Redesigning Income Tax

Here is an opinionated proposal, having no chance whatsoever of adoption, for how taxes ought to be levied on income. This post was originally scheduled for Income Tax Day here in the good old U.S.A., but I was having trouble with the algebra and then I was on vacation. So instead you get it for Canadian tax day. Everything is calculated in US dollars and compared to existing US systems, but I don’t see any great difficulty translating it to other countries.

Premises for this redesign:

  • The existing tax code is way too damn complicated.
  • It is the rules that need to be simplified, not the mathematics. In particular, the marginal tax rate does not need to be a step function just to simplify the arithmetic involved. You look that part up in a table anyway.
  • All individuals’ take-home pay should increase monotonically with their gross income, regardless of any other factors.
  • High levels of income inequality constitute a negative externality; income tax should therefore be Pigovian.
  • Tax rates should not vary based on any categorization of income (e.g. interest and capital gains should be taxed at the same rate as wages). This principle by itself removes a great deal of the complexity, and a great deal of the perverse incentives in the current system as well.

Read on for concrete details of the proposal.

The first thing we do is institute an unconditional basic income. (Just to poke David Weber in the eye, let’s call it the Basic Living Stipend.) Every adult gets BB dollars every year, in monthly installments, unconditionally and untaxed. The value of BB is set by statute when the reforms go into effect and automatically adjusted for inflation thereafter. In this hypothetical I’m setting BB to $24,000 for concreteness; this is a nice round number—$2000 a month—that happens to be a little more than 200% of the (USA) Federal poverty line for a one-person household in 2014, according to

We also institute a unified national pension. It works hand in hand with the tax scheme, so I’ll explain that first and come back to this, but you need to know the pension exists. It differs from existing pensions in one important way: it starts paying immediately upon your having made any amount of contribution; there is no age or disability requirement. (It may not pay out very much, though, as I’ll explain below.) Income from the pension is not taxed either, but it raises your marginal tax rate as if it had been taxed. The combination of the BLS and the pension are intended to replace all existing government-administered pension plans (Social Security, the Railroad Retirement Board, etc.), disability benefits, unemployment insurance, etc.

All income from other sources is taxed according to the same formula. This tax replaces all income and payroll taxes collected by the IRS. There are no deductions, exemptions, credits, special categories, or anything else. Congress gets one and only one adjustment knob: the set point, (s,r)(s,r). A marginal tax rate of r%r\% is charged on the ss’th dollar of income above BB. The marginal tax rate MM on the ii’th dollar of income is

M={r(Bi)r(si)sifi>B0otherwiseM = \begin{cases} \frac{r(B-i)}{r(s-i)-s} & \text{if}\:\: i > B\\\\ 0 & \text{otherwise} \end{cases}

and one’s after-tax income, AA, if one earns II dollars in total (of which BB are from the BLS and PP the pension), is

$$\begin{aligned}\displaystyle A = B + P + &\int_{B+P}^I 1-M(i)\;di\\\\ = B + P + &\frac{rB+(1-r)s}{r}\, \Bigl[ \ln\, \bigl(rI+(1-r)s\bigr) - \ln\, \bigl(rB+rP+(1-r)s\bigr) \Bigr] \end{aligned}$$

These functions look messy, and possibly I am out of my mind to even suggest them to such a pack of know-nothings as we have presently in Congress, but they have exactly the mathematical properties we want. MM is continuous, increases monotonically, and converges to 1 at positive infinity, but AA diverges at positive infinity, so there is no upper limit in principle on after-tax income. (As we shall see, though, in practice that next after-tax dollar gets very, very expensive past a certain point.) Also, the equations get a lot less messy if we substitute in numbers for some of the parameters. For instance, setting B=24000B = 24000, s=500000s = 500000, and r=40%r = 40\% (corresponding to the blue line below) gives us A=24000+P+774000(ln(0.4I+300000)ln(0.4P+309600))A = 24000 + P + 774000 \bigl( \ln\,(0.4I + 300000) - \ln\,(0.4P + 309600) \bigr) for the formula that taxpayers would actually have to wrestle with.

Below is a chart of the marginal tax rate and the after-tax income for several choices of rr, with ss fixed to $500,000. For comparison, the jagged gray line is the real marginal tax rate for the USA for 2013 (for individuals under the age of 65, all income wages, taking the standard deduction and one exemption, with no other adjustments or credits—this is a gross oversimplification, but attempting to factor in things like the EITC and the AMT was too complicated for me; if someone wants to provide me with a more realistic comparison curve I am happy to update the chart). Do keep in mind that after the reform, everyone has at least $24,000 of yearly income. The x-axis in both charts, and the y-axis in the right-hand chart, are on a log10 scale. Click to embiggen.

Tax rates and take home pay under the proposal, with comparison to USA federal tax for 2013.

You can see that regardless of the choice of set point, this is likely to be a modest tax cut for people earning less than $100,000 a year, and a hefty tax hike for people earning more than that. That’s by design. It should be almost unheard of for anyone to earn more than $500,000 or so a year after taxes. This is what makes this a Pigovian correction to the negative externalities involved in high income inequality. (For instance, an expected consequence of this reform is that corporations will stop throwing money away on their executives.)

Now, remember that pension scheme? That’s automatically funded for each individual by the taxes they pay in. This obeys a similar formula to the taxation itself. There are two control points: the first dollar paid in taxes returns a pension of p0p_0 dollars per year, and the ss’th dollar paid in taxes returns a pension of prp_r dollars per year, where pr<p0<1p_r < p_0 <1. The marginal pension payout pp on the tt’th dollar paid in taxes is

p=p0pr(1s)p0prs(p0pr)tp = \frac{p_0 p_r (1-s)}{p_0 - p_rs - (p_0 - p_r)t}

and the cumulative payout on TT dollars paid in is

$$\begin{aligned} P &= \int_1^T p(t)\,dt\\\\ &= \frac{p_0 p_r (s-1)}{p_0 - p_r} \Bigl[ \ln\,\bigl( p_r s - p_0 + (p_0 - p_r)T\bigr) -\ln\, p_r (s - 1) \Bigr] \end{aligned}$$

The amount paid into the pension scheme accumulates year over year, but every year it’s multiplied by a decay factor, d<1d < 1. The next chart shows three hypothetical yearly pretax incomes (not including BLS or pension), pension accumulation, and the resulting after-tax income, all as a function of time, for plausible choices of the parameters: s=500000,r=40%,p0=0.50,pr=0.05,d=0.99s = 500000,\: r = 40\%,\: p_0 = 0.50,\: p_r = 0.05,\: d = 0.99.

Three hypothetical pension patterns.

The intent here is that you can build up a pension sufficient for a comfortable retirement either by earning relatively small amounts of money over a long time, or by earning large amounts of money over a relatively short time. That way, the system acts to smooth out the take-home pay of people whose income comes in bursts, which is characteristic of a lot of creative jobs (that people generally prefer over day jobs, if given the choice). Unfortunately this did not work out as well as I was hoping it would; I think the decay mechanism needs to be more sophisticated, possibly with TT initially earning interest rather than decaying. But I’ve spent enough time messing with this. More fully baked ideas solicited.

It is probably a good idea for the BLS to phase in starting at age 12 give or take, and it is probably also a good idea to have pension contributions at least partially transfer to one’s heirs upon death (if only to reduce people’s need for life insurance), but I haven’t thought these bits through carefully.

One final consideration is that in the USA, lots of people have tax-advantaged retirement accounts holding much of their savings. It probably makes sense to preserve these, if only to smooth the transition. In keeping with the general no-questions-asked principle behind this proposal, something like this might work: A long-term investment account is defined as a bank or brokerage account intended to accumulate capital over the long term. It must invest the money according to a fixed algorithm (this list of stocks is a valid choice); the algorithm and/or its parameters may be changed no more than once a month, and all earnings from the investments must be reinvested according to the same algorithm. You can stick as much of your pretax income in one of these as you want. If you’re content to live on the BLS despite earning $10,000,000 a year, your tax obligation can be zero. You can also withdraw money from the account whenever you want. Withdrawals count as regular income; there is no calculation of cost basis, length of holding, or anything like that.

If this were actually going to be implemented, existing pension plans would need to be converted to the new system (providing an equivalent benefit at the time of the conversion, ideally), it would need to come along with a sane national health insurance scheme (read single payer of some variety), and it might be a good idea to manipulate the states into scrapping their own income taxes in favor of some sort of share in the national income tax. While we’re at it it would make sense to make property taxes Georgian and replace sales taxes with an at-source carbon tax, but that would be the pony to go along with the impossible wish.

In case anyone wants to play with the numbers, the R script that generated the graphs is available here.

Responses to “Redesigning Income Tax”

  1. Emanuel Hoogeveen

    I’ve often considered schemes similar to this (motivated primarily by getting rid of the silly step function that the Dutch system also uses), but never worked them out in such detail. Bravo!

  2. Gervase Markham

    How do you think people earning $5M or $10M a year would react if your proposal was enacted? For the sake of argument, I’m willing to disallow the option influence people to get the proposal de-enacted.

    (Hint: I suspect the answer is not simply pay up.)

    1. glandium

      It’s easy to know what they would do: just look at what the did when France increased taxation of the richest. Some moved to a country that is friendlier to their money.

  3. Greg K Nicholson

    Gerv: That’s exactly why this has no chance whatsoever of adoption.

    Power begets power, thus inequality begets inequality.

  4. Gervase Markham

    Greg: did you read what I wrote carefully? I said, for the sake of argument, that we can disallow the possibility that the legislation gets repealed.

    If this legislation was enacted, what do you think would happen?

  5. Gervase Markham

    Zack: also, your Unconditional Basic Income - how is it provided?

    Are you simply saying that the income tax threshold starts at $24,000 (and so people without a job or with a low-paying job may not actually have that level of income)? Or does the state give everyone a lump sum of $24,000 regardless of job status? Or is the minimum wage $24,000, so everyone in a job gets the basic income but those without a job do not? Or does the state simply top up your income to $24,000 regardless of whether or not you have a job? If that’s how it works, is there a minimum wage at all, or not? If not, how do you prevent employers paying people very little because the state will pick up the slack? If there is a minimum wage, what is it?

  6. Gervase Markham

    A $24,000 basic income for 250 million people (rough guess at those over 18 in the USA) is 6 trillion dollars a year. That’s 33% of the US GDP, and slightly under twice the entire US Federal budget.

    So I assume you are not saying that the government should simply give everyone $24,000, regardless of other income. (Although that’s the definition of Unconditional Basic Income in the Wikipedia page you link to…)

  7. Zack Weinberg

    Unfortunately I don’t have time today to discuss this as much as I’d like, but I can respond briefly to Gerv’s questions:

    Yes, I am seriously proposing that the government should simply give everyone $24,000 regardless of other income, even though that is twice the (current) Federal budget in aggregate. It replaces Social Security, SDI, unemployment insurance, and a bunch of other entitlements, which collectively add up to something like a third of the existing budget, but still, this is not revenue-neutral nor is it meant to be: this is, deliberately, a thought exercise in much more aggressive redistribution of wealth than we currently undertake.

    As to minimum wage, one of the reasons unconditional basic incomes find favor among economists regardless of their political leanings is that they may mean you don’t need a minimum wage anymore. Among the potential upsides of this plan are that a class of organizations—mostly not for-profit businesses—will be able to draw more volunteer labor and/or pay only token amounts, and there will no longer be political pressure to preserve jobs that could either be done by robots, or do not need doing at all.

    As to people who will see substantial cuts in their take-home pay due to this plan: I do in fact expect base salaries to come down as a consequence (this is desired; that’s what I mean by income tax should be Pigovian), and for corporations to, at first, try to slither around the rules by enhancing other aspects of their compensation packages. This is (part of) why there are no categories of income, and this is is why I am not 100% on the long-term investment accounts idea. I think that, should a miracle occur and the reforms actually be enacted, it would make most sense to wait about five years to see what the second-order consequences were, then adjust as necessary.

    (If you are envisioning that the very rich have more ability to shift money around to avoid taxation: that is already illegal. I do expect that the IRS enforcement department would need to be beefed up for at least a few years.)

    (An optional line item in this reform, which did not make it into the final draft, is one-time punitive confiscation of all individually-held assets in excess of $1 billion, which would, apart from everything else, put a major dent in the extremely rich cohort’s ability to buy politicians.)

    1. glandium

      It replaces Social Security.

      That’s the worst possible thing to do. Where social security is the most required is for high medical costs, and $24k does not cut it.

      1. Zack Weinberg

        I believe you have mixed Social Security up with Medicare. I did mention that this only works in conjunction with a sane national health insurance program.

  8. glandium

    I don’t know how tax rate works in the US, but considering it works the same in the few countries where i know how it works, I’ll guess it’s the same in the US. And tax rate is not a step function. When you switch tax rate section, the actual tax rate for your income is not /that/ tax rate for the entire income. For example, taking approximate numbers from your graph, if your income is, say $130k, your tax rate is 29%… on the $30k above $100k. The rate is then 25% for the part between $65K and $100K, etc. All in all the amount of tax you pay vs. income is a continuous function, with its slope changing at the income points where the tax rate changes.

    1. Zack Weinberg

      The marginal tax rate is a step function; the total tax assessment is indeed continuous (when all the special cases are ignored). If you look again at the first set of graphs, you should see that this is already taken into account.

  9. Gervase Markham

    The incentive to do productive, paid work would be massively reduced. Why should I go to work all day to earn $30,000 a year, when I could sit at home and earn $24,000? Therefore, the GDP of the country would shrink massively. Even if it didn’t shrink as far as to make the cost of your scheme more than 100% of the country’s income, you would effectively end up taxing at 100% everything anyone earns above $24,000 in order to pay everyone the $24,000. And the incentive to work would be eliminated entirely. There would be a vicious cycle of lower incentives → lower productivity → lower GDP → tax rises → lower incentives.

    Secondly, almost all the rich and entrepreneurial people would emigrate. There are plenty of other countries in which it is pleasant to live who allow them to keep what they work to earn. This would further depress your tax revenues, as you are depending on them for a lot of it.

    BTW, it is not illegal in all, or even many circumstances to shift money around to avoid taxation. There are plenty of legal things one can do to avoid tax. If they are illegal, it has a different name - tax evasion. If you control a company, then tax avoidance is the thing you have to do in order not to be sued by your shareholders for failing in your fiduciary duty to them, and tax evasion is the thing you have to not do in order to stay out of jail.

    This plan also means that the government would have to stop doing all the things it does other than hand out money to people, in order to pay for your program. (These vary from country to country; apologies if not all apply in the USA.) No army, no police, no infrastructure or road maintenance, no education, no healthcare. As it happens, I don’t think the government should provide education or healthcare, but I suspect you do.

    Lastly, all this tax taken at a federal level would mean no money left for tax at a state level, so you would be effectively abolishing the principle of subsidiarity in the USA, and merging the country into one big state.

    I’m not sure your experiment would be counted a success by those watching in horror at the implosion of society.

    1. Zack Weinberg

      You have admirably summarized the contra-minimum-income position which I am dismissing and mocking by reference when I say that we should call it the Basic Living Stipend just to poke David Weber in the eye. If you have not read those books, they detail the course of a war (IN SPACE, but that’s not important for this discussion) between two nation-states, one of which has experienced just such an implosion as you postulate and is now resorting to imperial expansionism to try to make the budget balance.

      I am again very busy today and don’t have time to argue the contrary case point by point, so I’m just going to hold out my basic philosophical problem with your position: Why do you believe more than a trivial number of people would be content to watch TV all day for their entire lives? I have had to watch TV all day for short periods, when I was too sick to do anything else, and I was bored of it almost instantly.

      It is certainly true that there is a class of jobs (let us call them drudge work) which it would become impossible to pay anyone enough to do while still making a profit. That’s a feature. To whatever extent that work actually needs doing, it will be automated; to whatever extent it does not need doing, perhaps those businesses will cease to exist, and that’s fine. Meanwhile, I expect that we will see a tremendous increase in creative work, done by people who are no longer forced to work drudge jobs to make ends meet, and/or by people who can now expand the hobby that they no longer feel guilty for wasting time on when they could be earning money.

      In the even larger picture, it seems to me that is it profitable? has become almost totally uncorrelated with is it something that needs doing?; this perhaps does not completely remove the incentive to make profit at the expense of doing what needs doing, but I don’t see that you can get there from here without it.

      Finally, mail every citizen a check every month (or, more likely, electronically deposit $X in every citizen’s bank account every month) requires rather less administrative overhead than all of the things it replaces; and because it’s unconditional, there are no more people whose job is to ruin citizens’ lives by denying them benefits. The volume of money being handled is greater, but the government itself has less work to do and is less intrusive.

      1. njn

        An argument between zw and gerv about taxation? This will surely end productively :P

      2. Gervase Markham

        Why do you believe more than a trivial number of people would be content to watch TV all day for their entire lives?

        Because I’ve met some of them? Although you narrow things too much by saying watch TV all day. There are certainly people who would be content not to do productive paid work for the rest of their lives. You agree that these people exist - in fact, it’s a feature of your system. You talk about the large increase in creative work - people will quite happily spend all day writing poetry, painting pictures, going for walks in the woods, taking photographs, if someone else is paying them to do so. Not that there’s anything wrong with any of those things, but the idea that faced with the choice of working 40 hours a week or doing that, most people will joyfully choose the work, seems incredible.

        This really does remind me of Animal Farm, although they at least said that it would be achieved incrementally - There’ll be a 3-day week! Maybe even a 2-day week!. How would you compare your scheme to other political efforts to achieve redistributive equality in the past?

        The government is less intrusive on the payout side, but it’s much more intrusive (given that I count removing one’s ability to do what one likes with what one earns as intrusive) on the taxation side. (Note: to avoid the straw man: I’m not arguing for zero taxation.)

        What I still don’t get is, faced with the figures, how you think this could possibly work economically, even if there was a majority in the legislature for it? Your sums don’t add up. So what’s the point?

    2. Al Billings

      I suggest you may want to read up on the idea of a basic guaranteed income. It isn’t a new idea and studies have been done on it. It works.

      Your example is not real. It isn’t sit home and make $24K or work and make $30K. You get the $24K whether you work or not (in this example). If you earned another $30K, it would be on top of that for a total of $54K. That’s part of the point. The idea is that citizens are guaranteed enough money to live, eat, and put a roof over their heads so we don’t have people starving, being homeless as much, or otherwise living in extreme poverty.

      Most people link this also with national healthcare (with which I suspect you are familiar) and then a dismantling of welfare and certain other social programs, since a guaranteed income and government healthcare will effectively replace the need for many of them.

      1. Zack Weinberg

        I’ve taken the liberty of correcting the typo in this comment and removing the later comment pointing it out.

      2. Gervase Markham

        I understand the idea. But I think wholesale theft is too high a price to pay. (And it wouldn’t work anyway.) I define theft as taking that which you have no right to, and it doesn’t make it legal if people vote for it. The government has no right to the money I earn if it’s using it for something which is not a valid purpose of government.

        So I guess the real discussion, as it always ends up being, is about the purpose of government. I don’t think it’s a valid purpose of government to try and create economic equality by taking from one group and giving to another. I think the purpose of government is to create a legal framework (police, courts, contracts, keeping promises) in which people can be safe and generous to one another. I would love to see nobody starving, or homeless, or living in poverty. And I would love to see it done by people like you and me being freely generous with our time and resources.

  10. Al Billings

    Given how many people I know who work drudge jobs with no point while yearning to be artists, thespians, and the like (or even take care of families) but simply can’t afford to do so, a basic income makes for a better, less odious, society.

  11. me

    How do you account for the inflation that your idea causes?

    The logic problem is simple. Why is your number set so low for basic income? Why not 50k? Why not 100k? Why not 1 billion dollars?

    What happens to the price of a loaf of bread if I give everyone 1 billion dollars? Or even in your case 24k. You have obviously taken a few econ classes. Run the curves.

    Like many wealth redistribution schemes they work very short term. It is the next iteration 10 years after you want to see what your work has wrought.

    There is a second flaw to your system. If you want to simplify the tax system there needs to be 0 deductions (which is what you really created with the living stipend). Deductions are how we end up with complexity and inequality and a form of wage slavery. Deductions are a form of slavery. Your stipend is an even better way to shackle people. Do as I say or loose your stipend. That sort of thing.