The Twelve Days of Christmas: An Analysis

There was a funny piece on the radio about the song "The Twelve Days of Christmas," imagining the woman's response to all those gifts. She starts out thrilled and touched by her partridge in a pear tree, but as the days go on and the presents keep piling up, she goes from gentle dissuasion to chilly formality to outright hostility.

It had not occurred to me that the woman would end up wilth twelve partridges in pear trees. Moreover, matters were getting worse, as she would get two turtledoves a day for days two through twelve, for a total of twenty-two turtledoves, and similarly, thirty French hens. On the other hand, the numbers did not keep increasing for all twelve days: she would get, fortunatelv, only twelve drummer drumming.

In fact, I realized, there are two effects in opposite directions: as the days go by, the gift gets bigger, but it is received for fewer days. Specifically, for the gift of day x, the recipient will get

x(13 - x)

copies, where the first part is copies per day (the number of geese a-laying or whatever), and the second part is the number of days the gift is received. This expression has a maximum between 6 and 7, and in fact our lucky love-object will get:

12 drummers druming;
22 pipers piping;
30 lords a-leaping;
36 ladies dancing;
40 maids a-milking;
42 swans a-swimming;
42 geese a-laying;
40 golden rings;
36 calling birds;
30 French hens;
22 turtledoves;
 and of course,
12 partridges in pear trees.

A few final comments: If you add up all the gifts, they total 364. If the true love had wished to demonstrate less romantic flamboyance and more dedication, he could have given her a present every day for an entire year, leaving her birthday as the one day when he gets her something she actually wants.

Of course, that would make a very long and and very dull song. "On the sixth day of March, my true love gave to me/ A French hen. On the seventh day of March, my true love gave to me/ Another French hen. On the eighth day of March, my true love gave to me/ Another French hen. On the ninth day of March, my true love gave to me/ Another French hen. On the tenth day of March...."

CNN Debate Math

The Democratic debates on July 30 and 31 were a little less than 3 hours long each. A conservative estimate would be 150 minutes.

150  minutes /10 candidates = 15 minutes/candidate

Now if you were CNN, and you had 15 minutes per candidate to allocate, which of these would you choose?

A. Ask each candidate five questions, allowing her or him three minutes to respond to each.

B. Ask the candidates three questions of three minutes, and let them comment on three other questions for two minutes each.

C. Ask a whole lot of questions and allow candidates sixty seconds to respond to each. If the candidate  attacks another candidate, allow the second candidate thirty seconds to respond.

If you voted for alternative  (C), your name is probably CNN.

What Should the Democrats Stand For? I: Equality

A party as large and varied as the Democrats needs some core that people can use as a shorthand for what the party stands for, and that make sense out of a welter of policy  positions. I'll be making some suggestions; here's my first.

I. Equality

"We hold these truths to be self-evident, that all ... are created equal..."

Equality is a founding value of the American republic, the first of the "self-evident" truths in the Declaration of Independence. Yet while we hear a lot these days about inequality, it's hard to find anyone talking about equality as a political issue. When we're talking about wealth and income, the argument is over how unequal they should be, and whether they've become too unequal.

But the promise of the American Revolution was of a nation where people, whatever their differences in position or privilege, had equal rights as citizens. How are we doing?

Equality of Political Power

The fact is, most people do not feel they have a say in our political life equal to that of people with money. A recent New York Times/CBS poll found that 66% of Americans think that "wealthy Americans have more of a chance to influence the electoral process than other Americans." And not just the electoral process but the whole political process: A poll last year found that 75% thought that people like them have too little power and influence in Washington (with similar percentages for working people and, to my surprise, poor people), while 82% thought that wealthy people have too much power and influence (69% for large businesses).

Here's the thing: they're right. A startling recent piece of academic research looked at the outcomes on almost 1,800 policy issues, and concluded: "... analysis indicates that economic elites and organized groups representing business interests have substantial independent impacts on U.S. government policy, while average citizens and mass-based interest groups have little or no independent influence."

There are a lot of ways the rich and corporations could exert influence, but surely the main one is through campaign contributions. Any doubts people might have had about this were surely removed by the Republican panic around their recent  tax bill, when a congressman from New York made the memorable statement, "My donors are basically saying, ‘Get it done or don’t ever call me again.’ "

Public patience with the situation has worn thin. In a 2015 poll, 85% (including 81% of Republicans) say either that the system for funding political campaigns needs fundamental changes or that it needs to be completely rebuilt.

Yet at the same time, the Supreme Court  has handed down a series of rulings, beginning with the famed Citizens United v. FEC decision of 2010, that have seemingly made it nearly impossible to restrict the role of money in politics. The Citizens United case, as you may recall, involved an organization that wanted to air a film critical of Hillary Clinton shortly before a  primary. In that decision and later ones, the  Court, while upholding the right of Congress to restrict contributions to candidates, has essentially said that any attempt to restrict independent expenditures for or against a candidate is an impermissible infringement of freedom of speech. Some of the rulings seem bizarre--for example, the Court has held that providing matching funds to a candidate who is being outspent places an unacceptable burden on free speech.

So it has increasingly seemed impossible to stop the flood of big money into politics. Fortunately, we don't need to.

Wait...what?

Actually, we don't need to keep big money out of politics-- we just need to get small money in. Let's do the arithmetic. In 2016 a total of $4 billion was spent on Congressional races, and another $2.4 billion on the Presidential race.  There are roughly 250 million voting-age people in the US, and around 93% are citizens-- call it 230 million. A campaign contribution of $50 per person would yield more than $11 billion, completely swamping big-money contributions.

Now, how do we get 230 million people to contribute $50 each? Several variants on a solution have been proposed by me and better-known people. My preferred version is to simply give everyone a $50 tax credit for contributions to a candidate for Federal office. A tax credit, not a deduction: the first $50 of any contribution would from the donors viewpoint be free. The credit would be refundable, meaning that even those with no tax liability would be eligible to receive $50. Some minor tweaks would be necessary to prevent fraud.

But, you object, even though the contribution costs the donor nothing, surely not everyone will be interested enough to contribute. True. Let's assume that after advertising to inform people about the law, half contribute. So divide expected contributions by two. But there is only one Federal election every two years, so multiply by two. Result: more than $11 billion.

A law like this could have powerful effect on the way politics is practiced. In theory, politicians could go on trying to supplement their small-contribution funds with large contributions from wealthy donors, but those who did would be vulnerable to attacks from rivals who promised not to accept large contributions. To be sure, those who went the small-money route would have to develop new strategies for fund-raising. Instead of spending hours every day on the phone with wealthy people--unconsciously soaking up their view of the world--they would have to (and now could!) spend more time in touch with their constituents. As for voters, contributions would no longer be an elite activity for the wealthy and the ideologically committed, but could become as commonplace as voting.

Combine the voter hunger for a solution with the intuitive appeal of this approach (and add a catchy name-- my suggestion is the "U.S. Grant," after the face on the $50 bill, but maybe "The Fifty-Buck Plan" gets the idea across better) and this could be a very strong campaign issue for the Democrats.

Equality Before the Law

If equality means anything, it means that the law--specifically, the criminal-justice system-- should treat everyone equally. And this seems not to be true for some people. Most notably, it seems not to be true for African-Americans.

It is difficult for lifelong whites like me to wrap our minds around how differently blacks view the prospect of an encounter with police. I found anecdotal reports like this one to be the most illuminating.

But there is ample survey evidence of differences in attitudes to back it up. In a 2015 Gallup survey, for example, that asked, "Thinking about the community where you live and work, do you think the local police treat minorities more harshly, less harshly, or just as they do anyone else?" 19% of whites said "more harshly;" so did 54% of blacks. (This may partly reflect the fact that they live in different communities.) And asked, "Do you agree or disagree: These days police in most cities treat blacks as fairly as they do whites," 31% of whites disagreed; so did 76% of blacks. Most poignantly, when Gallup asked, "Have you ever warned your children to be careful when dealing with the police?" 32% of whites said yes, as did 74% of blacks.

It is, of course, the spate of videos of police killing unarmed black men and boys that raised this issue to public (meaning white) notice. Are police really more likely to shoot unarmed blacks than unarmed whites?  When I took a look at this question a few years ago, I found that, while armed blacks and whites were killed by police at similar rates, blacks were greatly overrepresented among the unarmed who were killed by police. More recent research has come to a similar conclusion.

It's unlikely that this mostly represents racist killers on our police forces. But there are situations where cops have to make very quick decisions weighing the threat to their own lives against the risk of killing an innocent civilian. Those situations might be turning out worse for blacks because cops unconsciously view them as more threatening than whites. Or they might be turning out worse because cops unconsciously think lives of innocent blacks matter less than lives of innocent whites.

Notice how framing the issue as "equality," instead of "identity politics" (whatever that is) changes the debate. The response of many whites to the shooting of an unarmed black man is to focus on what the victim should have done differently. For example, Timothy Russell and Malissa Williams would undoubtedly be alive today if they had not led police on a high-speed chase. But undoubtedly there have been unarmed white couples that did that. The question is, have any of them ended up being shot by police a total of 47 times? If so, I haven't heard about it. In a society where people are equal, we should not tell a subset of citizens, "Behave perfectly all the time, and we'll let you live."

But, perhaps with one nervous eye on the white working class, Democrats have had a hard time talking about this issue-- witness the strange, flustered response of Nancy Pelosi to a question about Black Lives Matter. Here's all she needed to say:

"I think there's been a lot of confusion among whites about what the phrase 'Black Lives Matter' actually means. As I understand it, it's saying that that the life of a black should matter as much as the life of a white-- it's about equality. And as a principle, I don't see who could be against that."


Equality of Opportunity

If the American Revolution was anything, it was a rejection of the European idea of a hereditary ruling class; the Constitution even says explicitly, "No Title of Nobility shall be granted by the United States." Yet today, the chance that someone born in the bottom 20% of the income distribution will end up in the top 20% is higher in Britain than in the U.S., and in our New World neighbor Canada it's almost twice as high as in the U.S.

Consider that passport to the top 20%, Harvard. Two-thirds of its undergraduates come from the top 20% of the income distribution. A startling two in five come from the top 5%, and 15% from the top 1% By age 34, Harvard grads from poor backgrounds are doing nearly as well as people from wealthy backgrounds, but there were few from poor backgrounds to begin with.

The story is the same, or worse, at other Ivy League schools: Dartmouth, Yale, Princeton, Penn, and Brown all had more students from the top 1% than from the bottom 60%. I doubt it's because admissions officers prefer to admit people of their own social class. Rather, it's because of the accumulation of privileges of upbringing and schooling that parents in the upper 20% are able to bestow on their children.

Finighan and Putnam talk about a "growing opportunity gap in America." They point out that someone from a disadvantaged background with high test scores has about the same chance (around 30%) of graduating from college as someone from an affluent background with low test scores; that over the 35 years from 1972 to 2007, the top income decile doubled the amount it spends on its children, to around $6,000, while spending by the lowest deciles remained flat at around $1,000 (to be completely clear, I am not blaming poor parents for this-- it mirrors what happened to incomes over this period); and so on.  In particular, while the more affluent find it increasingly difficult to cover the cost of high-quality child care, working-class families find themselves priced out of the market altogether, and must settle for lower-quality child-care, such as with unlicensed providers.

If we want to avoid--or undo--the development of a de facto hereditary aristocracy ,we need to take some serious steps at both ends of the existing public school system. The first step would be to come closer to equalizing the early childhood environments of children from different income classes by establishing universal preschool. This would also be a bread and butter issue for many middle-to-low-income families, for whom child-care expenses are a significant burden. The second step would be to offer free or nearly free college, so that students get used to thinking of college as something achievable.

This is going to cost some money, much more than the U.S. Grant plan I discussed above. The cost of providing universal "quality preschool education" has been estimated at $34 billion for 4-year-olds and $35 billion for 3-year-olds. Bernie Sanders estimates the cost of his plan to cover 2/3 of the cost of tuition at state colleges and universities  (with states paying the rest) at $47 billion-- it's unclear to me whether this number includes other parts of his plan, such as the reduction in student loan payments.

So for the full two years of preschool plus the Sanders plan, the total is $116 billion per year. That's around 9% of the total US discretionary (i.e., excluding thing like Social Security, Medicare, and Medicaid) budget, or around 19-20% of the non-military discretionary budget, which seems like a lot. On the other hand...

On the other hand, the recent Republican tax cut is projected to add $1.9 trillion to the debt over ten years, which averages out to $190 billion per year, for something that had very little effect on the economy other than making some rich people much richer. Should we not spend a third less than that for something that promises to increase U.S. productivity, improve life for struggling families, take seriously the promise of equal opportunity regardless of social background, and maybe make a start on healing the cultural chasm that is America today? I think we should.

Note: If you've been following the Democratic candidates closely, you may be wondering  how this sort of preschool plan compares to Sen. Elizabeth Warren's universal child-care proposal. As far as I can tell, the terms high-quality preschool and high-quality childcare  (for ages 3 and 4) are synonymous. Warren's plan costs around 50% more, but includes children from ages 0 - 3 in addition to 3- and 4-year-olds. The gap is filled by having parents, except low-income parents, pay up to a cap of 7% of income, which, as best I can tell, means that virtually everyone will get some degree of subsidy. I am not advocating for one plan over the other.

How Much Could We Raise Income Taxes on the Rich? Actually, A Lot.

Rep. Alexandria Ocasio-Cortez really set the cat among the pigeons with her recent remarks about taxation. Asked how she would pay for everything in the proposed marks about taxation. Asked how she would pay for everything in the proposed Green New Deal, she said:

You look at our tax rates back in the ’60s, and when you had a progressive tax rate system your tax rate, let’s say, from zero to $75,000 may be 10 percent or 15 percent, et cetera. But once you get to the tippy tops — on your 10 millionth dollar — sometimes you see tax rates as high as 60 or 70 percent. That doesn’t mean all $10 million are taxed at an extremely high rate, but it means that as you climb up this ladder you should be contributing more.

Feathers flew. Rep. Steve Scalise tweeted that Democrats want to  "[t]ake away 70% of your income and give it to leftist fantasy programs," to which Ocasio-Cortez tartly replied, "You’re the GOP Minority Whip. How do you not know how marginal tax rates work?" For those of you who find yourselves in the same boat as Scalise, the marginal tax is the amount of tax you pay on the next dollar of income; it's relevant when we're looking at your incentives. The average rate is the tax you pay divided by your income, or in other words, the share of your income that goes to taxes. Ocasio-Cortez is quite explicitly talking about marginal rates; Scalise's tweet mixes up marginal rates and average rates.

But in defense of Scalise, it's quite possible under Ocasio-Cortez's proposal for someone to end up paying very close to 70% of their income. Consider, for example, the 25 highest-earning hedge-fund managers and traders profiled by Forbes. They earned an average of more than $670 million each in 2017; if they were paying 70% on income above $10 million, virtually all of their income would have been taxed at 70%. If this strikes you as the job for you, by the way, don't be shy. Fully half of them, including some getting compensation over $1 billion, performed worse at picking investments than you could expect if you were choosing at random.

Rate Amnesia

In any case, Ocasio-Cortez is if anything understating the history of high marginal rates. From 1951 through 1963 the top marginal tax rate never went below 91%. From 1964 through 1980 it never went below 70%, and not until 1987 did it get below 50%.

Today, though, this (relatively recent) history seems to have been all but forgotten, as  attested by this clip from the World Economic Forum in Davos, Switzerland. An economist finally speaks up about the actual history of tax rates in the U.S., to incredulity from the interviewer. And even he understates the case: as we have seen, a 70% rate persisted through 1980. (Don't miss Michael Dell's smug performance as Davos Man.) 

High top rates were the rule during some of the strongest periods of economic growth in U.S. history, which suggests they weren't a huge burden on the economy. Yet the idea that high marginal tax rates have big negative effects on incentives is one of the most cherished beliefs of American conservatism. How much should we be worried about the economic consequences of raising rates?

As it happens, some extremely distinguished economists have just weighed in on that question. Two recent papers attempted to estimate the incentive effects of high marginal rates and to find the economically optimal top rate. Both find that the effect is small, and their estimates of the optimal top rate are correspondingly high: one estimate is 72%, the other 84%. 

It seems pretty reasonable, then, to tax the income of the rich at high rates. Yet Democrats have so far been quite bashful about proposing any changes to income taxes, even members of the progressive wing of the party, like Bernie Sanders, Elizabeth Warren, and Kamala Harris. To fund various ideas they have proposed an increase in the estate tax (Sanders,Warren, Harris), a tax on financial transactions (Sanders), and a tax on wealth (Warren).

There's nothing wrong with any of those taxes (with the possible exception of the wealth tax, whose constitutionality will surely be challenged, bringing it before a Supreme Court that has been fiercely protective of the rights of the rich). But it's long past time to reestablish the norm of taxing the rich and the ultra-rich at high rates. There doesn't appear to be any political downside: a poll in January showed 59-41 support for a top tax rate of 70 percent.

Raising Income Tax Rates on the Rich

Let's see what the revenues might be from an increase in tax rates at the top. The boundaries of the top 1%, 0.1%., and .01% make convenient tax bracket cutoffs: roughly $500,000, $2,000,000 and $10,000,000 in a year  (Table I, p. 575). Using information about those three income classes, I've done some rough estimates of the added revenue from relatively "moderate" increase in tax rates to 50%, 58%, and 65%. (I've posted an explanation of my methodology here.)  I get an estimate of $222 billion.  (Interestingly, of the three new steps, two-thirds of the revenue comes from the first one, the increase to 50%, and nine-tenths comes from the first two.)

To be sure, $222 billion is not enough to put much of a dent in the cost of Medicare for All, which would run to between two and three trillion dollars a year. But $222 billion is enough to fund some things that could have a really dramatic impact on people's lives. Leaving aside items that have already been proposed by one or another Presidential candidate, here's one cut:

• Spend $150 billion per year eliminating America's infrastructure spending shortfall;
• Treat with buprenorphine the 2.1 million people with prescription-opioid use disorder at $5980/year each, for a total cost of $13 billion.
• Increase the salary of each of the 3.6 million public school teachers by $10,000, for a total cost of $36 billion;
• Increase by 50% the budgets of the National Science Foundation ($3.9 billion) and the IRS ($5.8 billion) 

That still leaves us more than $13 billion in the black. And we haven't raised taxes on anyone in the lower 99% by one cent.

And don't worry that we'll be leaving the 1% destitute.  They're currently paying 27% of their income in Federal taxes (Table 1, last row); this increase would raise that to 38%.

It's All About the Base

It's easy, though, to be hypnotized by the controversy about tax rates and miss an equally important question: What is the income base to which those rates are being applied? If we say the top rate is 70%, we need to remember to ask: 70% of what?

When it comes to taxing the rich, there are two big items in the definition of the tax base.  The bigger of the two is tax treatment of capital gains. Capital gains are what you net when you sell an asset for more than you paid for it; the difference, the capital gain, is taxable income. But if you held the asset for more than a year, you are taxed at rates much lower than those on ordinary income. The usual justification is that it encourages long-term, and discourage short-term, investment. This claim, though, is controversial. 

The other and more recent tax break is the special treatment of "qualified" dividends. The idea is to extend the reduced rate on capital gains to dividend income as well. Both these tax breaks are, to some extent, used by the non-rich as well as the rich. 

But they are used a lot more by the rich: this table shows that these two tax preferences were used for more than three-quarters of the taxes paid by those with incomes over $1 million. In no other income class did those tax breaks account for even ten percent of taxes paid, and in no class making less than $100,000 did they account for even  two percent. A repeal of those provisions would be nearly as well targeted as a rate increase.

The Treasury Department has estimated (items 69 and 70) revenue loss from the qualified dividend provision and the capital gains provision to be $29 billion and $110 billion, respectively.  Adding that revenue to our estimate of the revenue from raising marginal rates gives a total of just over $360 billion-- or, as they would say in the Washington style of talking in ten-year chunks, $3.6 trillion. (That's without taking account of interaction effects, i.e., the fact that higher rates would now be  applied to a bigger base.)

That is a lot of money. It's enough to fund what you could either call a leftist wish list or a transformation in the lives of ordinary people. Take a moment to contemplate, for instance, the Brown-Khanna bill to dramatically increase the Earned Income Tax Credit. At a cost of $140 billion, it would raise the incomes of more than a third of working households in the US, in most cases by thousands of dollars, and reduce the poverty rate by a third. 

Bear in mind, too, that the revenues we've been discussing here are only those from the personal income tax, and not the corporate "income" tax (which no longer is based on corporate income). That's way too complicated to get into now, so for the time being I will simply assert that a selective undoing and alteration of some of the changes of the 2017 tax legislation could produce revenue of at least $170 billion a year, with very likely a net gain in economic efficiency.

In his inaugural address in 1989, President George H.W. Bush said, "We have more will than wallet." That wasn't true then, and it's even less true today. There's plenty of wallet. What's been lacking is the will.

Note on Methodology

Start at Table 1, the first column, "Top 1%".

Take "Number of Returns" (first row) and multiply it by $466,950 , which I got from here, as the boundary for the top marginal rate. Fortunately, it's very close to the cutoff for the top 1% (second row from bottom). I used the rate for "married filing jointly." I take the product of those two numbers to be that income of the top 1% which is taxed at less than the top rate.

Subtract that number from "Adjusted Gross Income." I take the result to be that income of the 1% which is subject to tax at the highest rate. I'm using 35% as the highest rate; I use 2016 data because it was the newest I could find.

I now have $1.345 trillion. I next included an adjustment for the negative incentive effect of the tax. Romer and Romer estimate the elasticity of supply at at 0.2. The percentage change in the after-tax wage times the elasticity gives the percentage change in the supply. I got an estimated change of -5%, so I reduced the revenue accordingly.

Then I subtracted 23% as an allowance for deductions from taxable income. I got 23% here. It's the approximate average deduction in both the second and the third highest income groups, taken at the midpoints. I didn't use the highest group because there's no midpoint.

We multiply that by .50-.35=.15 to get the additional revenue from raising rate from 35% to 50%. I ended up with $147 billion for this piece.

Now we add to that the additional revenue from the 58% and 65% rates, which I'll take to apply to the .1% and the .01%, as I indicated in the post. Table 3 gives $966 billion for the income of 0.1%. I don't have an estimate of income for the "tippy top" group, but looking at Table I on p. 575 under "Pretax national income/Income share" it is apparent that there is a strong tendency for the top 10% of any group to get about 45% of the income for that group. So take 45% of $966 billion to get $434.7 billion for the top .01%.

Now we proceed as before. The calculated incentive effects this time are 9% for the increase from 35% to 58%, and 12% for the increase to 65%, and the deductions are as before. Since we already counted these people when we raised the rate to 50%, we multiply only by .58-.50 and, similarly, .65-.58. My totals are $54 billion and $20.5 billion, for a grand total of $222 billion.

Note that the increase to a 50% rate accounts for two-thirds of total revenue, and the increase to 58% another quarter, while the final increase to 65% accounts for less than a tenth.


I've done this wrong about seven times up to now, so if you see what looks to you like a major error, please email me at hfrant@post.harvard.edu.