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Wednesday, August 26, 2015

How to Eliminate the Capital Gain Deferral Distortion

And now for the thrilling conclusion of the blockbuster series of posts on the capital gain tax deferral distortion! We have seen how it arises, how some common-sense fixes cannot work, how bond taxation addresses it imperfectly, and how it can be exploited to shield even current investment returns from taxation.

The solution proposed herein has many virtues. It completely eliminates the distortion. It does not depend on accurate intermediate valuations. It is superior to the OID rules which it would replace as it has less administrative overhead, raises no liquidity problems, and fully, rather than just partially, eliminates the distortion. It even obviates the clever schemes to turn current returns into deferred capital gains.

True, it is slightly more mathematically complicated than the current scheme, which may explain why it was not adopted in the times of the mechanical adding machine. But today even the feeblest computer could readily calculate it in a single spreadsheet cell.

Indeed, the solution was already implicit in the original discussion to which I here shall repeatedly refer and of which gentle readers may wish to refresh their memory.

The solution is, simply, to continue to charge capital gains tax only upon realization (that is, to allow deferral), but to vary the nominal rate of taxation of long-term capital gains sufficiently as to offset the benefits received by the deferring investor A over the concurrently tax-paying investor B. The net effect would be to have both pay the same effective rate, thereby eliminating any distortion caused by the tax system.

Mathematically one would do this as follows. At the time of realization, one would first calculate the total return:

$$total return=\frac{sale price}{purchase price}$$

From this, one calculates the implicit pre-tax annual yield:

$$pretax yield=\sqrt[d]{total return}-1$$

where \(d\) is the time span between purchase and sale, measured in years. From this, one computes the corresponding annual post-tax yield:

$$posttax yield=pretax yield (1-tax rate)$$

Next, calculate what the value of the investment would have been, had taxes not been deferred.

$$posttax value=purchase price (1+posttax yield)^d$$

Then tax the excess of the sale receipt over the implicit posttax value:

$$tax = sale price - posttax value$$

Putting it all together into one formula:

$$tax = sale price - purchase price (1+(\sqrt[d]{\frac{sale price}{purchase price}}-1) (1-tax rate))^d$$

Any computer can calculate this tax in the blink of an eye, given only the known purchase and sale prices and dates and the tax rate. That's all there is to it.

One objection that would doubtlessly be raised to this formula is that, for very-long term, profitable investments, the nominal tax rate, calculated just as fraction of the difference between of purchase and sale prices, could be very high.

That is true, but misleading. Using the original assumptions, the nominal capital gains tax rate for investor A would rise from the same statutory 40% as investor B pays in year 1, to 60% after 20 years, to 80% after 40 years, to 97.5% after 100 years. But, in fact, both investor A and investor B really only do pay the same statutory 40% rate of their yield. The difference is that investor B paid it concurrently every year as the investment appreciated, while investor A was able to defer it for a long time with the a balloon tax payment only coming due once at the end of the period. But both of them end up with exactly the same 6% post-tax yield over the period of their investments.

A much stronger objection is that this change would result in a, possibly substantial, increase in tax revenues. That is a very serious concern. As a clever man once wrote, giving money and power to the government is like whiskey and car keys to teenage boys; disaster is sure to ensue. Indeed, I would deem this adverse consequence so significant that I would oppose the proposal on this basis were it to be advanced as a stand-alone reform.

Fortunately, it does not have to be for there are so many harmful taxes which could be cut in tandem, rendering the proposal as whole revenue-neutral or preferably revenue-decreasing and capturing the economic benefits both of eliminating the deferral distortion and the elimination or reduction of these other taxes and without centralizing even more resources into the hand of the state.

First, one should reduce the statutory investment tax rate. Second, one should deflate capital gains by an inflation index; something readily done by slight adjustments to the formula above. Third, one should make corporate dividends expansable which would effectively eliminate the corporate income tax—a tax that is so without intellectual justification that one can attribute its continued existence and public defense only to profound economic ignorance or bad faith. Finally, one should dramatically reduce the individual income tax rates. A combination of these options would ensure that there would be no windfall for the state.