Marginal vs. Effective Tax Rates

Last week Presidential candidate Mitt Romney released his tax returns, and the news channels were abuzz with commentary about his effective federal tax rate of 13.9% on $21.7M of income.  I will refrain from my own commentary on his situation, but what particularly piqued my interest were the quotes I heard from “ordinary” people on the radio.  Everyone, it seems, claims to pay a higher federal tax rate than Mr. Romney.  Typical was a person interviewed in a news report who stated “I pay 28% in taxes and have trouble every month making my rent.”

Listening to people comment on their own tax rates left me with two impressions.  I couldn’t help but feel that most, if not all, of the people I heard were severely overestimating their own effective federal tax rates, and I suspected that most people did not understand the difference between effective tax rate and marginal tax rate.  I also saw an opportunity to fire up Analytica to explore the relationship between the two concepts.

Before proceeding, I should disclaim that I am not an accountant or lawyer, or in any way certified to give tax advice.  Nothing I am discussing here should be construed as tax advice.  Yada yada yada.

Your effective tax rate is simply the amount of tax you pay divided by your total income.   Your marginal tax rate in percent is equal to the number of cents that your tax liability would decrease if your income decreased by one dollar.  The term tax bracket identifies your marginal rate.  If you are like most people who derive the bulk of their income from wages and earned income, the progressive structure of the US income tax rate results in your marginal tax rate being higher than your effective tax rate.

To explore these concepts, I created an index named Tax_bracket and an edit table titled “Lower taxable income in bracket” (with identifier Lower_taxable_income), and populated the edit table with 2011 income thresholds for a single filer:

Smallest taxable income in each tax bracket

For an arbitrary Taxable_income, the following Analytica expression looks up the applicable marginal tax rate from the table:


By defining Taxable_income as Sequence(0,$250K), we obtain a graph of marginal tax rates as a function of taxable income:


Marginal tax rate vs taxable income

To arrive at taxable income, you need to subtract your deductions from your net income and make numerous other adjustments that embody the complexity of the US tax code.  The average person with $100K of taxable income has a total income of around $125K.

Now, how do you go from here to effective tax rate?  This requires two steps.  First, you need to compute your tax liability (i.e., taxes paid), and then you need to divide by total income (rather than just by taxable income).  Given a particular taxable income, the tax liability is the area under the above curve falling to the left of your taxable income.  With Taxable_income defined as a sequence, we can compute income Tax_liability using:


I will ignore other non-earned sources of income (e.g., capital gains income) for simplicity, which would have to be added to this as well.  The second piece, relating total income and taxable income, is far more involved.  To avoid getting mired down in the complexities of deductions and tax code, I’ll simply use a quick and dirty approximation for an average:

Total_income = $5800 + 120% * Taxable_income

The $5800 is the standard deduction for a single filer in 2011, and the 120% comes from my quick-and-dirty assessment of the ratio of taxable to non-taxable income, with an assumption that this stays relatively constant over all income levels.   There are many articles on the web providing average deduction levels for US tax payers at different income levels.  I invite you to find those and compare how my quick and dirty approximation fares, or to simply compare to your own tax returns.   We are now in a position to compute Effective_tax_rate as:

Tax_liability / Total_income

To produce a nice graph comparing the two tax rates as a function of total income, I created a variable titled “Marginal vs. Effective” and defined it as a list:

[Marginal_tax_rate, Effective_tax_rate]

From its result view, I pressed the  [XY] button and added Total_income as a comparison variable

Dialog for selecting total income for comparison

Leaving us with this final graph

Marginal and Effective Tax rates

Recalling the person on the radio who claimed a 28% tax rate but could barely make his rent each month, this graph makes it evident that he was confusing his marginal (the red line) with his effective (blue line) tax rate.

When you engage in national debate about whether your taxes are too high, the effective tax rate is clearly the relevant number.   However, when you are considering tax consequences when making a personal decision, the marginal tax rate is the pertinent value.  Is the $20/hr pay for working an extra hour each week worth sacrificing your discretionary time?  If your marginal rate is 25%, you should yourself if your discretionary time is worth $15/hr.

I have made my Analytica model (Marginal vs Effective Tax Rates.ana) available, and I welcome you to continue this exploration further using this model as a starting point.  For example, you might explore how things change for people like Mitt Romney who derive most their income from capital gains and dividends.  To make changes of your own, you will need either a licensed version of Analytica Professional, Enterprise or Optimizer, or the Analytica Trial edition.

You can also view (but not change) the model without having to install Analytica using the Analytica Cloud Player at Marginal vs. Effective (on Cloud).

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    1. Right on see my Letter to Columbus Dispatch of two weeks ago. And see my comments on Blodget’s and Simon’s attempt to flummoxx the American People with the Old rate trick….. Folk’s it’s ‘dollars and cents’…. you can’t spend a rate, you don’t pay in ‘rates’… but you can spend and pay your taxes in ‘dollars and cents.’


      • Joseph has a good point that we always need to look out for as model builders. The metrics we use to depict a result can make a big difference to the insights we might gain from the analysis. Our metrics are often various ratios or percentages, and different ones often lead to different insights. One of the beauties of presenting a model, rather than presenting a simple written article, is that it can be quite easy to give the user several perspectives. There may be multiple insights to be gathered from different views.

        As you view the model that I shared above, I encourage you to look at the graph of “tax_liability” (vs. Total income) as well as the marginal vs. effective tax rates. Obviously, the point of my article was to clarify the difference between Marginal and Effective rates, so that is where the emphasis of the article is. But I certainly agree that it is a good idea to get a feel for the amount of taxes paid. The insight obtained from different metrics may relevant to different decisions.

        With the upcoming presidential election heating up, I repeatedly see the question raised who (i.e., which income levels) are paying or not paying their fair share of taxes? As analysts, we should ask whether “total taxes paid” or “effective tax rate” is the more informative measure? Joseph clearly believes that total taxes paid is the appropriate measure. I disagree — I think effective tax rate is a better measure. Let’s apply this to Mitt Romney to see why I say this.

        The following sentences contain the same information, but use different metrics:
        * Mitt Romney had an effective tax rate of 13.9% on $21.7M of income.
        * Mitt Romney paid $3M in taxes on $21.7M of income.
        * Mitt Romney took home $18.7M after taxes on a total income of $21.7M

        Each of these might lead to slightly different insight. But most likely, we’re going to compare this to others at different come levels. For example:
        * Jane had an effective tax rate of 18% on $75K of income
        * Jane paid $13.5K in taxes on $75K of income
        * Jane took home $61.5K after taxes on $75K of income

        When you try to compare these with the corresponding Romney income, the effective tax rate is very easy to compare. The 13.9% and 18% are in the same units, and hence are directly comparable. When we try to compare $13.5K to $3M and simultaneously compare $75K to $21.7M, it is like comparing apples to oranges. You almost need to take the ratio, which puts you right back to effective tax rate. Thus, because of the natural ability to compare, due to the use of the same units, effective tax rate is the better metric for this type of thing. One of the points of my article, however, is that it can be misleading if the consumer of this information confuses effective tax rate with marginal tax rate. The people I heard on the radio were incorrectly comparing Romney’s effective tax rate to their own marginal tax rate — once again, that is comparing apples to oranges.

        Anyway, thank you Joseph for the comment. Cheers!

    2. Ha! This has been bugging me greatly, and I’m glad you’ve made this chart to show it to people. I understood this intuitively, and would like to point out that one way to greatly reduce your taxable income is to make tax-deductible donations. These are not funds that stay in your accounts to be spent. These are no longer yours, and are used to benefit some cause that you feel is appropriate.

      Really, the greatest measure of equality in taxation like this is on retained income vs. tax liability. It come pretty close to matching the marginal rates (after deducting the standard deduction). I have no problem with Romney (or any wealthy person) paying an effective rate of 13% or so if their retained income is in line with it. After all, there were many years where my marginal rate would have been 25% if I hadn’t had the default deduction, and a few other deductions. It got adjusted to 15%, and the effective rate was lower still (because my retained income included those deductions!).

      It’s so important that statistics and data be identified and understood in political (and other) debate.

      • Good points. Effective tax rate uses total income in the denominator. What I called taxable income is essentially what you are calling retained income (to the resolution of this discussion), and it is a trivial matter to add a variable “tax_liability / taxable_income” to the model to view that. I don’t think accountants would not be termed “effective tax rate” any more. You might call this just “tax rate” (with no modifier).

        You might be right that this is a better metric to compare in the public debate. The potentially controversial part is whether all deductions should be removed from the denominator, or whether certain types of deductions (e.g., perceived “loopholes”) should be retained in the denominator.

        Thank you Joel for the feedback.

    3. Nothing to add to the comments except thank you for present a layman’s explanation on the topic.

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