stimulus effects of the program might easily tilt the balance in current lousy-economy times. It sure beats digging holes and filling them up.

Update: Cash for Clunkers is over now. But these calculations, similar calculations by others, and arguments made by Brad Delong, Jim Hamilton, and others, have convinced me C4C was far less than ideal. The biggest benefit was the stimulus and that seemed to work reasonably well. To some extent, the verdict on stimulus is still out: it will be interesting to see if car sales are sustained now that the program is over. But I don't see how destroying the clunkers could have been socially beneficial.