26 Nov 2013

Clarifying the “Tax Interaction Effect”

Climate Change 14 Comments

David R. Henderson favorably reviewed Ross McKitrick’s presentation (at IER’s Carbon Tax conference last summer) on the “tax interaction effect,” and then in a follow-up post David pursued Greg Mankiw’s writings on the topic.

In the comments of David’s second post, someone wrote:

If my microeconomic intuition — that taxing harmful externalities will enhance net welfare, and to a greater degree than some regulatory regime — turns out to be wrong, then I wonder what else I might be wrong about? After considering tax interaction effects, should we not be so hard on speeders? Maybe even encourage them? And what about theft, of various sorts? Keeping Coase (rather than Pigou) in mind, I sometimes think about uncompensated environmental externalities as a form of theft. I wonder if theft, generally, might turn out to be beneficial in some CGE model beyond my ability to comprehend.

OK, putting aside what seems to be sarcasm, it’s clear that this guy doesn’t really understand what the TIE [tax interaction effect] claim is. That’s not entirely his fault, because it’s a very subtle issue, and I don’t think the actual economists publishing on the topic have spelled it out in crystal-clear fashion. The more I think about it, the more “obvious” it seems to me, but it has taken me a long time to get here. At IER, I will soon have a post trying to walk through the whole thing, but because I explain it from scratch, it’s pretty long. In the present blog hit, let me summarize the key issues (as I now conceive them) in a hopefully intuitive way, for people who are familiar with the standard Pigovian framework.

(Note: Silas Barta had a great idea when he flipped the “stacking” of the taxes; his analysis clarified my own thinking on this.)

* * *

(A) Assume people are annually emitting 30 billion tons of carbon dioxide with no carbon tax. Assume the marginal/average “social cost of carbon” for current emissions is the same, at $30/ton. So if nothing is done, Earthlings are causing $900 billion annually in future negative externalities (present discounted value).

(B) With no other taxes, “optimal” thing to do according to textbook is to levy a $30/ton carbon tax, the receipts of which are distributed lump-sum back to citizens. Assume this makes people cut emissions in half, down to 15 billion tons. There is a reduction in climate change damages of $450 billion. However, the conventional economy is hurt; after all, businesses and consumers are now facing a constraint to use less carbon-intensive techniques. (If someone could magically cure climate change, the carbon tax would obviously hurt the economy, so it’s still having that effect now, even though we’re superimposing a stabler climate on top of the hurt economy.) Suppose that the harm to the conventional economy from the optimal carbon tax is $100 billion. Thus the net benefit of the carbon tax is $350 billion; this is the maximum, by the way, because we’re choosing the $30/ton tax optimally. If we had made it $31/ton, then climate change damages would be only $440 billion but economic damages would rise to $111 billion, putting the net gain at only $349 billion. Going the other way, if we had only set the carbon tax at $29/ton, then climate damages would be $461 billion while economic damages would be $90 billion, for a net gain of the carbon tax of $349 billion. So the optimal carbon tax of $30/ton–which is the “social cost of carbon”–maximizes the net benefits of a carbon tax, which makes sense.

(C) Now re-do the analysis, but this time suppose there was an income tax. We all know income taxes are distortionary. Suppose this income tax (considered by itself, without a carbon tax) caused $1 trillion in deadweight loss on the economy. We also know that if you increase the income tax rate, then the deadweight loss increases more than proportionally. So, if you are going to implement this identical income tax code, not starting from scratch, but on top of a carbon tax of $30/ton–which itself is already causing $100 billion in harm to the economy–then the marginal deadweight loss of the income tax code is $1.2 trillion, rather than the $1 trillion if there is no carbon tax. Thus, the “tax interaction effect” here is $200 billion. This is in addition to the $100 billion harm to the economy coming directly from the carbon tax. The tax interaction effect’s $200 billion harm is an indirect effect of the carbon tax, because it makes the deadweight loss from the income tax that much higher.

(D) With the above numbers, it’s still better to impose a carbon tax at $30/ton than to do nothing at all. Note that we are still returning the receipts of the carbon tax back to citizens in lump-sum checks. By imposing that tax, you reduce climate damages by $450 billion, while the economy suffers damages of $100 billion (direct hit) plus $200 billion (tax interaction effect), for a total hit to the economy of $300 billion. But $450 bn – $300 bn = $150 billion, which is the net gain of doing the original $30/ton carbon tax.

(E) Ah, but the $30/ton carbon tax is no longer optimal. On the margin, the carbon tax is causing more damage in the presence of the income tax, than it would in a textbook scenario with no other taxes. So if we reduce the carbon tax down to, say, $15/ton, we now achieve the optimum of a (say) $220 billion gain in welfare, from imposing the tax. This of course is lower than the $350 billion gain we achieved in (B). This makes sense too; since we have to worry about the carbon tax exacerbating the deadweight loss of the income tax, it is no longer as useful a tool, so the total social gains we can derive from it are lower than in a scenario with no tax interaction effect.

(F) Ah wait, we can actually do something better. We can use the receipts from the new carbon tax to reduce the income tax rates. In the absence of the carbon tax, reducing the rates of the income tax obviously reduce its deadweight loss; this is the “revenue recycling effect.” So now, in addition to its beneficial effects in terms of reducing emissions and hence climate change damage, the carbon tax has two other effects that cut in opposite directions: The tax interaction effect makes the income tax worse, pushing us to levy the carbon tax at less than the social cost of carbon. But the revenue recycling effect makes the income tax better, pushing us to levy the carbon tax at more than the social cost of carbon. Which effect dominates? This is an empirical question, but the intuition on this particular point (as to whether TIE <> revenue recycling) is that a carbon tax has a base smaller than a typical income tax, and so on that score you would think intuitively that raising $1 billion from a carbon tax is more harmful to the conventional economy than raising $1 billion from an income tax.

(G) In light of all the above, it is probably the case that (given our other numbers) the new carbon tax, if levied on top of the pre-existing income tax but with all carbon tax receipts being used to reduce income tax rates, will have an “optimal” rate lower than $30/ton but higher than $15/ton. Note that such a number is also higher than $0/ton. Thus, even after you’ve absorbed the standard tax interaction effect analysis: It is still true that a negative environmental externality can be fixed with a Pigovian tax, and it is still true that using carbon tax receipts to reduce other income tax rates (rather than increasing government spending, or even returning receipts back, lump sum) is “good for the economy.” However, it is NOT true that the presence of a distortionary income tax bolsters the “case for a carbon tax,” and it is really really not true that if you disregard environmental benefits, you can still get a “pro-growth” tax reform by implementing a carbon tax and reducing income taxes accordingly.

14 Responses to “Clarifying the “Tax Interaction Effect””

  1. Blackadder says:

    Makes sense.

    • Silas Barta says:

      Good to hear! You and I were both unclear on what exactly the purported mechanism was supposed to be in Bob’s previous post on this.

      For my part, the explanation sounded like “Here’s the standard intuition. But it turns out, [miracle occurs] so it’s all wrong!”

  2. Silas Barta says:

    I was hoping for more interest in this …

  3. thinkingotherthings says:

    Yet since Scenario #3 leaves us with an income tax and the new carbon tax, operating side by side, we have to consider the tax-interaction effect. Is it possible that the total distortion to the economy, caused by the combination of the income tax (albeit at lower marginal rates) and the new carbon tax, is higher than the original deadweight loss due to the income tax alone (albeit at its higher, original marginal rates)?

    So this tax interaction effect argument assumes, if I’m reading this correctly, that the carbon tax itself imposes distortions that create deadweight loss. That seems wrong to me. Yes a carbon tax will change relative prices for output goods and input factors associated with the polluting process, but that’s the whole point of taxing a negative externality in the first place – you are attempting to adjust prices to fully reflect costs and benefits. Even though the new prices will be higher, that doesn’t create deadweight loss if the prices were too low prior to the tax being imposed.

    • Bob Murphy says:

      thinkotherthings wrote:

      Is it possible that the total distortion to the economy, caused by the combination of the income tax (albeit at lower marginal rates) and the new carbon tax, is higher than the original deadweight loss due to the income tax alone (albeit at its higher, original marginal rates)?

      I’m not sure what you mean by “total distortion.” Before we answer that, you need to be clear about this part when you write:

      So this tax interaction effect argument assumes, if I’m reading this correctly, that the carbon tax itself imposes distortions that create deadweight loss. That seems wrong to me.

      Forget the income tax. Just consider (A) and (B) right now. Imposing the $30/ton carbon tax is optimal, but it causes real GDP (as conventionally measured) to drop by $100 billion. It looks like a “distortion” and “deadweight loss.” But, that $100 billion “distortion” is counterbalanced by a $450 billion reduction in climate change damage.

      (The difference between these two things is really easy to see with climate change, since the negative effects of the emissions don’t manifest themselves right away.)

      So in one sense, adding the carbon tax made humanity get richer by $350 billion on net, but in another sense, it caused a $100 billion “distortion” to the economy.

      So I can’t answer your first question because I’m not sure you’re getting this more basic point.

  4. gofx says:

    I am rusty on this, but within the bounds of standard micro, in order to figure out the “optimal” taxation (especially Pigouvian) for this externality you also must take into account the market structure and other divergences from marginal cost (regulatory costs, related and unrelated taxation, existing control and mitigation costs etc.) in the extant and related output and factor markets. A sufficient number of positive divergences of price from marginal private cost may already be yielding a price at marginal social cost. For example, monopolies tend to underproduce relative to demand. This is sort of a nod to the Theory of the Second Best, but its more than that. Many prices for products we buy (especially heavily regulated industries such as utilities) already exceed marginal private cost by quite a bit.

  5. Tel says:

    I wonder if theft, generally, might turn out to be beneficial in some CGE model beyond my ability to comprehend.

    That would be the standard Keynesian position going by the name of The Tradgedy of Thrift, by stealing your savings and putting that money to work elsewhere in the economy they activate idle resources and thus boost the economy to the benefit of everyone. Anyhow, if you worked hard to save that stuff the first time you might as well keep working.

    The process is fairly easy to comprehend, although one might argue the morality is questionable. Externalities are not about morality though, they are about arbitrary people finding ways to make claims on whatever you are doing that might look productive.

  6. Tel says:

    … the intuition on this particular point (as to whether TIE revenue recycling) is that a carbon tax has a base smaller than a typical income tax, and so on that score you would think intuitively that raising $1 billion from a carbon tax is more harmful to the conventional economy than raising $1 billion from an income tax.

    I must admit I don’t follow the intuition here. Firstly the Carbon tax may well have a bigger base than income tax, but beyond that, the whole idea of Pigovian tax is to be selectively targetting the “bad guys” amongst us (which in the case of a Carbon tax happens to include just about everyone). That’s assuming the whole externality caper makes sense at all… something I’m running with for the sake of argument.

  7. Mark Harrison says:

    “but the intuition on this particular point (as to whether TIE revenue recycling) is that a carbon tax has a base smaller than a typical income tax, and so on that score you would think intuitively that raising $1 billion from a carbon tax is more harmful to the conventional economy than raising $1 billion from an income tax.”

    I know that is how Goulder explains it, but it has never made much sense to me. By that logic, it can never be optimal to depart from a broadbased tax by raising the tax rate on one good. But we know from corlette and Hague (and Ramsey) that if we have a uniform consumption tax, which results in a substitution to too much leisure, then it can improve efficiency to tax the complements to leisure.

    So isn’t the relevant question whether ‘carbon’ is a substitute or complement for leisure. If it is a substitute, then raising the tax on it will lead to a substitution to leisure, exacerbating the existing tax distortion (we will take even more lesiure and lose some income tax revenue). We have always known that a revenue neutral increase in the tax rate on one good and cut in the bvoradbased tax may increase or decrease welfare (at the second best Ramsey optumum, the two effects would offset and leave welfare constant).

    Empirically, itr seems ‘carbon’ is a substitute for leisure (eg we use petrol to drive to work), so taxing it leads to a social loss from the tax interaction effect.

    • Silas Barta says:

      By that logic, it can never be optimal to depart from a broadbased tax by raising the tax rate on one good.

      Doesn’t follow at all. Of course a Pigovian tax *could* make sense in this framework; the question is just about the relative magnitude of the prevented harm from that externality tax vs the utility loss from the “base shrinkage”.

      • Mark Harrison says:

        I meant through the tax interaction effects, ignoring the direct gain from internalising the externality.

        Say we have an income tax which results in excessive leisure, and tennis rackets are a complement with lesiure. Rejigging the tax system by raising the tax on tennis rackets and lowering the income tax rate slightly could improve efficiency. But Goulder would come along and say raising the tax rate on tennis rackets is inefficient because it is such a narrow base.

        My point is that the substitution relationships between the goods is what is crucial here, assuming that you want to engage in second best optimising. I have a lot of sympathy with the Harberger view that we don’t have the information to do that and a uniform broadbased tax is best and the issue is what should be included in the base. Further, we don’t want the government engaging in setting different tax rates for different goods as political incentives mean they will use that power for re-election, punishing enemies, extortion, etc, rather than efficiency – just as they do with carbon taxes.

  8. Harold says:

    Thanks for a clearer picture. If there were no TIE, and there were benefits to the economy of shifting tax from income to carbon, (the win-win), then it would be a good idea to replace income tax with a carbon tax even in the absence of environmental cost.

    The base for a carbon tax it pretty wide as it affects everything that is made, warmed, cooled, distributed etc. Given that what is realistically earned income is often disguised as capital income, and even genuine capital income is spent on stuff that uses carbon, is it possible that carbon has a wider base than income tax?

    I don’t quite follow one points. You say ” if you increase the income tax rate, then the deadweight loss increases more than proportionally” You then say if you introduce the income tax on top of a carbon tax, “the marginal deadweight loss of the income tax code is $1.2 trillion, rather than the $1 trillion if there is no carbon tax” This does not necessarily follow, because you say if *income* tax rates increase, deadweight loss from the *income* tax increases more than proportionally. Here you have income tax on top of a different tax, and you conclude the deadweight loss of the *income* tax is larger than it would be without the other tax. It may be obvious that the situations are essentially the same in an economic sense, but it is not from a logical perspective. You have to show that one tax effects the deadweight loss of another – maybe that is trivial, but it seems to presume a “tax interaction effect” in order to explain it. I understand that you are not trying to prove the TIE, only to explain it.

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