14 Jan 2015

A Brain Teaser for Economists

Tax policy 20 Comments

This post is aimed at professional economists, but those of you with real jobs should feel free to chime in as well…

I’m working on a response to Charles Krauthammer’s call for a $1/gallon hike in the gas tax, and I am making the point that (absent negative externality issues) it increases the deadweight loss to enact an increase in a specific product tax coupled with a revenue-neutral reduction in payroll taxes. The reason is that the tax base on gasoline is much narrower than on labor, and so raising a given dollar amount in revenue through a gas tax is more harmful than raising the same revenue through a tax on labor.

Of course, make sure you agree with that first step in the argument. But assuming you do, then…

==> The same logic applies to another $1/gallon tax swap, this time with (say) milk. Starting with the situation after we just enacted $1/gallon tax on gas and used the proceeds to reduce payroll taxes, I would argue that once again it distorts the economy even more to add a new $1/tax on milk, and use the revenues to further cut payroll taxes slightly.

==> However, if at step 1 we implemented an across-the-board tax on consumption goods, and used the revenue to reduce payroll taxes, that would *reduce* the deadweight loss.

==> So does this mean the incremental harms of doing the individual-excise-tax-and-slight-payroll-tax-cut go down, and with some specific product–perhaps the 54th one–it flips to reducing the deadweight loss?

I think I know how to resolve all of this, but I want to see what you think. And it should go without saying that I’m using conventional tax analysis here, not libertarian theory about taxes being theft.

20 Responses to “A Brain Teaser for Economists”

  1. khodge says:

    I don’t agree with step 1 because gas taxes tend to be true user taxes: the roads are built and maintained with gas taxes and only gas taxes. It is closer to the libertarian ideal of users paying what they owe. When you couple (intermingle) gas and payroll taxes you end up supporting social security from that great big pot of government money that they keep in the basement of congress.

    A $1/gallon hike should be justified on argument that keep it a true user tax: better mileage justifies higher taxes because the road maintenance does not benefit from better mileage (except for, perhaps, lighter vehicles).

    • Bob Murphy says:

      OK that’s fine khodge but it’s not what Krauthammer is saying. He is saying flat out that it’s good for the economy to give a tax break to workers.

      Also your argument only works if, magically, they are exactly undertaxing road users by $1/gallon right now.

      • Anonymous says:

        It works pretty well if they’re undertaxed 95 cents too though 🙂 I have thoughts on your post too but I’m on my phone and I don’t want to type it all out.

        • Vangel says:

          But they are not undertaxed at all. While there is a shortage in the highway funds that is due to the fact that the taxes paid for by motorists have been used to fund all kinds of other projects. And as Bob pointed out, that was not the argument.

      • khodge says:

        Bob, of course you are right. My problem is that by giving the government a new avenue of taxation it does not ever close off the old avenue. Within two presidential terms government will have reclaimed the original avenue while keeping the new avenue. I very rarely get past the point where some economist says there is a trade-off because the government doesn’t trade…it only makes temporary concessions to establish new hooks into its servants (us).

    • Major.Freedom says:

      khodge:

      “the roads are built and maintained with gas taxes and only gas taxes”

      Money is fungible. Taxes collected and spent cannot be parsed out that way.

      • khodge says:

        Of course it can; bond covenants do it all the time; sales and use tax forms require that these items be reported separately. I think that your confusion lies in a business like a government where tax dollars set aside statuatorily for, say k-12 education are offset by general obligation funds that would go to education now going to healthcare. If the only funds going to roads are gas taxes and gas taxes go only to roads then there is no shuffling going on.

        • Major.Freedom says:

          Not even bond covenants work that way. No bond has a covenant where specific dollars collected (meaning from specific people) must be used to pay for X. That is why covenants always have the form of requiring the firm to maintain ratios, or retain ownership in a quantity of something.

          When you hear things like “house taxes pay for schools” what that means is that the quantity of dollars collected from house taxes must be allocated to school exenditures. It does not mean that the specific dollars collected from house taxes must be kept in a lock box (if they are paper dollars), or in an encrypted seg fund that does not allow the bank to even transfer one dollar for another within their treasury (if they are digital dollars). It means the amounts.

  2. Daniel Kuehn says:

    That 95 cent one was me

  3. Tel says:

    I’m not a professional economist, although the work does seem a little easier than professional engineering, if anyone wants to swap places for a while.

    Charles Krauthammer is strongly arguing on the basis of negative externality due to oil money going to fund those nasty foreign terrorist countries. This is a separate issue, we maybe should discuss, but it’s based on geopolitical interpretations which are a lot more individually subjective than (say) driving to work and back. It’s not really a discussion of economic theory.

    To look at Bob’s problem (absent negative externality issues) I think this is the key step:

    The same logic applies to another $1/gallon tax swap, this time with (say) milk. Starting with the situation after we just enacted $1/gallon tax on gas and used the proceeds to reduce payroll taxes, I would argue that once again it distorts the economy even more to add a new $1/tax on milk, and use the revenues to further cut payroll taxes slightly.

    At least in theory, the additional tax on milk slightly reverses out the distortion previously imposed by the tax on oil. As you tax more and more different items (i.e. move towards a broad base consumption tax) you end up bringing more and more items into line with one another, therefore not prejudicing the buyer toward one or the other.

    However, a 1$/gallon tax on octane is not really equivalent to a $1/gallon tax on milk, because you have to try hard to drink a whole gallon of milk. The typical approach to a broad based consumption tax is a flat percentage (like Australia’s 10% GST which does exclude fresh food, bank fees and some other things, but still kinda broad), or the VAT type tax that is popular in Europe.

    There’s a bunch of secondary subtleties: the demand curve for transport fuel is stiff (people need it to get to work and back), the demand curve for milk is softer (you can easily live without milk), even if government imposes the same percentage on everything, purchasing behaviour will change, often in unexpected and unusual ways. Also, the GST is cunning to make the person on one side of the transaction into the tax collector, but the person on the other side of the transaction into the tax reporter (because business hands in their dockets to claim back GST). This interlock is designed to make tax evasion more difficult and it worked in Australia. Income tax for example, is very much open to “cash in hand” deals where people simply don’t bother reporting all of their income.

    A tax where most people follow the rules is probably better than a tax most people evade and only a few suckers get stuck paying (on both the broad/narrow arguments and also on the externalities involved in paying people to be criminals).

  4. Daniel Kuehn says:

    So presumably there’s a tipping point at some point, but the one thing that a consumption tax has in its favor (that a tax on specific consumption goods would also have in part) is that it increases savings and (if we’re not in a liquidity trap) investment. So instead of reducing labor supply and taxing savings we are leaving labor supply untouched and not taxing savings. So that gain is going to balance out some of the deadweight loss. Obviously the distortion dominates a single tax on a single product (if we’re not considering externalities), but even individual product taxes still have this dual property of (1.) not reducing labor supply and (2.) not taxing savings.

    I’m not sure if this is related to what you were thinking.

  5. Tel says:

    So does this mean the incremental harms of doing the individual-excise-tax-and-slight-payroll-tax-cut go down, and with some specific product–perhaps the 54th one–it flips to reducing the deadweight loss?

    I say, no there isn’t a phase change. It’s incremental with each step.

    However, if you impose different rules on each item, there will be a phase change when the complexity of the rules gets to the point where just say “Foo to this, I can’t be bothered dealing with this paperwork any more.”

    Compliance costs are real, and large. That’s why flat percentage tax is at least something easy to deal with and doesn’t piss as many people off.

  6. Andrew_FL says:

    For all the political talk of “lower rates, broader base” the most popular taxes always seem to be those with the narrowest bases possible.

    Just look at cigarette taxes. They get hiked pretty consistently with little opposition.

    This is, how you say? Democracy: Two wolves and a sheep deciding what’s for dinner.

  7. Josiah says:

    Wouldn’t the ‘flipping point’ come when the tax applied to enough products that the base was larger than for the gas tax?

  8. Transformer says:

    So you move from 100% of taxes being raised by payroll tax to the same tax revenue being raised by 100% sales tax. This is done by gradually taxing more goods and at the same time reducing the payroll tax

    Say the tax on the first good reduces the payroll tax to 99% of revenue and increases the sales tax to 1% of revenue. Isn’t it possible that the deadweight gain from the reduced payroll tax outweighs the deadweight loss from the single good taxed ?

    In other words couldn’t the deadweight loss just gradually reduce between the two extremes ?

  9. Toby says:

    Isn’t the keyword here that you’re keeping the amount of revenue raised constant? As you broaden the base you lower the tax rate and as deadweight loss increases in the square of the tax rate you lower the deadweight loss: i.e. x^a + y^a 1.

    • Toby says:

      i.e. x^a + y^a 1*

    • Toby says:

      Great, I see I can’t insert an equation then just do it verbally. I.e. the sum of two numbers squared is lower than the square of the sum of those numbers. This works with every power larger than 1.

  10. gienon says:

    I think you have answered 95% of your question. It’s less of a burden (or deadweight loss in S&D curves terms) to extract a given amount of revenue from a bigger spending stream so I think the critical product is the one that tips the scale of bigger spending in the consumption tax’s favour.

    • gienon says:

      Scratch the above. I misunderstood the problem.

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