Friday, 5 August 2011

Capital Gains Taxes Redux

A couple of comments on my previous posts have suggested two possible efficiency motivations for having capital gains taxes. Both are theoretically correct, but neither makes a convincing case for a real-world CGT, in my opinion.

First, Bill Kaye-Blake suggests they can be a way of capturing otherwise untaxable non-market activity. The idea here is that DIY work does not involve a market exchange and so is taken out of the tax net. The whole optimal tax literature from Ramsey on is predicated on how to minimise the inefficiency arising from this inability to tax some goods. As an example, I had an uncle who was a keen DIYer. He liked buying houses in need of repair and then doing them up. Once finished, he would sell and move on to a new fixer-upper. For him it was just a hobby, but an unintended consequence was that he was able to move into better and better houses through the untaxed return on his DIY labour that manifested itself as a capital gain. The argument here is perfectly valid, but as a reason or having a CGT, it would be like giving yourself acupuncture with a fork (Ron Jones’ expression). For the very small amount of non-market income-generating activity that would be captured indirectly by a CGT (not my uncle, if first houses are exempt), one would have to bear the other costs of the tax. Even if the net efficiency and equity benefits of the tax for all other reasons were zero and not negative, it is pretty hard to see that this benefit would outweigh the enforcement and compliance costs.
Second, Michael Reddell cites the 1990 consultative committee on the taxation of capital income as stating that capital-gains taxes can be efficiency enhancing when the changes in gains or losses in asset values are not windfall changes. I have not been able to track this document down, but I am guessing that the idea here is related to a 1964 paper by Samuleson, which Andrew Coleman has pointed me to. Samuelson’s paper is very elegant, but it isn’t an easy read, so let me try to illustrate his result with a simple model. Those who don't like models expressed without equations just jump two paragraphs at this point.
Consider a world in which there is a perfectly elastic demand for domestic saving in international markets at an interest rate of 5%. This means that, in the absence of taxes, there is an opportunity cost to both a saver and the country of investing in the creation of a local physical asset in the form of an ongoing return of 5%. It will therefore only be efficient for the country to invest in the asset if the present value of the future payments from the asset exceed the cost of the creating the asset, when the future is discounted at 5%. If we now put on a 40% tax on interest income, then local savers will use the after-tax interest rate of 3% to discount payments, which will lead to a higher present value of a given flow of payments from an asset. If, however, the 40% tax is also levied on the payments from the asset, there will be an offsetting reduction in the present value. In the special case where there is a constant flow of payments, these two effects will exactly offset. In this case, private incentives will lead to the efficient level of investment in local assets—namely invest only if the social rate of return is in excess of 5%.
Now consider an asset which will produce a constant payment in perpetuity but starting in one year’s time, with zero payment before then. The price of the asset in one year will be unaffected by the tax, but the private saver will discount this value back one year at a rate of 3% rather than the socially optimal 5%. As a result, the present value will be overstated and there may well be overinvestment. The reverse situation applied for assets whose payments fall over time. The problem arises because of the compounding of interest, which means that taxes on interest imply a larger proportionate reduction in the rate at which values are discounted at longer time horizons than in the near term.

The bottom line of this is that the tax system creates a distortion in which there is an incentive to invest too much for long-term gain, and not enough for shorter term gain.
Now, if payments from an asset are going to predictably increase over time, then so will the market value of the asset—that is, there will be capital gains. Similarly, predictable decreasing payments will lead to predictable capital losses. Samuelson’s very neat mathematics shows that if you tax capital gains and subsidise capital losses at the same rate of tax as is applied to interest and payments from the asset, then the distortion in favour of long-term returns over short-term returns is removed.
So why is this not a strong argument in favour of capital gains taxes: I can see three reasons:
  1. Samuelson’s result requires symmetric treatment of capital losses and capital gains, and no distinction between realised and unrealised gains. If this is not going to be the system implemented (which real-world capital-gains-taxation regimes ever are), the result does not apply.
  2. The result is partial equilibrium, dealing only with the distortion across time horizons. But the excess discounting that arises from the magic of compounding is exactly the reason that capital taxation is found to have greater efficiency costs than labour taxation. A regime without capital-gains taxation, may lead to some inefficiency in the time horizon of investments, while enhancing efficiency in the margin between consumption and saving.
  3. With a 5% before-tax interest rate and a 40% tax rate, it takes a horizon of 25 years before the future is excessively discounted. Do we really need a complicated tax regime to dampen the amount of saving going into investments with payoffs beyond 25 years? Can any proponent of capital gains taxes state with a straight face that this is the problem they are seeking to solve?
I am definitely not an expert in capital taxation, and so am open to being convinced by counter-arguments. My problem with much of what I have read in public discussions, however, is that the putative benefits are couched in vague terms (like “productive investment”), which I have a hard time converting into a model that lays bare the underlying assumptions. I would love to see the models made explicit.


  1. The way I understand it (and I admit I could be wrong), if you have some capital which you would like to get a profit from, you can either put it to work generating income (as in selling ships, shoes, sealing wax...) or you can put the capital into something which looks like it will grow more valuable (such as property) and wait for the sale price of that property to go up.

    The former is captured in the tax base whereas the latter is not, which encourages more people to invest in the latter way, which in turn results in greater tax losses to the govt. These have to be either offset by increasing taxes to someone else, or by running a deficit.

    labour's plan to reduce the deficit that we have indeed run by bringing this kind of profit back under the taxation system... that's the way I understand it but I know there are some holes in my understanding of economics. Apologies if I'm too far wrong.

  2. Ben,

    The issue is not, or at least should not be, whether revenue is lost through not having a CGT. Revenue is lost through not having any tax: e.g. through not having a 20% GST, through zero-rating exports in the GST, through not having a separate excise tax on, say, blogging, etc. The issue, or should be, whether the not having a CGT leads to resource allocation being directed in part because of tax advantage rather than the true underlying benefit.

    Now, it would seem that if people invest in order to earn a return as non-taxable capital gains, then that would suggest that resources are being misdirected, but it is not that simple. First, if the change in behaviour simply consists of which second-hand goods (shares, houses, whatever) a particular saver purchases, then we simply have a change of ownership of existing assets and we need to look further to see if that has had any impact on which new assets are calculated. This was the point of the second of my CGT posts: you can tell a story in which there is a misallocation of resources in the creation of new assets, but it is a pretty long stretch. More to the point, public discussions of CGTs never seem to even attempt to draw the link between CGTs and new asset creation.

    And the public discussions have a second, more severe, limitation. All the theoretical cases for CGTs that I know of require offsetting treatment of capital gains (taxed) and capital losses (subsidised) and equal treatment of realised and unrealised gains and losses. If such a tax policy is not being proposed, the debate also needs to make the case for why a tax on realised gains only with no offset for losses would be better than nothing for addressing the theoretical inefficiency of a no CGT regime.