A recent post discussed the problem of a periods functions which, when given a potentially infinite list, will reliably determine whether that infinite list is periodic and, if so, with which parameters. It was claimed that a general strong periods function, which always works, is impossible because it would imply a solution to the unsolvable halting problem. Instead, a weaker, but still useful, periods function was offered that produces useful output, but does not terminate on infinite lists.
Monday, August 31, 2015
Wednesday, August 26, 2015
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.
Recent posts have described how capital gains tax deferral allows investors to reduce their effective tax rate asymptotically to zero, how this distorts investment decisions, how market-to-market cannot fix the problem, and how bond taxation partially deals with the problem. Before the eagerly anticipated revelation how the tax code could fix this distortion to come in a future post, let me describe another method by which this deviation can be further exploited.
If you are dealing with infinite, but potentially periodic, series, you may sometimes have wished there was a function, let's call it periods, that could be given such a series and tell you whether it is periodic and, if so, the length and starting point of the period.
Sadly, such a function is impossible. There is no way for the function to determine whether any apparent period is genuine or there is a break at the \(n\)th element without looking at every single element. And checking every single element of an infinite series obviously cannot be done in finite time.
One question one might have after going through the Haskell Tribonacci problem is why it should be necessary to go through all that complication with recursive matrix multiplication in order to calculate such a simple function. Surely, one might say, there must be a mathematical formula into which you just plug in \(n\) and out pops the corresponding Tribonacci number.
Friday, August 21, 2015
A previous post discussed the economic distortion caused by deferral of capital gains tax, another, why market-to-market cannot fix this distortion. This post shows how the tax code tries, but does not entirely succeed, in addressing this issue with regard to bonds.
Tuesday, August 18, 2015
This is the second entry in an intermittent series of posts on how to optimize some basic mathematical functions in Haskell. The previous entry is here.
Consider the following problem: A person is ascending a staircase with \(n\) steps. The ascendant is sufficiently tall and the steps sufficiently shallow that with each gait, the ascendant can take one, two, or three steps. How many different ways are there for the ascendant to reach the top?
A previous post discussed the issue of the deferral of capital gains tax and why, if there is going to be a capital gains tax, this deferral distorts economic decision-making. The issue of this post is whether mandatory mark-to-market taxation can fix the problem.
Monday, August 17, 2015
Imagine a 2017 with a newly sworn-in President Paul (or Cruz), but a Congress no more and perhaps less conservative than the current one.
The President announces as one of his main legislative priorities a comprehensive reform of the tax system, including reducing the top marginal individual federal income tax rate from the current 44% or so to 25%. However, after extensive debates accompanied by great acrimony and perhaps a filibuster or two, Congress refuses to enact the President's tax reform.
One under-appreciated feature of capital gains taxation are the substantial implicit benefits of deferral—capital gains are only taxed once they are realized (i.e., generally when the investment is cashed out), not when in any economic sense they are earned. Effectively, deferral renders any sufficiently long-term capital gain tax-free, regardless of what the statutory rate is.
To understand this counter-intuitive—after all, aren't long-term gain still taxed before you can ever get the cash?— conclusion, consider the following hypothetical:
Sunday, August 2, 2015
I am experimenting with switching from the Google/Blogger comment system to the Disqus system, which in my experience as a commenter is quite superior.
One consequence is that the old comments have disappeared—worry not, your words have not joined Lois Lerner's e-mails. They just don't show up as Disqus comments because the software to export Blogger comments to Disqus is currently broken. As soon as that problem has been alleviated they will show up in the Disqus system.
Comments on comments very welcome.