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While reading this blog post about effective marginal tax rates, I came across a reference to this scholarly article with the following abstract (emphasis mine):

The paper offers four main takeaways. First, thanks to the incredible complexity of the U.S. fiscal system, it's impossible for anyone to understand her incentive to work, save, or contribute to retirement accounts absent highly advanced computer technology and software. Second, the U.S. fiscal system provides most households with very strong reasons to limit their labor supply and saving. Third, the system offers very high-income young and middle aged households as well as most older households tremendous opportunities to arbitrage the tax system by contributing to retirement accounts. Fourth, the patterns by age and income of marginal net tax rates on earnings, marginal net tax rates on saving, and tax-arbitrage opportunities can be summarized with one word -- bizarre.

I have since read most of the paper itself, including what I believe to be the relevant portions. I am not certain that I have a firm grasp on the "potential for arbitrage of the tax system" by the relevant groups, but I will post my working theory as an answer.

It does not account for the Roth-IRA arbitrage portion of the paper, which I confess still baffles me. If someone has a better answer, or corrections to my understanding, they are welcome.

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    Welcome to Money.SE. Have you read some of the highly rated questions on the site? Can you clarify your question? Why don't the dozens of existing questions regarding pretax savings provide adequate explanation? – JTP - Apologise to Monica Oct 11 '15 at 2:03
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    If nothing else, the use of the word arbitrage is horrible in that paragraph. Arbitrage has a very specific meaning (buying and then selling the same commodity/stock/etc. to take advantage of price differences), and it does not have that meaning (taking advantage of specifically designed tax incentives). – Joe Oct 16 '15 at 20:26
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    @Joe Indeed - otherwise, would someone call double-coupon day an "arbitrage opportunity"? Based on other comments / answers I'll add that using financial lingo like that is another way to intimidate the average reader of information. In this case, it seems that this intimidation is intentional, in order readers to seek the person's advice. – Grade 'Eh' Bacon Jul 6 '16 at 16:54
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    @farnsy Source? I've an economics background (not finance) and I've not heard of arbitrage being used so generally, nor can I find anything in the first several pages of google searching suggesting anything beyond 'exploiting price differences in two or more markets to make a guaranteed profit'. I find the broad definition including any possible transaction that can add wealth without risk to make the term rather pointless - and in the case above, I still don't see how that applies. – Joe Jul 6 '16 at 18:50
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    In particular, contributing to tax-deferred retirement accounts is not no-risk; it has an immediate cost (the contribution), a risk (decreasing financial situations requiring withdrawal of retirement funds at a penalty), and a very long-term payoff (typically, arbitrage implies a shorter term payoff). – Joe Jul 6 '16 at 18:52
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First, thanks to the incredible complexity of the U.S. fiscal system, it's impossible for anyone to understand her incentive to work, save, or contribute to retirement accounts absent highly advanced computer technology and software.

And yet, we all seem to work and make spending/saving choices every day. Keep in mind, the author of the paper is Laurence J. Kotlikoff, creator of software ESPlanner, which he (of course) sells. He has a vested interest in playing up the complexity of the tax code. His book "Get What's Yours: The Secrets to Maxing Out Your Social Security" makes similarly hyperbolic statements, such as noting there are over 1000 different scenarios to consider for Social Security benefits. No different than when I walk into a Subway shop and note the million potential combinations to construct my sandwich, yet, I order and eat a few minutes later.

Second, the U.S. fiscal system provides most households with very strong reasons to limit their labor supply and saving.

Most folk are one paycheck away from being able to buy next week's groceries. That's incentive enough to keep working.

Third, the system offers very high-income young and middle aged households as well as most older households tremendous opportunities to arbitrage the tax system by contributing to retirement accounts.

In general, pretax savings is withheld at the marginal rate, a couple paying 25% marginal for taxable income over $75K. Yet, the withdrawals have a $20K zero bracket (The combined standard deduction and exemptions) and then 10%, 15% , etc. So $95K gross yields $75K taxable (ignoring all other possible deductions) and a tax due of $10,300, or 10.8% average rate. Put another way, the $95K avoided $23,750 in tax going in, but on withdrawal only lost $10,300 back. That's the effect you were asking about. (Note: The word arbitrage really means something else, and the author is basically coining a phrase "tax arbitrage". Outside of this article, it's not common usage.)

Fourth, the patterns by age and income of marginal net tax rates on earnings, marginal net tax rates on saving, and tax-arbitrage opportunities can be summarized with one word -- bizarre.

Like when a single retiree withdrawing just $35K/yr from her IRA enters The Phantom Tax Rate Zone due to taxation of Social Security? Note - this negates a good chunk of the benefit of number 3 above.

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    I did not realize the paper was published by the makers of the tool. That makes the "absent highly advanced computer technology and software" seem kind of underhanded. – Michael Oct 16 '15 at 21:13
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Because retirement accounts are taxed upon withdrawal, they reduce taxable income when your income is high and taxed at the higher marginal rates. It is not taxed until the time of withdrawal, when you are no longer earning wages and your tax rate is much lower.

If you are earning at or above $70k/year, your effective marginal tax rate is 40%. Each additional dollar in wages grants you 60¢ of after-tax income. If you chose to put that into a tax-deferred retirement account, and later withdraw the money you saved, it will be taxed at a rate beginning at the bottom of the marginal tax rate, up to the rate for the amount you withdraw in a year.

So even if you withdraw $70k/year, your effective (not marginal) tax rate is about 30%, because the income below the $70k/year rate was taxed at a lower rate.

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    This presumes traditional, rather than Roth, accounts. And the assumption that your tax rate will be much lower may depend on how much nonsalary income you have. Buy in general.. – keshlam Oct 10 '15 at 18:07
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    My understanding is that this is the point. Governments encourage people to save for retirement by essentially giving them a net tax break. I didn't think this was news. – DJClayworth Oct 11 '15 at 1:05
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    Any hint on how you get 40% and 30% in this answer? – JTP - Apologise to Monica Oct 13 '15 at 23:50
  • @JoeTaxpayer: The 40% was from the first chart in the blog post which cited this CBO Report (page 7). Upon further reading, it seems that may be specific to a single parent with one child. The 30% came from interpolation of the graph on this page. – Michael Oct 15 '15 at 13:30
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    40% includes federal payroll taxes, which are still paid on 401(k) contributions. It's specious (or at least, wrong) to consider that part of your marginal tax rate for this particular argument, since they're paid now regardless. Only consider the federal (and, possibly, state) income tax. (I say possibly state, because states treat things differently based on lots of factors, and most have fairly flat taxes so it's often better to only factor in federal). – Joe Oct 16 '15 at 20:33
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The complexity of the labor/savings problem in the US. It is well-known that the optimal investment decision is extremely difficult. In particular, there are many unknowns that are important for deciding retirement decisions--for example, what will be the average performance of the asset classes going forward and how will the covariances between asset classes change. This paper analyzes an apparently simpler problem: how much should people save (in pre-tax and Roth-type accounts) given different incomes and ages in the current system in the US. The authors show that the enormous complexity introduced by the various tax brackets and tax incentives/penalties/transfers in our current system creates a very complex mathematical problem. If you know your age, income, expected life span, expected asset performance, etc., and want to have nice smooth consumption throughout your life, there is an optimal savings strategy, but to get it perfectly right, you would have to do a great deal of computation. People will do the best they can, but the authors suggest that there is a perfect answer if you know these parameters but the math to get there is too hard for a lay person to do.

Tax arbitrage. Arbitrage has several definitions, but generically if you can enter into a transaction that will increase your wealth without taking on additional risk, you can call it an arbitrage. Putting money away pre-tax in a 401(k) style investment when your marginal tax rate is high and then spending it when your marginal tax rate is low is an example of such an arbitrage if you compare it to saving outside of a 401(k). Of course, if you are in a low tax bracket because your income is low, you will get little benefit in the form of tax savings from contributing to your 401(k). This is one reason this type of account benefits some people more than others.

Roth arbitrage Saving in a Roth account increases the wealth of anyone who uses it instead of using a regular taxable brokerage account. In either case, taxes are paid at the time you earn the money, but if the money is placed in a Roth, it is never taxed again. If it is saved in a taxable account, taxes must be paid on the capital gains and interest every year. So if you are long-term saving, it is unambiguously better to do so in a Roth account than in a taxable account. Normally I'd say what's not unambiguous is whether it's better to save in a Roth or Traditional IRA. Most people would say it depends on your income. However, within the constraints of their model, the authors show that the arbitrage for a 401(k)-style savings decision is uniformly larger than that of the Roth. If we believe the assumptions of their model, we should stick with traditional IRA and 401(k) contributions and pass on the Roth.

The nature of the paper. At the end of the day, this is an academic exercise that makes strong (not necessarily true) assumptions about people, about the market, and about the future of the tax system. However, the authors try hard to use all available rules to figure out the optimal strategy given all the complexities of our current system. They use their results to teach us (as individuals an a society) some lessons. To society, they say that the system is too complex for people to use effectively and that the current system pushes people to make some savings/labor decisions they wouldn't otherwise make and that may not be optimal. Moreover, there isn't a coherent logic to who the current system penalizes and rewards if you consider age and wealth. To individuals they have advice like "avoid Roth accounts" as mentioned above.

  • If your tax rate is higher in 20 years than today, you will have lost out by taking the deduction today. This means that there is risk in investing in an IRA, and use of the word 'arbitrage' is incorrect. – Grade 'Eh' Bacon Jul 20 '16 at 19:38

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