Thursday, August 19, 2010

Imperfect analysis and high speed trains

I've heard some very good arguments against high-speed rail projects -
- many are being undertaken in areas without the population density required for them to be worth their cost
- buses are more flexible and cost-efficient
but the article's objections don't seem to pass muster.
When you get someone off the road and into a faster railcar, it does 3 things:
1) it gets them to their destination faster
2) it allows them to spend time on the train doing other things rather than driving
3) it clears the roads for other drivers
The article focuses entirely on the (limited) first benefit, when I'd argue that the second piece is the most important and the third is as important as the first.
Let's say it takes T minutes to drive from point A to point B with no rail option. There are N people who try to do this. A rail option reduces travel time for those people who use it by Y%, and they can work e% as efficiently on the train as they can when not traveling. If X% of people take the train instead, your net benefits end up as follows:
Effect 1:  X% * N * T * Y%
Effect 2: X% * N * T * (1-Y%) * e
Effect 3 is the hardest to calculate and actually requires a functional form assumption, but presumably the first derivative of X on effect 3 is positive and the second derivative is negative. The reason for this is somewhat intuitive - when you go from 1 car to 2 cars on the road, congestion isn't much worse, but when you go from 1000 cars on the road to 1001, it can slow things up a lot for everyone else (a product of limited space - clearing the road for other drivers even a little bit is particularly important in crowded areas.).
for Y = 33% (from the article) and a reasonable e (If I have internet, my efficiency working on trains is not much less than my efficiency in real life - sometimes higher because i'm forced to sit there, but usually maybe 80%), effect 2 is actually going to be larger - with those numbers, over 60% higher.
Effect 3 is even more interesting. Without an explicit assumption (which I'm not qualified to give), you can't calculate the exact number, but because of the derivative behavior, even at small X%, you can end up with large net benefits for the other (1-X%) via effect 3. If taking 10% of the cars off the road made car travel 33% faster, then effect 3 would be 9 times as important as effect 1.
I'm not supporting or opposing high speed rail, I'm criticizing the method of analysis. Any analysis needs to ballpark all three of those effects. I guarantee the DoT has data on effect 3, and some psychologist has an estimate of e for effect 2.

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