Friday, 6 May 2011

Elasticity and taxes

Tyler points to Matt Rognlie:
A famous result in public finance, the Atkinson-Stiglitz theorem on the optimality of direct taxation, captures this intuition in a striking way. Atkinson and Stiglitz show that if the utility function is weakly separable between consumption of various goods and labor (intuitively, the amount you work has nothing to do with your consumption choices, except insofar as working more gives you more money to spend), then no consumption taxes are needed to attain the optimum. You don’t levy higher taxes on gas than soy milk because soy milk has a higher elasticity; you just determine the optimal tax schedule on income and then stay away.
Matt then uses this to argue against petrol taxes as being particularly efficient: petrol demand is relatively inelastic, so some folks reckon it ought be taxed more heavily for revenue reasons. I agree with Matt's conclusion, but for different reasons.

I'm sure Seamus will correct me if I have this wrong (in his usual very polite "I think you meant to say" kind of way), but I thought the implication of Atkinson-Stiglitz was that when consumption of various goods is more strongly a complement of leisure than of work (weak separability from labour fails), taxation of commodities strongly complementary to leisure may become optimal. We can't tax leisure directly and so people choose too much of it relative to an ideal; taxes on complements to leisure become a second best. I'd be very surprised if petrol were a stronger complement to leisure than to labour. And so the Ramsey-style case for petrol taxes fails.


  1. I had the same thought with regard to labor vs. leisure substitutes & elasticity; Atkinson-Stiglitz assumes weak separability, so if not, then not.

    However, my understanding was that petrol may be a leisure complement, so there may be a Ramsey case for a petrol tax in return for a lower labor tax (on the other hand, since there may be distributional concerns, which in the standard model would argue for less petrol tax in general). IIRC, West & Williams have some papers on this.

  2. If it's a stronger complement to labour than to leisure, the case falls apart. It's likely a complement to both.

  3. Will have to check the papers though.

  4. Here's one paper (just by Williams) which has the nice feature of trying to find a "quasi-Pareto" improvement (i.e., obviously some people are going to be hurt, but he tries to find a solution that doesn't seem to hurt any particular income group, at least in expectation)

    One thing I wanted to add, which I think gets lost in some of these debates is that a lot of the applied papers estimating "optimal gas taxes" don't actually yield terribly large numbers. The paper above, for example, argues for a tax of 91 cents (US) per gallon (24 per liter). Although somewhat higher than the marginal damages figure they use, it's still quite a bit lower than, for instance NZ's current rate (though obviously since he's using US micro data for labor/leisure estimates, this isn't applicable) and not really seismically more than the average in the States.

  5. That's not the usual argument I hear for gasoline/petrol taxes. Usually I hear:
    1)Infrastructure spending on roads drawn from general funds would be a subsidy on driving; so we offset that roadway spending with gasoline taxes.
    2) Burning of fossil fuels produces negative externalities.

  6. @Fnord - I think some folks have been trying on the argument that there's a double efficiency to petrol taxes - that in addition to internalizing externalities, they're also a more efficient form of taxation due to their inelasticity of demand with respect to price. But that additional case falls apart unless petrol is a stronger complement to leisure than it is to labour.

    @Ryan: I've always had a hard time believing that Ramsey style taxing (the "complement to leisure" version) is implementable, or that any implemented version would be an improvement over the status quo.

  7. You're quite likely right. In fact, we might even take the simple magnitude of calls for higher gas taxes as evidence of this