Thursday, 29 April 2010

More on Ramsey Taxation

As Eric has noted, the Treasury implicitly invoked the idea of optimal Ramsey taxation in its letter to the New Zealand Law Commission, commenting on the Marsden Jacob report. The key paragraph in the letter is the following.

Treasury recognises the need to reduce taxes on capital and labour and supports funding these reductions through increases in taxes least likely to reduce welfare. Welfare losses from excises taxes on alcohol are likely to be lower than for many other forms of tax.

Now the idea of increasing taxes that produce lower welfare losses could be invoking either the idea of optimal Ramsey taxes (basing tax rates on elasticities of demand) or Pigouvian taxes (taxing goods that produce negative consumption externalities). The Treasury go on to note that:

More specifically, the report relies on recycling all revenue raised from increased excise taxes directly to taxpayers via a rebate or a reduction in
other taxes. By doing so, the report concludes that welfare can be enhanced despite conservative consumer sovereignty assumptions. This revenue
constraint needs to be clearly conveyed when
any policy recommendations to increase the excise rate are made. In particular, using any increased excise revenues as “tied taxes” to fund the costs to Government of alcohol consumption would violate this constraint.

Now if higher alcohol taxes is motivated by Pigouvian considerations, it is not necessary for the income to be rebated to achieve welfare gains (although doing so can make the gains higher), so the Treasury comment must be invoking Ramsey taxation.

As I noted here, the principles of Ramsey taxation are often misunderstood. The Ramsey result is also called the the “inverse elasticity” rule, which is sometimes taken to mean that higher taxes should be placed on goods whose demand is relatively inelastic. This is not strictly true for two reasons. First, the elasticity that is referred to is the elasticity of the Hicksian demands. That is, it refers to the effect of changes in price if at the same time income is changed to maintain spending power. Second, the elasticities referred to are the elasticities of goods with respect to all prices, not just the price of the particular good. The inverse elasticity rule is that the set of all taxes should lead to an equal percentage reduction in the Hicksian demands for all goods.

To take the second caveat first. Two goods might both have highly elastic demand because each is a close substitute for the other. But that doesn’t automatically imply that both should have a low tax rate. If both are taxed at the same rate, then the tax system will not induce substitutions between those two goods. In essence, the Ramsey rule is that uniform commodity taxation (in addition to any Pigouvian taxes for goods that generate consumption externalities) is optimal if all goods can be taxed. If there is one good, leisure, that cannot be taxed, then the highest tax rates should go on those goods that are most complementary with leisure. Furthermore, if most goods are generally complementary to leisure rather than substitutes for it, then optimal taxation is going to be approximately uniform anyway.

So, is alcohol a good that is more complementary with leisure than other goods? I would be interested to know how Treasury reasoned that it is. I am dubious about the ability of econometric models to answer that question, as it requires estimating a full general-equilibrium set of own-price, cross-price and income elasticities for all goods, with the income elasticities calculated from changes in incomes for the same person rather than cross-section differences across individuals. (This caveat is because income variation across individuals is highly correlated with individual characterstics including preferences.)

Given the data difficulties, I prefer to reason from introspective intuition. Consider the following thought experiment: Imagine there is a general cut in income taxes, thus increasing after-tax wages, but that at the same time, everyone has to pay a lump-sum tax to the government that will leave them with the same purchasing power if they don't change the amount they work. Would this lead to people chosing to work more? If your answer is no (either because of preferences or because work opportunities are lumpy and the opportunity to work an extra hour or two at the margin doesn’t exist), then you are arguing that the optimal Ramsey tax system is uniform. If you believe that people would on average choose to work more and thus have more income, there is a role for differential commodity taxation. The question then is which goods would see the greatest proportionate rise in expenditure. These are the goods that are the least complementary to leisure and are therefore the ones for which the optimal Ramsey taxation is the least. My intuition is that alcohol along with consumer durables would be in this category, with the highest Ramsey tax rates needing to go on goods consumed by the leisure classes, such as gym membership, cafĂ© expenditure. etc. I certainly find it difficult to believe that alcohol would be a good whose consumption increase would be unusually low.


  1. Seamus: it's less clear to me that it's necessarily a complement to leisure. I far more enjoy a beer after a day's work than if I'm just lounging around. Indeed, after the brief fisk of the Marsden Jacob report, I treated myself to a fine Renaissance Chocolate Oatmeal Stout; I wouldn't have had it had I gotten nothing done that day. Lots of folks find alcohol a complement to business lunches and meetings. Ever been to a hospitality suite at an economics convention?

  2. Eric,

    You are agreeing with me. You are saying that alcohol is a complement to work and a substiute for leisure. Ergo, efficient Ramsey taxation would have alower tax on alochol than other goods.

  3. Ah, good.

    And even if it went the other way, that would just say that there should be positive excise, not that the rate should be higher or lower than at present.