Having completed a thorough analysis of the impact of Bernie Sanders’s tax plans on incomes for individuals and families across the income spectrum, I was curious to see why the numbers in this article by Dylan Matthews in Vox were so different. Reviewing his analysis, I found that there were some analytical decisions we differed on, a few tax policies that Mr. Matthews omitted or implemented inaccurately, and some significant errors in his math. The result is that Matthews’s exaggerated all of the rates in Bernie’s plans. Even if we grant his decision to pool employee and employer taxes together, which I contend is misleading for a general audience, it turns out that his infamous 77% figure for the top bracket exceeds the real rate by nearly 10 points.

The figure above includes an accurate representation of total effective rates with taxes and average family healthcare costs included. As in Matthews’s analysis, I have pooled both the employee and employer contributions. While this gives a complete picture of the impacts of Bernie’s plans in comparison with current rates,the rates can be misleading if you’re curious what these plans mean to you. Some portions of the costs shown are paid out of an employee’s paycheck, but other portions are paid by employers behind the scenes. Additionally, the net differences (savings and increases) include the pooled amounts saved or paid by both employers and employees. If you’re looking for figures that relate more directly to what you could expect to save or pay, take a look at my previous post on Bernie Sanders’s tax plans. Otherwise, continue reading below for the details of where Mr. Matthews went wrong in his analysis.

Analytical Differences

I made some different judgment calls compared to Mr. Matthews. Neither choice in this section was strictly correct or incorrect, but I will explain why I believe my decisions better represent how Bernie Sanders’s proposals would impact the general public. Despite our differences, I do want to praise Matthews for sharing the details of his calculations (just as I have published my source code), which facilitates these comparisons of our methods and explanations of our different results.

Marginal v. Effective Tax

We use a marginal tax rate system for income and several other taxes in the U.S. In a marginal system, your income is broken up into chunks that are each taxed at a different rate. Take income tax for example. For married joint filers, the first $18,450 of taxable income is taxed at 10%, and the next chunk, $18,451 up to $74,900, is taxed at 15%. If your taxable income is $48,450, your top marginal tax rate would be 15%, but your actual tax rate would be lower than that. You’d separate out $18,450 and tax that at 10% ($1,845) and then tax the remaining $30,000 at 15% ($4,500). Your total tax bill would be $6,345 ($18,45 + $4,500), and that amounts to 13.1% of your $48,450 income. This 13.1% figure is called the effective tax rate, the actual tax rate paid when all is said and done.

You don’t care whether one was taxed at 10% and the other was taxed at 15%; you care that there is $2 in your wallet

Tax plan proposals, like Bernie Sanders’s Medicare-for-All plan, list tax brackets and marginal rates because that’s how tax laws are constructed, but it’s primarily only legislators and accountants that care about marginal rates. If you look at two dollar bills in your wallet, you don’t care whether one was taxed at 10% and the other was taxed at 15%; you care that there is $2 in your wallet. Because of this, my analyses use what matters to most: effective tax rates. I will grant that determination of effective tax rates is difficult and perhaps beyond the reach of the tools and skills available to most journalists. However, I would argue that, for any journalist forced to settle for a discussion of marginal rates, great reporting would take care to explain the difference and clearly label marginal rates when they are presented.

Ignoring Healthcare Savings

Matthews’s analysis includes only the new costs of buying healthcare in bulk as a nation and ignores the savings from no longer having to buy healthcare individually

Imagine you were considering whether to buy toilet paper in bulk. You could choose a 24-pack for $12 instead of frequently buying 2-packs for $2 each. If you were to consider costs alone and ignore savings, you would conclude that buying in bulk raises your toilet paper budget by $12. That is, of course, ridiculous, as you would instead be saving $12 because you were no longer buying all of the 2-packs. Matthews’s analysis includes only the new costs of buying healthcare in bulk as a nation and ignores the savings from no longer having to buy healthcare individually through premiums, co-pays, and deductibles. This does not present an accurate view of the impact of Bernie Sanders’s proposals from the perspective of an individual or a family, and that is why my analyses include estimates of savings from the elimination of current healthcare costs.

Pooling Employee and Employer Burden

Bernie Sanders’s tax plans include increases in taxes both in the withholding taxes individuals see on their paychecks (such as income tax and Social Security tax) and in the payroll taxes that employers contribute behind the scenes. Several economists have argued that these should be considered together because, from the employers perspective, these are all part of the total compensation cost for an employee.

When the new plans result in savings for the employer, I doubt that they would just hand out raises with all of the extra money

I agree that both the individual and employer perspectives should be considered (and I included both in my previous post on Bernie Sanders’s tax plans), but I am hesitant to pool them because I do not think that presents an accurate picture of what an individual could expect to experience under Sanders’s plans. First, if the cost of an employee increased, I do not think all employers would implement pay cuts to compensate. Employment contracts and union agreements would take this option off the table in some instances, and the cost to employee morale and turnover for a business would discourage the practice somewhat. More importantly, when the new plans result in savings for the employer, I doubt that they would just hand out raises with all of the extra money. Since I have found that employers would indeed save money on any employees with salaries in the range of about 70% of American families, I had decided not to pool employee and employer results in my previous analyses because it would overestimate the amount that most would be saving under Sanders’s plans, making the results for individuals look better than they really were. If, on the other hand, you compound the decisions to ignore savings and to pool burdens, as in Matthews’s analysis, then you end up grossly exaggerating the impact to individuals with middle class incomes.

Tax Policy Implementation Oversights

Matthews’s calculations have omitted one tax, missed a significant quirk in the proposed implementation of another, and ignored tax deductions and credits altogether.

Federal Unemployment Tax

The Federal Unemployment Tax Act applies a tax of 6.0% to the first $7,000 of wages for all employees. Employers can receive credits for taxes paid into state unemployment programs, but a minimum of total of 6.0% is always collected between state and federal programs. This tax appears to be absent form Matthews’s calculation spreadsheet, but it is included in my analyses.

Social Security Cap Backlog

Sanders’s proposed lifting of the Social Security wage base limit has a quirk to it that is not included in Matthews’s calculations. At present only the first $118,500 of an employees income is subject to the two 6.2% Social Security taxes (one for employees and one for employers). Sanders’s proposal (pdf) is to lift that cap and apply the taxes to all income, but with a catch: the cap is only lifted when the total income is $250,000 or more. This means that incomes between the current cap and $250,000 would pay the same as they do today, but once the new threshold is passed, Social Security tax would be due for all of the “gap” income ($118,000 – $249,999).

In his analysis, Matthews’s only applied new Social Security taxes to income above the new threshold, and, unlike in my analyses, he did not add in the backlog of tax ($8,153) for the gap. In another example of the limitations of reporting on marginal rates, this policy’s large jump in taxes at the new threshold would essentially create a tax bracket from $250,000 – $250,001 in which $8153.06 of Social Security tax is due. Expressed in Matthews’s preferred terms, this $1-wide bracket has a marginal rate of 815,306%.

Deductions and Credits

In his figure, Matthews reports that income above $0 and up to $18,550 has income tax applied at a rate of 10% and 12.2% for the current and proposed rates, but this is simply false because tax deductions and exemptions save the first portions of income from the federal income tax and from Sanders’s proposed Medicare-for-All tax (pdf, footnote 3). Matthews is using the 2016 tax brackets for married individuals who file a joint tax return. All married and jointly filing couples will be able to deduct at least $12,600, most would deduct $20,700 or more (those earning less than $311,000), and those with children would deduct even more. This means that the actual rate paid on at least the first $12,600 would be 0%.

Changing the figure label to “taxable income” would alleviate the deductions issue, but it would also widen the rift between the information presented and values actually applicable to readers. However, there would still remain the issue of tax credits. The Earned Income Tax credit ensures that couples with a taxable incomes below $20,330 (or $49,974 with 2 kids) pay lower tax rates than what is listed in Matthew’s charts, and the Child Tax Credit offsets rates even further and extends to incomes slightly above $100,000. All of my analyses include the exact amounts for standard deductions, personal exemptions, Earned Income Tax Credit, and Child Tax Credit that apply to each income level. Admittedly, these issues only have a significant impact on tax rates for the bottom 99% of Americans, but Matthews was more focused on rates for extremely high incomes. For these high incomes, however, Matthew’s rates are still overestimated due to the mathematical errors described in the next section.

Mathematical Errors

When determining tax rates for his analysis, Matthews has made the mistakes of adding incompatible percentages and ignoring effective income.

Consider a simplified example to illustrate the problem: a $10,000 income with a 10% income tax and a 10% payroll tax paid by the employer. In this example, the employee would pay $1,000 in income tax and take home $9,000. The employer would also pay $1,000. If you followed Matthews’s process, you would add the 10% income tax and 10% payroll tax to get a total rate of 20%. However, if we deduct that 20% rate from the $10,000 income, then we would expect a take-home pay of only $8,000. Since we already know that the take-home pay is actually $9,000, we know that Mathews’s math doesn’t add up.

To understand the mistake, one must consider how the taxes are applied. While income tax is taken out of the wages paid to an employee, the payroll taxes that employers pay are paid in addition to the total wages. In the above example, the employer would be paying a total effective income of $11,000 ($10,000 on-paper income paid to the employee and an additional $1,000 in payroll taxes paid). When including the effective income, we find that the true tax rates are lower that what Matthews’s method suggests. Each of the $1,000 taxes represents 9.09% of the $11,000 total, and the sum of these (18.18%) is the real tax rate. To check our math, we can deduct this 18.18% true rate from the $11,000 total, and we get $9,000, the correct amount for take-home pay.

The conversion from Matthews’s listed rates to the real tax rates is not complex, all rates must simply be divided by the sum of 1 plus the employer-paid rates. In the table below, I have applied this correction to all of the marginal income tax rates presented in the Vox article and also added in the FUTA tax that was missing. Bear in mind, however, that these rates still suffer from all of the other issues discussed in this article, and I do not consider them an accurate representation of current or proposed tax rates.





Taxable Income Above Tax Plan Real Marginal Rate Matthews’s Rate Size of Error $0 Current 27.5% 25.3% -2.2% Bernie 33.3% 34.1% 0.8% $18,550 Current 28.1% 30.3% 2.2% Bernie 34.2% 39.1% 4.9% $75,300 Current 37.4% 40.3% 2.9% Bernie 43.0% 49.1% 6.1% $118,500 Current 27.5% 27.9% 0.4% Bernie 33.7% 36.7% 3.0% $151,900 Current 30.5% 30.9% 0.4% Bernie 36.5% 39.7% 3.2% $231,450 Current 36.3% 35.9% -0.4% Bernie 42.0% 44.7% 2.7% Taxable Income Above Tax Plan Real Marginal Rate Matthews’s Rate Size of Error $250,000 Current 36.3% 36.8% 0.5% Bernie 54.1% 62.0% 7.9% $413,350 Current 38.2% 38.8% 0.6% Bernie 54.1% 62.0% 7.9% $466,950 Current 42.8% 43.4% 0.6% Bernie 54.1% 62.0% 7.9% $500,000 Current 42.8% 43.4% 0.6% Bernie 59.4% 68.0% 8.6% $2,000,000 Current 42.8% 43.4% 0.6% Bernie 63.8% 73.0% 9.2% $10,000,000 Current 42.8% 43.4% 0.6% Bernie 67.3% 77.0% 9.7%

The corrections show that Matthew’s calculations have overestimated the real marginal rates in Bernie Sanders’s plans for every single tax bracket. That overestimation was by 5 or more percentage points for two-thirds of brackets, and the largest error was with the highest tax bracket wherein the true rate was exaggerated by nearly 10 points.

The Real Top Marginal Rate

Even when granting the decision to pool employer and employee costs, his reporting of a top marginal rate of 77% has overestimated the real top marginal rates in Bernie Sanders’s tax plans by 9.7%

The table above corrected Matthews’s math, but those figures still suffer from the other issues discussed in this article:

Using misleading marginal rates instead of practical effective rates

Ignoring healthcare savings

Assuming employers can and will pass on 100% of savings or costs to employees

Skipping the backlog of social security tax for incomes over $250,000

Ignoring tax credits

While the above issues have major impact on tax bills and take home pay for Americans with incomes in the bottom 99%, they are less consequential for the ultimate discussion of the top marginal rates. To confirm the true top marginal rate with all factors included, I have run my effective tax engine with extraordinarily large income levels up to $10 Billion.

Before discussing the top rates, there are two other features of these tax systems worth noting in this chart. First is the absurd regressivity of the current system. When including both the employee and employer healthcare contributions for the average family, taxes and healthcare consume more than 50% of total compensation for employees with middle class incomes, and this amount far exceeds the share of income contributed by the wealthiest. Additionally, it is worth noting the social security backlog tax bump under Bernie’s proposed plans. When income crosses the $250,000 threshold and social security taxes kick back in, the combined employee and employer tax bill leaps by over $16,000 and causes a sharp spike the in the effective rate. Both of these are discussed in more detail in my previous post on Bernie Sanders’s Tax Plans.

In regards to the top marginal rates, the above plot reveals these as the points where the effective rates level off for the highest incomes. This occurs as the portion of income in the top bracket grows to dwarf all other income, and the effective rate becomes essentially identical to the top marginal rate. Therefore, the top marginal rate for the current system is shown to be 42.8%, and the top marginal rate under Bernie’s proposed plans is 67.3%. These match exactly my results in the previous section for the top marginal rates, confirming the accuracy of the findings despite being calculated through an entirely different process.

The issues I have described in this post detail how Dylan Matthews’s analysis has resulted in inaccurate figures being published in his Vox article. Even when granting the decision to pool employer and employee costs, his reporting of a top marginal rate of 77% has overestimated the real top marginal rates in Bernie Sanders’s tax plans by 9.7%.

Take Action

What do you think? Should we work together fix this system where middle and lower class families are contributing a larger share of their earnings than the wealthy? If so, join Bernie Sanders’s political revolution:

Disclosures: I am an active volunteer for the Sanders campaign, but this content is not supported nor endorsed by Bernie Sanders or his campaign.