Wednesday, November 1, 2017

Tax Graph

The tax discussion is moving to personal income taxes, and the world is waiting to hear the actual Republican proposal, due tomorrow (Thursday).

With apologies to blog readers who know all this in their sleep, I thought I might explain just why (some) economists keep chanting "broaden the base, lower marginal rates," or why I keep saying that taxes don't matter, tax rates matter to economic growth.  This is grumpy economist, Saturday morning cartoon edition. Perhaps a colorful graph will help as you try to explain taxes to relatives this Thanksgiving.

Start with the blue line. Suppose you work 40 hours a week, and make $100,000. Suppose the government wants half of it. One way to get that is with a flat tax -- for every dollar you earn, send 50 cents to the government.  The government gets $50,000.

Now consider the red line. This line can represent a progressive tax: Exempt the first $50,000 of income, so people who make less have to pay a smaller share of their income in taxes, and charge a 100% tax rate on the rest. Equivalently, this line represents $50,000 of tax shelters and deductions -- employer-provided health care, charitable contributions to a foundation that employs your relatives and flies you around on private jets, a deduction for home mortgage interest, credits for the solar cells on your roof, and so on.

At first glance, this tax system raises the same amount of money. (That's "static scoring.")

You can see the hole in the argument. If we tax the marginal dollar after $50,000 at 100%, you won't bother working the second 20 hours, and the government will get no revenue. More deeply, slowly, and insidiously, in my view, people choose easy college majors that lead to $50,000 jobs, not harder ones that lead to $100,000 jobs, or they don't start businesses.

The green line is an economists' ideal tax.  Everyone pays the first $50,000 no matter what and then keeps everything after that. People would choose to work more than 40 hours a week, and the economy would take off.

Of course, that's not realistic as an income tax, but it's the idea behind "land" taxes, the recent fashion for "monopoly" taxes, and so on. Find something to tax that has no disincentive effects, and tax the heck out of it. One of my graduate school professors explained (in jest!) that we should tax kidney-dialysis machines. If you need it, you really need it and you'll pay anything to get one.

But at least we can move from something like the red line to something more like the blue line. Broaden the base, lower the marginal rate.

Here I think we have gotten to an unproductive argument. See the next graph

If we broaden the base, and lower the rate, we increase incentives to work. Then, to raise the same revenue, we don't have to make the lines cross at the old revenue. The new line can lie below the old line at the old work effort, but greater growth will make up the revenue, as shown.

The argument is not whether "tax cuts pay for themselves." That's an extreme possibility. But tax rate cuts do partially pay for themselves, so one can raise the same revenue from a tax system that appears, on static scoring (ignoring that the points move to the right) to raise the deficit instead.

This argument is correct, but it leads to a huge fight over just how much growth will increase, and when. It is hard to quantify. It is especially hard, in my view, because most government analysis ignores all the important channels. We focus on labor effort. But once we have chosen careers and jobs, most people work the same amount. The damage is more insidious. Slowly, people drop out of the labor force. Slowly, people chose easier college majors. Slowly, people choose safe and steady but not well paying jobs rather than risky high reward business startups. Slowly, people invest in  complicated lawyer-intensive tax-avoidance strategies. This all takes time.

And we have a huge deficit. So, I would prefer not to fight this argument. Broaden the base and lower the rates on static scoring. When money starts roaring in, cut the rates. Agree on the structure of the tax code for a generation, and let rates adjust as needed. Yes, many readers will worry that lots of revenue will lead to lots more spending. OK, let's write in that rates go down further if and when the revenues increase, rather than cut them now.

Furthermore, if we had to make a revenue-neutral reform, I think the pressure to get rid of the deductions would be much stronger. These mostly benefit the rich anyway (class warriors, why are you so silent on the regressive effects of home mortgage, charitable, employer health care, and state and local deductions??) You just can't get significant rate reductions on a revenue neutral basis without really cutting the deductions, tax expenditures, and with them much of the complexity and corruption of the code.

Alas, this eminently sensible idea -- broaden base, lower marginal rates, redistribution-neutral, and revenue-neutral, growth-oriented reform -- does not characterize much of what I'm hearing about the upcoming personal income tax changes.

One thing we are hearing more of is expanded deductions, for example for child care.  This is supposed to give a "tax cut to the middle class." Well, again, a tax cut and a marginal tax rate cut are entirely different things, and have different effects on growth.

The next graph gives the "middle class" a "tax cut" in two different ways -- by lowering the marginal rate, or by offering a new deduction or credit, and keeping the old rates intact. At the blue dot, our taxpayer has received the same "tax cut." But notice that by adding a deduction, we have done nothing to improve our taxpayer's incentives. In fact, we have made matters worse. There are offsetting "income" and "substitution" effects in provoking effort. As we get wealthier, we choose to work less. As opportunities are larger, we work more. This is all income effect, and no substitution effect.

It gets worse. The budget impact of this deduction is obviously large. Everybody in the US gets the deduction, all the way up the income scale. For that reason, most of these deductions phase out. Sure, "gazillionaires don't need help with their childcare expenses." (A good example of bad economic thinking all around.) So the credit phases out. The next graph shows what happens if we add a deduction or credit that phases out with income:

The steepest part of the line -- the greatest disincentive to work -- is in the phaseout region. In fact, the Americans facing the highest marginal tax rates are those precisely in the "middle class," where earning an extra dollar phases out credits, health insurance subsidies, food stamp subsidies, and so forth. On average, pretty much from 0 to $60,000 there is very little incentive to work -- or, again, to study, to choose harder professions, to move to take a job, to start a business and so on.

This is a little bit unfair. The credits and deductions do have incentive effects. That's half of why they're there. The mortgage interest deduction gives people an incentive to buy rather than rent, to borrow rather than save, to buy bigger rather than smaller, and to refinance frequently. (Interest payments are tax deductible, principal payments are not.) The childcare credit gives people an incentive to have children. (That this incentive is inversely scaled with income is another interesting issue.) The health care deduction encourages us to spend a lot more on health insurance and less on solar cells and electric cars. The solar cell and electric car deduction encourages us to spend more on those and less on food. And so forth.  If these activities encourage economic growth, perhaps it's worth suffering the disincentive to work, study, save, or start businesses.

An honest economist must admit that for economic growth, taxes do not matter. Marginal tax rates matter.  If there were a way to "tax the rich" without raising the disincentive to all the socially useful activities that becoming rich, or working to pass wealth on to your children entails, and if our society decided it wanted such redistribution, we would have much less argument against it. We would do the world a favor, I think, to harp most on incentives, which the world seems to ignore, and much less on our personal moral feelings about redistribution, pro or con.

How high are our marginal rates? Another important principle: All taxes matter, not just federal income taxes, and benefit phaseouts are just as important as actual taxes. Add to the Federal 43% top marginal rate the state income tax -- 13.5% in my California -- plus sales taxes on everything yo buy -- 9% in lovely Palo Alto. Pundits' habit of only quoting the federal income tax in isolation is profoundly wrong. And if you're one dollar below the medicaid cutoff, you face an essentially infinite marginal tax rate.


  1. Why does a tax rate cut partially pay for itself? In my case if you just cut my top rate then I will have more income, and I will want to work less! I guess if you cut my top rate, but raise the lower bracket rates, so I end up getting taxed the same amount then I have no reason to work less and some reason to work more.

    1. Because you lack agency. If you possessed agency we would have to concern ourselves with your risk vs. reward for a business you might start or investment in an existing business that you might make if you perceived profits large enough to offset the risk of failure, or your decision as to if it is worth the extra time and match to learn economics instead of marketing.
      As the Author states these effects can be slow, but they are also cumulative as each business that doesn't expand because the 40% of profit it would keep doesn't cover it's risk reduces the paid employees who could be customers to make it's neighbors expansion profitable.

    2. I lack agency? Not sure what you mean, that I don't own a business? Sounds like you are saying that you only care about business owners? So if you cut the top rate for business owners they will all want to work harder or invest more? Thats not how I see it. Some will want to work harder but some will want to work less. I only ever hear that cutting the top rate will make some work harder, but never that anybody will work less.

    3. I keep hearing from "real business owners" that they don't care what the tax rate is because they don't make decisions based on tax rates, but on demand.

      The whole point of collecting taxes is to pay for the services of government. Figure out how much you want to spend on the government and then come up with a tax scheme that minimally distorts the market and is at a minimum non-regressive and at best progressive.

  2. John,

    "The green line is an economists' ideal tax. Everyone pays the first $50,000 no matter what and then keeps everything after that. People would choose to work more than 40 hours a week, and the economy would take off."

    Anyone making less than $50,000 has no after tax income? How is this ideal?

    The function of green line (for wages above $50,000) is:
    Tax Rate = $50,000 / Wages
    For everyone else the tax rate is 100%.

    Instead start with a maximum tax rate (100%) at $0.00 of wages and draw this curve instead:

    Tax Rate = $50,000 / (Wages + $50,000)

    Here the line starts sloping down immediately from a 100% tax rate at $0.00.

    1. I think you misunderstood what is meant by ideal. He is optimizing incentives. If you don't actually "make money" until after you earn $50,000, you have a HELL of an incentive to be productive.

      His point is that what maters to the economy is not the total tax bill, it is how the tax structure marginally impacts decisions and incentives. Right now, our deductions and credits and assistance programs give TERRIBLE incentives in increasing your earning. You have sour spots, where you lose a dollar of direct aid or refundable tax credit for every extra dollar you bring in meaning it does not make any sense to strive to earn that extra dollar and people become "stuck".

    2. Matt,

      "I think you misunderstood what is meant by ideal. He is optimizing incentives. If you don't actually make money until after you earn $50,000, you have a HELL of an incentive to be productive."

      No, you have a HELL of an incentive to turn down every job that pays under $50,000. Starting pay coming out of college averages ranges from about $65,000 (Engineering) to $35,000 (Teaching) - and most of those are salaried (not hourly positions). See:

      My point above was that the incentives should begin on the first $1.00 earned / hour worked and continue from there. Meaning working 5 hours instead of 1 hour or earning $10,000 pretax instead of $1,000 pretax should incorporate the same type of incentives.

      That was my problem with John's graph. There is nothing magical about $50,000 a year or 40 hours a week. I understand the incentive effects just fine.

  3. John,

    Change the bottom of your first graph from hours worked to total wages. I can either work 60 hours instead of 40 hours or I can be 50% more productive in those 40 hours that I work. Also, it is not always possible to work more hours because of safety, seasonality, or other concerns.

    Would you get on the road behind a truck driver that hasn't slept in 5 days?
    Would the Chicago Cubs man the bases in December in three of snow at Wrigley?

  4. This comment has been removed by the author.

  5. (sorry I might have sent a blank test comment previously)
    I consider the 100K example to be a bit of a Rigid exaggeration of a progressive tax system, 50% of a 100K income is much higher than most countries with progressive tax systems. Additionally a 50K tax free threshold is insanely high. What do you think of a 35% negative income tax kicking in at 35K and 35% thereafter. Assume no sweeteners or a minimum wage.

  6. John,

    One part that you are missing is the effect of increased productivity on prices. Okay, I have a debt fixed in nominal terms (say my interest payments are $5000 nominal per week). I can work 40 hours to produce 1000 widgets and sell them for $5.00 a piece or I can work 80 hours to produce 2000 widgets and sell them for $2.00 a piece.

    Negating the possibility that I may actually want to work 80 hours a week just to keep busy, why would I work those extra 40 hours to earn $1000 less income and default on my loan payments?

    Tax policy (deductibility of interest payments) get's you part of the way there, but not all of the way. An individual cannot deduct the real cost of debt service, only the nominal part.

    If you want people to work longer hours / produce more goods through tax policy incentives, then those tax policy incentives must allow for the real cost of debt service to be reduced (not just nominal cost).

  7. A tax cut pays for itself if the present value of all future federal revenues is the same or greater after the tax cut as it was before. Based upon the latest CRB LTBO assumptions and using the Social Security Trustees' "to the infinite horizon" methodology, eliminating the entire corporate income tax would pay for itself if long-term RGDP growth increased by 0.02 percentage points (i.e., from the CBO's assumption of 1.90% to 1.92%). So, all supply-side tax cuts pay for themselves. The only thing that really matters is the rate of RGDP growth. Everything else is a second- or third-order issue.

    1. This comment needs to be cut out and framed. Nothing matters next to long run growth. If tax rate cuts can raise long run growth, even by minuscule amounts, they pay for themselves. Moreover, the wake the golden goose. Growth is about better lives not just tax revenue. More gently, we should expect the revenue enhancing effects of tax cuts to take a long time. Sure "studies" find little effects in a year or two. That's not the point. The point is research, new businesses, new products, new ideas, people's lifetime decisions to study and start businesses or take it easy and safe, a new culture even. Even if the growth rate doesn't rise permanently all these effects take decades -- and their insidious opposites also settle in over decades, and people puzzle why the economy is growing slowly.

    2. To make this feel grounded I wanted to see what these proposed growth numbers would look like after 50 years. Looking at 1.90% vs 1.92% growth over a 50 year horizon the benefits do not seem that large:

      1.0190^50 = 2.56276, 156.276% GDP growth
      1.0192^50 = 2.58803, 158.803% GDP growth

      Based on this I would think that boosting annual GDP growth from 1.90% to 1.92% would only make the economy 0.986% larger after 50 years. In the meantime you have dropped 9% of federal tax revenue, and either you have massively cut federal programs (possibly hurting assistance and education programs that affect the economy's human capital) or you have increased the deficit and added to compounding debt payments.

      In my mind creating incentives for companies to invest instead of hoarding cash (changing the tax code for offshore profits?) could have a large impact on growth with a much smaller footprint on federal revenues.

      Please let me know if I am focusing on the wrong problem or have made an error in my calculations. The idea that "all supply-side tax cuts pay for themselves" in our lifetimes seems dubious to me but I am always happy to be corrected. Thanks for the thoughtful discussion.


    3. John,

      "This comment needs to be cut out and framed. Nothing matters next to long run growth. If tax rate cuts can raise long run growth, even by minuscule amounts, they pay for themselves."

      There is a long time between now and the infinite horizon. Sure, if the federal government could borrow out to that infinite horizon, then any shortfalls could be covered by borrowing and made up for when the growth comes back. Government cuts taxes, sells perpetual bonds that pay off interest and principle at the end of time, and waits for the growth to catch up.

      Instead, tax cuts must pay for themselves over an intermediate horizon (under the Byrd Rule I believe it is 10 years). And the reason is that as debt accumulates, interest payments can grow until they are the only expenditure the government can pay out of current revenue.

    4. Cash flow discounting exists for a reason. Even absent inflation a dollar this year is worth a lot more than a dollar fifty years from now. You can do useful stuff with it for fifty years. Is supply side tax cut theory not using DCF? If not then no wonder it was dubbed "voodoo economics".

    5. -E5,

      Cash flow discounting works fine as long as it is used properly. The discount factor to be used is the sum of the prevailing interest rate and the growth rate of the debt.

      If a certain tax policy raises debt outstanding by 4% per year and prevailing interest rates are 3% per year, then the tax policy must increase growth by 7% per year to be neutral.

  8. "Slowly, people abandon complicated lawyer-intensive tax-avoidance strategies." I think you mean the opposite of 'abandon'.

    Good post.

  9. What about a flat tax, John, not on revenue, but on capital? It works a bit like a forfeit tax, with a zero marginal rate during the period. Once your revenue is above the threshold, you just keep it all. The taxman is, so to say, in the position of a debtholder, instead of being in the position of an equity holder in the case of a flat tax on revenue. Inventives are good: you work hard to pass the threshold! Latifundists, who do not care much about their holdings, are progressively run out of business. Of course, like for debt leverage, it’s procyclical: it goes both ways. But, with a sufficiently low rate, and a corresponding reduction in the income tax rate, this can be muddled through. I’d like your opinion on that. Thanks.

  10. Now that we've seen the bill, I'm hearing complaints (mostly from fellow PhD holders!) about removing the tuition-waiver exemption for masters/doctoral students. My first reaction is--isn't this exemption another one that is based on no identifiable principle, and that should go on your list of things that make the tax code less progressive? What's your take on it? (The change in the treatment of endowments is a different story...)

  11. "If there were a way to "tax the rich" without raising the disincentive to all the socially useful activities that becoming rich, or working to pass wealth on to your children entails, and if our society decided it wanted such redistribution, we would have much less argument against it."

    To tax the rich, you do not need to care about incentives to work 40 hours or more. Rich do not work at all, so they do not care about incentives. The only way to become rich is letting other people work for you.

    And with a progressive income tax they are very easy to identify and to target: the rich are those with the most money. A property tax and inheritance tax would work as well.

    And regarding incentives: those, who produce all wealth by doing all the work are not affected at all.

    But if you do the opposite and try to not tax the rich, you must get the money from somebody else and do a high taxation of those, who do all the work to produce wealth. And those people are already privately "taxed" by the rich, because that is how profits are generated. So by avoiding taxes for the rich you get a double taxation of those you care about the incentives to work.

    And we have not talked about demand yet. High profits reduce demand because rich consume only a small fraction of their income. If they are not taxed, the only way to create the missing demand is debt.


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