Series on tax: Part 2b – let’s experiment with explanations

In the second part of my series on taxation I wrote about distortion and burden.  But I’m not sure whether my description about wedges and how people respond to prices was necessarily clear enough for a non-economist audience.  So I’m going to experiment with some other ways of articulating what I mean – ways that are equivalent, but for different people may be clearer.

Note:  I apologise in advance if this is a bit scattered – if you have questions or comments note them down in the comments, you’ll be doing me a favour 🙂

Paying our labour and capital

Remember that I stated in part 1 that we want to think about taxation, and spending, in terms of changing the allocation of goods and services.  This is not saying that goods and services are “fixed” and we are moving them around – no no no no.  It is saying that we are instituting policies that change the mix of goods and services, giving up some and increasing the amount of others.  We are thinking about how to use our scarce inputs to create outputs.

Now I have a strong preference towards private provision, given that voluntary prices are truly democratic and combine knowledge we don’t share as a society (but have internally as individuals), so let’s not get too ahead of ourselves in thinking we can “plan” the economy.

But, when looking at the issue we can say that we have a government sector, and a non-government sector. Labour and capital combine in both sectors to make goods and services … these are government goods and services and non-government goods and services.

Now if the government sector made goods and sold them to the public for a price, without raising any taxes, they would be just like any other firm.  In this case, the price paid for the government goods creates the income to pay for the labour and capital, and the labour and capital owners will purchase a mix of government and non-government goods at the relative prices 🙂

But government doesn’t work this way.  It pays for its goods by taxation instead of setting a price.  It uses this tax money to pay labour and pay capital when they create government products.  There is likely to be a reason for this, such as the existence of public goods, the urge to redistribute some products by providing them publicly, the desire for equal access to health and education.  That is cool.

In this context, the taxation is the government “claiming some proportion of non-government goods” to pay labour and capital with – since the labour and capital who produce government goods want to consume both government and non-government goods.  The government taxes non-government good providers, taking some of their output, and then sending over some of the produce of government production.

In this way, the tax exists in lieu of a price.

Now, while a price would see government goods and non-government goods produced with respect to their relative market value, taxation and spending is unlikely to lead to this same case for two reasons:

  1. The government goods are explicitly being produced beyond their relative market value – as we believe there are non-market benefits associated with it.  This is redistribution through tax and corresponding spending.  In of itself this isn’t necessarily inefficient – with a lump sum transfer relative prices will just adjust.  We can view this as changing the “endowment” of underlying resources for different people.
  2. Depending on the type of tax there are relative price effects, which reduce efficiency directly.  This occurs because it creates a gap between the cost of the good for the person buying it and the return for the person selling it (the “wedge”) – and so the very existence of the tax changes where people work, what they consume, and where capital ends up relative to the case where prices represent underlying value given the allocation associated with the government transfer.  This only occurs with taxes that influence relative prices – so not lump-sum taxes.

A web of prices, an ideal frontier, the fundamental welfare theorems

Now here is the way I see this idea when we think of spending, taxation, and the economy.

There is a set of resource (land, labour, capital, enterprenuers) and agents are endowed with some quantity of these resources.  Through trade, and the establishment of institutions and contracts, this leads to outcomes.  Prices in this case represent a set of relative values, and there is a frontier of outcomes (depending on initial endowments, that can be changed through lump sum government transfers) that can be seen as “pareto optimal”.  This is really just the fundamental welfare theorems which hold for perfect competition.

When we have a tax that isn’t lump sum, so it creates a wedge between the buyers and sellers price in a market, we end up in a situation “below” this frontier, which is in turn pareto inferior to a potential outcome.  This is why you will often see economists arguing for the idea of a poll tax with a progressive transfer system.  I’m not entirely sure – as I inherently see the transfers as having the same impact in terms of labour supply (unless we actually delink the benefit system from work), and believe that when equity concerns are taken into account some of these outcomes are not truly “pareto inferior”.

Now we don’t have perfect competition, it is more likely that we have monopolistic competition and the associated inefficiencies of that.  Modern policy oriented models do assumes this (eg DSGE models) and work from there.  However, even given this the tax principles are not terribly different – and as a result, I stick with useful simplifying assumptions to describe tax policy.

Furthermore, issues of information, incomplete markets, endogeniety and co-ordination failures, and oligopolistic competition do push us away from this idea, and provide scope for government interventions that are win-wins!  But at the current margin we already allow for those with policy – the “marginal” concept of taxation is very much along the area of trade-offs I’m discussing in these articles.

Trust me, these additional issues do play a significant role in how we try to discuss interventions – and many current interventions are based on it (eg monetary policy that tries to close output gaps, government intervention in markets over competition and consumer issues). Even if we “unrealistically” assumed perfect competition and perfect knowledge, the distributional impact of tax changes are insanely hard to work out – the best we can do (and that I’m aiming to do) is to provide a flavour for the direction of the different trade-off between taxes, not the magnitude or an implication of what we should do.

When we look at a range of marginal ideas such as “shall we try to ramp up healthcare” we are facing the traditional transfer problem akin to the fundamental welfare theorems, and this sort of exercise is useful.

That is so unrealistic, man economists say such stupid thing

I have tried to be honest about assumptions.  Often when an economist does this, someone is a dork and says something like the above.  If someone appears that feels like commenting in this way, I am replying to you right here.

Excuse me for admitting that allocation is an incredibly complicated issue that requires great care and thought when setting up a policy.  Why don’t you just go back to telling the world about your “make everyone better off by magic plans” and not bother talking to me again.

Why am I bothering with this comment – because there are innumerable people out there who simultaneously believe:

  1. There are really obvious and easy solutions to economic problems.
  2. Economists make really dumb assumptions and are stupid.
  3. Economists massively overcomplicate issues with maths and terminology.

I find those assumptions mutually inconsistent, and whenever I meet a person like that (which is far too often) I can’t help but feel that there is really something wrong in their life that they are trying to make up for.  If I had any empathy I’d be sympathetic – instead I’m going to write this part of my post to insult them.

To everyone who has avoided their snark and has constructive things to say – thank you, I want to give you a hug.


Hopefully these examples helped to clear up the idea of burden and distortion – it is an interesting issue, and one that requires careful analysis when we actually go to investigate policy!  Next week I will have an article up with some “ideal taxes” (poll taxes, land taxes, ability taxes), and I will touch on ideas of horizontal and vertical equity!  With all that we will be ready to hit factor taxes and consumption taxes the following week, inflation taxes the week after, and externality taxes the week after that.

Where I have gone in parts of this post is beyond where I’m heading on the Rates Blog posts – quantitatively I am talking about the same results, but the description involved is more involved.  It wouldn’t be fair to burden that on the larger public on Rates Blog who are less likely to be as nerdy as anyone over here 😉 … unless they are interested in the ideas, in which case I hope they see it!

By the end of it, we should all have an idea about the framework we view tax within.  Given that, we can make our own judgments about what is fair, and interpret the evidence about burden to try to figure out whether that makes much sense.  To be honest, all of that is far beyond me 😉

  • I’m enjoying this series Matt.
    In terms of analysing the distributional impact of tax changes, I think we’ve worked ourselves into a corner through having a complex web of inter-related tax & welfare policies.
    For example, the change to building depreciation rules hasn’t been discussed when it comes to supply side restrictions in the property market.
    We know that people can have excessive sensitivity to tax changes in consumption, so they sure can have excessive sensitivity to changes in tax rules. Just think back to the increase in trust retained income after the introduction of the 39c tax rate in 1999.
    The ability of Inland Revenue to obtain Taxation Review Authority rulings that clearly exceed Parliament’s intent also introduces enormous uncertainty for firms looking at capital investments financed in non-traditional ways.
    So for each individual tax policy there are enormous secondary effects that no one talks about, but our basic model assumptions at least help us tell a sensible story about what the real distribution “could be”!
    Non-economists want one story to explain *everything* and forget that for complex problems even Occam’s Razor hits a limit.

    • “I’m enjoying this series Matt.”

      Cheers, that’s nice to hear. I’m trying to make something that will be clear for both us economists, and for non-economists, without being a violent misrepresentation. And without just assuming “these are the properties of a tax system we want” as a starting point like most tax things do. We’ll see how it goes 😛

      “In terms of analysing the distributional impact of tax changes, I think
      we’ve worked ourselves into a corner through having a complex web of
      inter-related tax & welfare policies.”

      We’ve pinned down the fact that our knowledge of changes can be pretty limited – which is why our analysis is often fairly partial eqm. On top of that, we can’t do real distributional analysis with CGE models for the most part, making this all very difficult. Of course, just like you, I have a preference for at least using the partial eqm logic rather than assuming arbitrary things as politicians and interest groups often do 😉

      “For example, the change to building depreciation rules hasn’t been
      discussed when it comes to supply side restrictions in the property

      That is a very interesting one. I remember at the time there were a number of economists who liked it because they believed that it would more closely align incentives between owning and renting with fundamentals. However, I’m not really sure this is the point.

      We should be looking at rental investment property as an investment – and simply ensuring it is treated in a way consistent with other investment vehicles.

      In this context, reducing the depreciation rebate reduces the incentive to invest, which in turn will reduce the rental stock and increase rents.

      These things are all well and good, I suspect that one of the issues is that we talk about housing affordability, but we never clearly define what it is 😉

      “So for each individual tax policy there are enormous secondary effects
      that no one talks about, but our basic model assumptions at least help
      us tell a sensible story about what the real distribution “could be”!”

      Amen. And this is one of the key reason economists favour flat and broad tax schedules, combined with targeted progressive transfers. There are still unintended consequences, but what we are doing is a bit “clearer”.

      The hard thing is that I’ll say to people, “we believe this because we accept that is often insufficient information, or knowledge, to fiddle around with policies”. Then they will look at me blankly and say “but it’s easy”. I get this constantly, and I am sure people mean well, but I’m not sure they appreciate how prices work – and that is the real key to the complication.

      “Non-economists want one story to explain *everything* and forget that for complex problems even Occam’s Razor hits a limit.”

      This is true. Non-economists often don’t recognise the gap between core and peripheral assumptions as well. That is what I am writing in my NZAE paper this year – a paper that is turning out to have very little point 😛

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