A Ramsey twist

Catching up on open tabs and stuff I'd not managed to blog.

Olivia Wannan dropped me a line asking about a UK proposal to vary carbon charges with price elasticity, the idea being that consumption of luxuries was more elastic than necessities. If we define necessities as having very low price elasticity then I suppose that works.

But it seemed a fun kind of idea. Not a good one in practice, but a bit fun to think about. 

I'd sent this back, a small bit of which made it into the final piece (there's no way the whole thing could be used; I'd sent it more as background and to think it through).

Oh wow. 

This sounds like a mirror-image of a standard Ramsey drill. 

Background: Under a Ramsey model, we wouldn’t have a uniform 15% GST. We’d instead follow an inverse elasticity rule that put a higher tax on goods with inelastic demand and a lower tax on elastic demand. The idea is that it would aim to minimise overall distortions caused by consumption taxes by putting higher taxes on goods where demand wouldn’t shift much with the imposition of the tax, because it’s the shifts in consumption caused by tax that are distortionary and cause deadweight loss.

It sounds like they’re flipping that on its head, because if you’re wanting to reduce consumption of a bad, the substitution effects aren’t a distortion, they’re what you’re trying to induce. So flip the inverse elasticity rule. 

But it will wind up hitting the same problems that the Ramsey model hits. First, Ramsey starts breaking down when you get beyond undergrad treatments of it. Recall that the ultimate cause of distortions that Ramsey is trying to deal with is substitution from labour into leisure. So you then don’t really want an inverse-elasticity rule in consumption, you want to base it on cross-elasticities of consumption with leisure and labour: the Cortlett-Hague result. But more substantially, it’s just horribly horribly impracticable and incredibly risky. Doing it right would require getting elasticity estimates on everything and constantly updating them. And every one would be opened to lobbying. Commission an expert to come up with a different elasticity estimate. One of my econometrics profs in grad school joked, in antitrust context, that he'd been offered a boat if he could get an elasticity measure to show up on the right side of a line (he turned it down of course, and just used it as example for us of the perils of this kind of thing). 

If you went down this route, you’d wind up with all of the same stupid fights that the UK currently buys on deciding what’s essential and what’s luxury for application of their VAT – interminable lawsuits over tea cakes. One group would argue that driving is really essential for them rather than a luxury. Then you wind up with something like rural zones where a low carbon charge applies and urban zones where a high carbon charge applies – but how in heck would you ever run that system? It would be thoroughly rorted in minutes. Business groups would claim that their travel is really essential, as compared to tourist travel. Everyone would be commissioning experts to produce reports – great for economists with flexible morals, not so hot for the country. 

So while I’d buy that it’s entirely plausible that a blackboard exercise could show advantages from having a carbon pricing model that’s sensitive to price elasticity of demand, it would be a terrible idea in practice. And it’s not easy to see how you’d square it with an ETS: what, pretend that a tonne of emissions from one sector is different from a tonne of emissions from another?

Ugh.