Seeking comment on proposed revisions to Marginal Tax Rate and Traditional v. Roth wiki articles

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Re: Seeking comment on proposed revisions to Marginal Tax Rate and Traditional v. Roth wiki articles

Post by fyre4ce »

I'll weigh in here, hopefully doing more harm than good :-)

There are four tax rates that are being discussed. Putting the definitions aside for a moment, we can describe what they are, ordered in increasing size of the denominator.
  1. Actual tax rate on $1 (or $0.01) of increased income, as calculated by the IRS. Because the IRS rounds figures to the nearest dollar, a $1 increase in income will usually (spikes excepted) result in either a $0 (0%) or $1 (100%) increase in the tax owed, like the example of going from $19 to $20 of earned income. If calculating with $0.01's, the penny will result in either $0 (0%) or $1 (10,000%) increase in tax owed. If the tax tables are being used, they are quantized in $50 increments, so a $1 increase in income will cause either a $0 (0%), $5 (500%), $6 (600%), $11 (1,100%), or $12 (1,200%) increase in tax due. (Those figures correspond to the 10%, 12%, 22%, and 24% brackets respectively). Multiply those rates by 100 if you want to use pennies instead of dollars. These numbers are "exact" but there are reasons why they are not useful for making decisions. We usually can't control our annual income down to the $1 to $0.01 level, so we usually can't optimize around these small little jumps. It would also wreak havoc on any kind of optimization algorithm to try to evaluate behavior over such an un-smooth curve and needing to constantly round off numbers. The only time this calculation should be done is when actually preparing taxes. Otherwise, the actual rates on $1 or $0.01 are basically useless.
  2. Tax rate on a "small" increase in income, which in this context means a change large enough to smooth out rounding to the nearest dollar, and if applicable, tax table jumps. $100 is usually a convenient "small" increase in income, because it's an even multiple of the tax table increments (2 x $50), and it will give you a precision down to 1%, which is usually good enough for most purposes. If you increase income by $100, and 24 of those dollars cause your tax to jump by $1, and the other 76 cause no change in tax, that's a tax rate of 24%. This is a "smoothed" version of rate #1 on a small scale. This is also analogous to the "slope" or "derivative" of the curve at a particular point. Unlike tax rate #1, this value is very useful for making decisions. When you are dealing with progressive areas of the tax curve, the well-known simple algorithm is contributing to pre-tax accounts until your predicted #2 withdrawal tax rate equals or exceeds your current #2 tax rate, then contribute any remaining money to Roth. Dealing with a smoothed rate also has advantages for software, as values can be represented easily by floating point numbers, and can be operated on without regard to small rounding.
    • Tax rate on an entire incremental change in income. For example, if you get a $100,000 bonus at work, and owe $26,400 more in taxes, your #3 tax rate is 26.4%. This rate is also useful in several situations. When you're dealing with a chunk of income that can't be broken down into smaller pieces (like, getting a fixed-size bonus), then this is what you care about, more so than the #2 rate on the first bit or last bit of income, which may be very different. The #3 rate is usually a composite (weighted average) of the #2 rates over the various sections tax curve that this change spans. In this example, if $70,000 of the bonus was in the 24% bracket and $30,000 was in the 32% bracket, that would give $26,400 ($70k x 24% + $30k x 32%) change in tax and the 26.4% rate. If you were choosing to take the bonus on this year's or next year's tax return, the better choice is the one with the lower #3 rate. This #3 rate is also useful when making traditional/Roth decisions when the tax curve is not progressive and smooth. The more complex algorithm becomes: (a) calculate a #3 tax rate on all possible pre-tax contributions starting from $0, (b) find the point of maximum rate, (c) if this rate is greater than the predicted withdrawal #3 rate, then contribute pre-tax, go back to (a) and recalculate starting from this new point; if at any point the rate is less than the predicted withdrawal rate, contribute any remaining money to Roth. The wiki contains a worked example.
    • Tax rate on the entirety of one's income (total tax / total income). Many people misleadingly use this rate to try to make T vs R decisions; it's not directly useful for that purpose. It does have a few uses, however, such as tax-weighting asset allocations between pre-tax and Roth accounts. A pre-tax account can be thought of as two separate accounts: an account owned entirely by the government which you manage the investments for, and a Roth account that belongs completely to you. The size of the "government account" equals the predicted #4 tax rate times the total account balance. Eg. if you have a $1M pre-tax IRA and you expect a #4 tax rate of 16%, you can think of it as a $840,000 Roth account and rebalance accordingly.
    I don't think any of that should be controversial. What can be controversial is what to call these four values. Here are my thoughts on these:
    1. This tax rate isn't commonly used and doesn't have a common name. Maybe "exact marginal tax rate" or "exact rate on the next dollar" would be appropriate, but should be accompanied by a description to avoid confusion.
    2. This tax rate should be called the "marginal" tax rate. This is the generally accepted term used in economics, and is also the term used by the "Personal Finance Toolbox" aka Case Study Spreadsheet.
    3. To my knowledge there is no generally accepted definition for this tax rate. "Incremental", "cumulative", "cumulative marginal", or "average marginal" may be appropriate, but should be accompanied by a clear explanation to about confusion. The PFT/CSS calls this "cumulative", which I thought was good enough that this was the term I used in the T vs. R tool I'm working on. I suggest avoiding "marginal tax rate" for this rate, to prevent confusion with #2.
    4. "Average" tax rate is used commonly enough that I think it's okay for this purpose.
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    Re: Seeking comment on proposed revisions to Marginal Tax Rate and Traditional v. Roth wiki articles

    Post by Lee_WSP »

    fyre4ce wrote: Fri Jul 02, 2021 7:57 pm [*]Tax rate on an entire incremental change in income. For example, if you get a $100,000 bonus at work, and owe $26,400 more in taxes, your #3 tax rate is 26.4%. This rate is also useful in several situations. When you're dealing with a chunk of income that can't be broken down into smaller pieces (like, getting a fixed-size bonus), then this is what you care about, more so than the #2 rate on the first bit or last bit of income, which may be very different. The #3 rate is usually a composite (weighted average) of the #2 rates over the various sections tax curve that this change spans. In this example, if $70,000 of the bonus was in the 24% bracket and $30,000 was in the 32% bracket, that would give $26,400 ($70k x 24% + $30k x 32%) change in tax and the 26.4% rate. If you were choosing to take the bonus on this year's or next year's tax return, the better choice is the one with the lower #3 rate. This #3 rate is also useful when making traditional/Roth decisions when the tax curve is not progressive and smooth. The more complex algorithm becomes: (a) calculate a #3 tax rate on all possible pre-tax contributions starting from $0, (b) find the point of maximum rate, (c) if this rate is greater than the predicted withdrawal #3 rate, then contribute pre-tax, go back to (a) and recalculate starting from this new point; if at any point the rate is less than the predicted withdrawal rate, contribute any remaining money to Roth. The wiki contains a worked example.
    [*]Tax rate on the entirety of one's income (total tax / total income). Many people misleadingly use this rate to try to make T vs R decisions; it's not directly useful for that purpose. It does have a few uses, however, such as tax-weighting asset allocations between pre-tax and Roth accounts. A pre-tax account can be thought of as two separate accounts: an account owned entirely by the government which you manage the investments for, and a Roth account that belongs completely to you. The size of the "government account" equals the predicted #4 tax rate times the total account balance. Eg. if you have a $1M pre-tax IRA and you expect a #4 tax rate of 16%, you can think of it as a $840,000 Roth account and rebalance accordingly. [/list]

    I don't think any of that should be controversial. What can be controversial is what to call these four values. Here are my thoughts on these:
    I understand the #4 calculation, but I don’t understand how #3 is not #4 just calculated for every incremental dollar? Marginal total tax rate perhaps?

    I other words, the cumulative curve in the PFT charts has values for every dollar along the $100,000 bonus has an incremental total tax rate plotted, unless I’m confused as to how PFT calculates the cumulative curve.

    Let me try and go along with your example.

    Actually, looking further into it, are you sure that the cumulative value given by the PFT would be 26.4%? Wouldn’t it be the total tax paid divided by the total income at the 100k point, the 90k point, etc etc.
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    Re: Seeking comment on proposed revisions to Marginal Tax Rate and Traditional v. Roth wiki articles

    Post by FiveK »

    fyre4ce wrote: Fri Jul 02, 2021 7:57 pm There are four tax rates that are being discussed....
    Pretty much agree with the gist of all that.

    One can say the first three are all marginal tax rates, just with different sized denominators. Paraphrasing the old joke, we’ve already established that [it's a marginal tax rate]. Now we’re just haggling over the [denominator size].
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    Re: Seeking comment on proposed revisions to Marginal Tax Rate and Traditional v. Roth wiki articles

    Post by Lee_WSP »

    FiveK wrote: Fri Jul 02, 2021 10:44 pm
    fyre4ce wrote: Fri Jul 02, 2021 7:57 pm There are four tax rates that are being discussed....
    Pretty much agree with the gist of all that.

    One can say the first three are all marginal tax rates, just with different sized denominators. Paraphrasing the old joke, we’ve already established that [it's a marginal tax rate]. Now we’re just haggling over the [denominator size].
    Agreed. I think marginal total tax is the easiest to apply and gives the same results as either of the other marginal rates.
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    Re: Seeking comment on proposed revisions to Marginal Tax Rate and Traditional v. Roth wiki articles

    Post by FiveK »

    Lee_WSP wrote: Fri Jul 02, 2021 9:54 pm I other words, the cumulative curve in the PFT charts has values for every dollar along the $100,000 bonus has an incremental total tax rate plotted, unless I’m confused as to how PFT calculates the cumulative curve.
    The "marginal" curve is calculated by (change in tax)/(change in x-axis variable) for adjacent spreadsheet rows.

    The "cumulative" curve is calculated by (change in tax)/(change in x-axis variable) for the current row compared with the very first row (cells S84 and T84).

    The marginal and cumulative values are in cells S84:S583 and T84:T583 respectively.

    When evaluating things like "how much Roth conversion?" and "up to the top of the 12% bracket" seems obvious to do, but there is a question of how much more, the starting value for the cumulative curve should not be $0 but rather the amount that gets one to the top of the 12% bracket.
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    Re: Seeking comment on proposed revisions to Marginal Tax Rate and Traditional v. Roth wiki articles

    Post by Lee_WSP »

    FiveK wrote: Fri Jul 02, 2021 10:54 pm
    Lee_WSP wrote: Fri Jul 02, 2021 9:54 pm I other words, the cumulative curve in the PFT charts has values for every dollar along the $100,000 bonus has an incremental total tax rate plotted, unless I’m confused as to how PFT calculates the cumulative curve.
    The "marginal" curve is calculated by (change in tax)/(change in x-axis variable) for adjacent spreadsheet rows.

    The "cumulative" curve is calculated by (change in tax)/(change in x-axis variable) for the current row compared with the very first row (cells S84 and T84).

    The marginal and cumulative values are in cells S84:S583 and T84:T583 respectively.

    When evaluating things like "how much Roth conversion?" and "up to the top of the 12% bracket" seems obvious to do, but there is a question of how much more, the starting value for the cumulative curve should not be $0 but rather the amount that gets one to the top of the 12% bracket.
    What is the bolded part in formula format?
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    Re: Seeking comment on proposed revisions to Marginal Tax Rate and Traditional v. Roth wiki articles

    Post by fyre4ce »

    Lee_WSP wrote: Fri Jul 02, 2021 9:54 pm
    fyre4ce wrote: Fri Jul 02, 2021 7:57 pm <snip>
    I understand the #4 calculation, but I don’t understand how #3 is not #4 just calculated for every incremental dollar? Marginal total tax rate perhaps?

    I other words, the cumulative curve in the PFT charts has values for every dollar along the $100,000 bonus has an incremental total tax rate plotted, unless I’m confused as to how PFT calculates the cumulative curve.

    Let me try and go along with your example.

    Actually, looking further into it, are you sure that the cumulative value given by the PFT would be 26.4%? Wouldn’t it be the total tax paid divided by the total income at the 100k point, the 90k point, etc etc.
    I put the example into PFT. I entered MFJ filing status, and earned income of $259,850, placing taxable income $70k below the bottom of the 32% bracket. I set the chartmaker to "Total Tax Rate vs. tIRA withdrawal" as a way to show changes in tax for additional income (technically a bonus would get treated as earned income and so would have payroll taxes etc, but it illustrates the point). The result is:

    Chart pic

    "Marginal" and "Cumulative" rates are what I described as "#2" and "#3" respectively. Note that the tool calculates the "Cumulative" rate relative to the baseline of no withdrawals, so it's basically the average tax rate over a withdrawal of that specific size. It doesn't average over your entire income. You can also scroll down and look at the table that generates those values. The Cumulative rate is 26.4%:

    Table pic

    Hope that helps!
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    Re: Seeking comment on proposed revisions to Marginal Tax Rate and Traditional v. Roth wiki articles

    Post by fyre4ce »

    FiveK wrote: Fri Jul 02, 2021 10:44 pm
    fyre4ce wrote: Fri Jul 02, 2021 7:57 pm There are four tax rates that are being discussed....
    Pretty much agree with the gist of all that.

    One can say the first three are all marginal tax rates, just with different sized denominators. Paraphrasing the old joke, we’ve already established that [it's a marginal tax rate]. Now we’re just haggling over the [denominator size].
    Haha, I got a kick out of that :D I would extend your joke to include #4 though, because again, it's still a tax rate, just on a bigger interval. It's "marginal" relative to a baseline of not earning any income.

    What you say isn't wrong, but it is important to remember that the marginal rate over a "small" interval (#2 in my list) has special status because it's useful in certain specific ways, much like in math how (change in Y) / (change in X) has a special name, symbol, etc when the limit of (change in X) -> 0 ("derivative"). You can calculate the slope of a tax curve or mathematical function over any interval you want, of course, and sometimes that's part of the process for solving some problems. But, if you do that, you need to be clear about what you're doing and explicitly state what interval you're using. If you say "marginal rate" without any qualifications, many people will assume you mean a "small" interval because that's how the term is most commonly used. Saying something like "marginal rate over the entire traditional contribution" should make it clear to most, although "average rate over the entire traditional contribution" or "cumulative rate over the entire traditional contribution"" might be a bit clearer.

    The two numbers are mathematically related. switching into PFT terminology... The Cumulative rate over an interval is equal to [ (area under the Marginal rate curve over that interval) + (any tax spikes/cliffs in the interval) ] / (size of interval). That's the more technical way to calculate the 26.4% in my simple example with Lee.
    Last edited by fyre4ce on Fri Jul 02, 2021 11:29 pm, edited 1 time in total.
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    Re: Seeking comment on proposed revisions to Marginal Tax Rate and Traditional v. Roth wiki articles

    Post by Lee_WSP »

    What happens if you set the range from 0-500k of income?

    I'd do it myself, but still don't understand the worksheet yet.
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    Re: Seeking comment on proposed revisions to Marginal Tax Rate and Traditional v. Roth wiki articles

    Post by FiveK »

    Lee_WSP wrote: Fri Jul 02, 2021 10:56 pm
    FiveK wrote: Fri Jul 02, 2021 10:54 pm The "cumulative" curve is calculated by (change in tax)/(change in x-axis variable) for the current row compared with the very first row (cells S84 and T84).
    What is the bolded part in formula format?
    Examples below from cells S90 and T90. Column Q is the tax corresponding to the conversion amount in column O. Column S is "marginal" and column T is "cumulative".

    S90 formula: =(Q91-Q90)/(O91-O90)

    T90 formula: =(Q91-$Q$84)/(O91-$O$84)
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    Re: Seeking comment on proposed revisions to Marginal Tax Rate and Traditional v. Roth wiki articles

    Post by fyre4ce »

    Lee_WSP wrote: Fri Jul 02, 2021 11:29 pm What happens if you set the range from 0-500k of income?

    I'd do it myself, but still don't understand the worksheet yet.
    You get this chart. You can clearly see the 32%, 35%, and 37% bracket boundaries. The cumulative taxes are still calculated relative to a baseline of 0 additional income.

    I'd encourage you to play around with the PFT when you have time. It's really useful and has a quick learning curve. Not necessarily for all the features, but the tax estimation and chart-maker is really easy - I was able to figure it out :-D
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    Re: Seeking comment on proposed revisions to Marginal Tax Rate and Traditional v. Roth wiki articles

    Post by FiveK »

    fyre4ce wrote: Fri Jul 02, 2021 11:28 pm
    FiveK wrote: Fri Jul 02, 2021 10:44 pm
    fyre4ce wrote: Fri Jul 02, 2021 7:57 pm There are four tax rates that are being discussed....
    Pretty much agree with the gist of all that.

    One can say the first three are all marginal tax rates, just with different sized denominators. Paraphrasing the old joke, we’ve already established that [it's a marginal tax rate]. Now we’re just haggling over the [denominator size].
    Haha, I got a kick out of that :D I would extend your joke to include #4 though, because again, it's still a tax rate, just on a bigger interval. It's "marginal" relative to a baseline of not earning any income.
    The issue with #4 is that the effective rate on all income can include income other than the Roth conversion (or whatever income/deduction one is considering). I know you understand the difference, but "way back when..." there were some big squabbles over whether "effective" or "marginal" was the correct withdrawal tax rate to use for comparison.

    See Roth vs Traditional 401K - earliest Bogleheads thread (at least I think that is the earliest). One might think that debate would have been long settled, but as the first reply in the Estimating withdrawal tax rates thread notes, "We regularly need to debunk the idea that your expected effective tax rate in retirement has any relevance to this decision, and the longer we need to make the explanation for what do do instead, the less likely it will sink in."
    What you say isn't wrong, but it is important to remember that the marginal rate over a "small" interval (#2 in my list) has special status because it's useful in certain specific ways, much like in math how (change in Y) / (change in X) has a special name, symbol, etc when the limit of (change in X) -> 0 ("derivative"). You can calculate the slope of a tax curve or mathematical function over any interval you want, of course, and sometimes that's part of the process for solving some problems. But, if you do that, you need to be clear about what you're doing and explicitly state what interval you're using. If you say "marginal rate" without any qualifications, many people will assume you mean a "small" interval because that's how the term is most commonly used. Saying something like "marginal rate over the entire traditional contribution" should make it clear to most, although "average rate over the entire traditional contribution" or "cumulative rate over the entire traditional contribution"" might be a bit clearer.
    It may be that those who have taken calculus "know too much". ;) The Comparison of difference vs. derivative section of the marginal rate wiki discusses this.
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    Re: Seeking comment on proposed revisions to Marginal Tax Rate and Traditional v. Roth wiki articles

    Post by FiveK »

    fyre4ce wrote: Fri Jul 02, 2021 11:34 pm I'd encourage you to play around with the PFT when you have time. It's really useful and has a quick learning curve.
    +1

    Might be old-fashioned, but reading the first ~30 rows of the Instructions tab can be useful. See also the Using a spreadsheet section of the Roth IRA conversion wiki for some relevant screenshots of where inputs go. To get the $500K chart in his post, one could guess fyre4ce changed cell P83 (where "170" appears in the wiki screenshot) to 1000.
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    Proposed Change to Marginal Tax Rate Page

    Post by Lee_WSP »

    Additional proposed change to Marginal Tax Rate Page.

    IMO, the wiki for "marginal tax rate" (https://www.bogleheads.org/wiki/Marginal_tax_rate) is incorrectly defining or using the word marginal as it is used in economics. The word marginal refers to the last unit of measure. When referring to taxes, we usually mean the last dollar, but maybe not. Maybe the unit of measure is $10,000 dollars or up to the next bracket (ie $15,236).
    the marginal rate is often described as the tax rate on the "next dollar" or "last dollar" of income
    can be changed to:
    the marginal rate is often described as the tax rate on the "unit of dollars" or "last dollar(s)" of income
    I'm not dead set on anything other than emphasizing that the marginal rate is not on the last dollar, but on the last unit of measurement, which is usually not a single dollar.

    edit:
    I'm fairly certain the proposed change only adds flexibility and takes away nothing. But if you disagree, please present some counterexamples and I'll see if I can work through them.
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    Re: Proposed Change to Marginal Tax Rate Page

    Post by FiveK »

    Lee_WSP wrote: Sat Jul 31, 2021 3:15 pm I'm not dead set on anything other than emphasizing that the marginal rate is not on the last dollar, but on the last unit of measurement, which is usually not a single dollar.
    No objection to that. :)
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    Re: Proposed Change to Marginal Tax Rate Page

    Post by fyre4ce »

    :confused
    Lee_WSP wrote: Sat Jul 31, 2021 3:15 pm Additional proposed change to Marginal Tax Rate Page.

    IMO, the wiki for "marginal tax rate" (https://www.bogleheads.org/wiki/Marginal_tax_rate) is incorrectly defining or using the word marginal as it is used in economics. The word marginal refers to the last unit of measure. When referring to taxes, we usually mean the last dollar, but maybe not. Maybe the unit of measure is $10,000 dollars or up to the next bracket (ie $15,236).
    the marginal rate is often described as the tax rate on the "next dollar" or "last dollar" of income
    can be changed to:
    the marginal rate is often described as the tax rate on the "unit of dollars" or "last dollar(s)" of income
    I'm not dead set on anything other than emphasizing that the marginal rate is not on the last dollar, but on the last unit of measurement, which is usually not a single dollar.

    edit:
    I'm fairly certain the proposed change only adds flexibility and takes away nothing. But if you disagree, please present some counterexamples and I'll see if I can work through them.
    That’s not consistent with the way the term is generally used in economics, which implies a “small” change. In this context, small means large enough to smooth out rounding and tax rate table quanta, but no bigger.

    Of course, you are free to calculate a tax rate over whatever interval you want. In some cases it’s more useful to use a wider interval. But, there will still be a number that reflects the “small interval” rate (possibly the same number as the wider interval number). The name commonly used in economics is “marginal”. The PFT uses the term “cumulative” for larger intervals pand I like that because it indicates that it’s a composite of the marginal rates, along with any spikes/cliffs, over that interval. If you say “marginal rate over the next $12,000” most people will know what you mean, but why cause confusion? I recommend the page stays as is.
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    Re: Proposed Change to Marginal Tax Rate Page

    Post by Lee_WSP »

    fyre4ce wrote: Sat Jul 31, 2021 9:17 pm :confused
    Lee_WSP wrote: Sat Jul 31, 2021 3:15 pm Additional proposed change to Marginal Tax Rate Page.

    IMO, the wiki for "marginal tax rate" (https://www.bogleheads.org/wiki/Marginal_tax_rate) is incorrectly defining or using the word marginal as it is used in economics. The word marginal refers to the last unit of measure. When referring to taxes, we usually mean the last dollar, but maybe not. Maybe the unit of measure is $10,000 dollars or up to the next bracket (ie $15,236).
    the marginal rate is often described as the tax rate on the "next dollar" or "last dollar" of income
    can be changed to:
    the marginal rate is often described as the tax rate on the "unit of dollars" or "last dollar(s)" of income
    I'm not dead set on anything other than emphasizing that the marginal rate is not on the last dollar, but on the last unit of measurement, which is usually not a single dollar.

    edit:
    I'm fairly certain the proposed change only adds flexibility and takes away nothing. But if you disagree, please present some counterexamples and I'll see if I can work through them.
    That’s not consistent with the way the term is generally used in economics, which implies a “small” change. In this context, small means large enough to smooth out rounding and tax rate table quanta, but no bigger.
    I disagree.

    As do all the top results in Google for Marginal rate economics

    https://www.tutor2u.net/economics/refer ... -economics

    https://www.investopedia.com/terms/m/ma ... alysis.asp

    https://en.m.wikipedia.org/wiki/Margin_(economics)

    https://www.economicsonline.co.uk/Defin ... _cost.html

    Even this one which uses the small definition switches to an additional unit.

    https://study.com/academy/lesson/margin ... mples.html
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    Re: Proposed Change to Marginal Tax Rate Page

    Post by fyre4ce »

    Lee_WSP wrote: Sat Jul 31, 2021 9:45 pm <snip>

    I disagree.

    As do all the top results in Google for Marginal rate economics

    https://www.tutor2u.net/economics/refer ... -economics

    https://www.investopedia.com/terms/m/ma ... alysis.asp

    https://en.m.wikipedia.org/wiki/Margin_(economics)

    https://www.economicsonline.co.uk/Defin ... _cost.html

    Even this one which uses the small definition switches to an additional unit.

    https://study.com/academy/lesson/margin ... mples.html
    My college economics textbook explicitly defines marginal as "small" here, here, and here.

    But aside from that, all those resources actually support this "small" definition. They all refer to "one additional unit", the implication being that's the smallest change that is still meaningful to analyze. If your factory makes widgets, you can't sell less than one widget, so your marginal cost of production is the cost of making one additional widget - it doesn't matter whether that widget is a 1 cent capacitor or a $100M communications satellite. The last link didn't "switch" between definitions, it applied the universal "small" definition to the context of production of discrete goods, in which case "small" refers to a single unit.

    The "small" definition is contextual. When it comes to tax rates, money is quantized into cents or dollars, but for the reasons I described above, in an earlier post, it is not meaningful or useful to calculate tax rates on this scale. An interval of $100 smooths out rounding and gets you a tax rate accurate to the nearest 1%. So, this is what would be meant when someone says their "marginal tax rate is x%". You can use bigger intervals if you need more precision, but you also increase the risk of crossing into a zone of the curve with a different marginal rate. If the IRS someday changes their tax computations down to the penny, rather than rounded to the nearest dollar, and does away with the tax tables, then using $1 could become reasonable.

    In both business and tax rates, it may make sense to use a larger interval for some purpose. To be crystal clear, I'm not saying it never makes sense to (say) calculate the tax rate on $12,000 of add'l income, nor the production cost for an add'l 50,000 capacitors or 20 satellites. In fact, my T vs. R tool uses rates on an entire contribution, rather than marginal rates, under the hood. But when you are choosing this larger interval, it's better to use another term besides "marginal" to avoid confusion. As I said, if you specify the interval (eg. "marginal tax rate on $12,000 of add'l income") most people will understand what you mean, though a few may wonder whether you meant the marginal rate on the last dollar of that $12,000, as opposed to the entire $12,000. That's why I favor "cumulative" in this context, which is also exactly the same terminology used by the PFT.

    When the term "marginal tax rate" is used without any indication of interval size, there is no doubt this refers to a "small" change in income, and this is the way we should use the term.
    Last edited by fyre4ce on Sat Jul 31, 2021 10:30 pm, edited 1 time in total.
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    Re: Proposed Change to Marginal Tax Rate Page

    Post by Lee_WSP »

    fyre4ce wrote: Sat Jul 31, 2021 10:27 pm
    Lee_WSP wrote: Sat Jul 31, 2021 9:45 pm <snip>

    I disagree.

    As do all the top results in Google for Marginal rate economics

    https://www.tutor2u.net/economics/refer ... -economics

    https://www.investopedia.com/terms/m/ma ... alysis.asp

    https://en.m.wikipedia.org/wiki/Margin_(economics)

    https://www.economicsonline.co.uk/Defin ... _cost.html

    Even this one which uses the small definition switches to an additional unit.

    https://study.com/academy/lesson/margin ... mples.html
    My college economics textbook explicitly defines marginal as "small" here, here, and here.

    But aside from that, all those resources actually support this "small" definition. They all refer to "one additional unit", the implication being that's the smallest change that is still meaningful to analyze. If your factory makes widgets, you can't sell less than one widget, so your marginal cost of production is the cost of making one additional widget - it doesn't matter whether that widget is a 1 cent capacitor or a $100M communications satellite. The last link didn't "switch" between definitions, it applied the universal "small" definition to the context of production of discrete goods, in which case "small" refers to a single unit.

    The "small" definition is contextual. When it comes to tax rates, money is quantized into cents or dollars, but for the reasons I described above, in an earlier post, it is not meaningful or useful to calculate tax rates on this scale. An interval of $100 smooths out rounding and gets you a tax rate accurate to the nearest 1%. You can use bigger intervals if you need more precision. So, this is what would be meant when someone says their "marginal tax rate is x%".

    In both business and tax rates, it may make sense to use a larger interval for some purpose. To be crystal clear, I'm not saying it never makes sense to (say) calculate the tax rate on $12,000 of add'l income, nor the production cost for an add'l 50,000 capacitors or 20 satellites. In fact, my T vs. R tool uses rates on an entire contribution, rather than marginal rates, under the hood. But when you are choosing this larger interval, it's better to use another term besides "marginal" to avoid confusion. As I said, if you specify the interval (eg. "marginal tax rate on $12,000 of add'l income") most people will understand what you mean, though a few may wonder whether you meant the marginal rate on the last dollar of that $12,000, as opposed to the entire $12,000. That's why I favor "cumulative" in this context, which is also exactly the same terminology used by the PFT.

    When the term "marginal tax rate" is used without any indication of interval size, there is no doubt this refers to a "small" change in income, and this is the way we should use the term.
    None of that is inconsistent with using the word unit and not necessarily limiting it to one dollar.
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    Re: Proposed Change to Marginal Tax Rate Page

    Post by Lee_WSP »

    fyre4ce wrote: Sat Jul 31, 2021 10:27 pm
    Lee_WSP wrote: Sat Jul 31, 2021 9:45 pm <snip>

    I disagree.

    As do all the top results in Google for Marginal rate economics

    https://www.tutor2u.net/economics/refer ... -economics

    https://www.investopedia.com/terms/m/ma ... alysis.asp

    https://en.m.wikipedia.org/wiki/Margin_(economics)

    https://www.economicsonline.co.uk/Defin ... _cost.html

    Even this one which uses the small definition switches to an additional unit.

    https://study.com/academy/lesson/margin ... mples.html
    My college economics textbook explicitly defines marginal as "small" here, here, and here.
    The textbook does not actually support your position. The formula is Delta of good. Delta means "change in". The change could be one good or ten goods. Further the second two pages make absolutely no mention of "small".

    Furthermore, a small change in income could be fifty thousand dollars, five dollars, or half a million dollars, it's all relative.
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    Re: Proposed Change to Marginal Tax Rate Page

    Post by fyre4ce »

    Lee_WSP wrote: Sat Jul 31, 2021 10:29 pm None of that is inconsistent with using the word unit and not necessarily limiting it to one dollar.
    "Unit" means that it can't be meaningfully divided further. It's another way of saying "small." One widget is the smallest amount of additional production a factory can produce. One third of a [capacitor, car, satellite] doesn't make sense to consider. The $100 of add'l income to calculate a marginal tax rate can't be divided further without introducing rounding errors. $12,000 can be meaningfully divided further, and for many taxpayers this amount of income will span multiple zones of tax with different marginal rates.

    Calling a marginal rate on the "last dollar" is technically inaccurate due to rounding, as I have admitted many times, but nonetheless instructive, which is why it's given by all of the top five Google search results for that term (here, here, here, here, here).
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    Re: Proposed Change to Marginal Tax Rate Page

    Post by Lee_WSP »

    fyre4ce wrote: Sat Jul 31, 2021 10:45 pm
    Lee_WSP wrote: Sat Jul 31, 2021 10:29 pm None of that is inconsistent with using the word unit and not necessarily limiting it to one dollar.
    "Unit" means that it can't be meaningfully divided further. It's another way of saying "small." One widget is the smallest amount of additional production a factory can produce. One third of a [capacitor, car, satellite] doesn't make sense to consider. The $100 of add'l income to calculate a marginal tax rate can't be divided further without introducing rounding errors. $12,000 can be meaningfully divided further, and for many taxpayers this amount of income will span multiple zones of tax with different marginal rates.

    Calling a marginal rate on the "last dollar" is technically inaccurate due to rounding, as I have admitted many times, but nonetheless instructive, which is why it's given by all of the top five Google search results for that term (here, here, here, here, here).
    Yes, but it doesn't have to be a single dollar.

    https://www.taxpolicycenter.org/briefin ... -tax-rates

    https://www.cbo.gov/topics/taxes/tax-rates

    https://www.irs.gov/newsroom/irs-provid ... -year-2021

    https://en.m.wikipedia.org/wiki/Tax_rate
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    Re: Proposed Change to Marginal Tax Rate Page

    Post by fyre4ce »

    Lee_WSP wrote: Sat Jul 31, 2021 10:39 pm The textbook does not actually support your position. The formula is Delta of good. Delta means "change in". The change could be one good or ten goods. Further the second two pages make absolutely no mention of "small".

    Furthermore, a small change in income could be fifty thousand dollars, five dollars, or half a million dollars, it's all relative.
    All three of those pages have the word "small" in the accompanying text. The proper way to indicate a small change with the math symbols is to use a d instead of an upper-case Delta, but this was not a calculus-based class so they did not apply calculus notation. Notice, in that third page they actually took the derivative of f(x)=x^2 but avoided using the "proper" calculus notation of a limit and d/dx. But, there is no ambiguity that they are talking about small changes there.

    "Small" is indeed relative, but not in the way you describe. $1,000 may be a "small" amount of money to some forum members in a way it's not to me. It doesn't mean in a personal sense, it means in an analytic sense - does it make sense to divide this quantum of [whatever] further? When tax rates are considered, the answer becomes "no" at $100 most of the time, irrespective of one's income or personal utility for more money.
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    Re: Proposed Change to Marginal Tax Rate Page

    Post by Lee_WSP »

    fyre4ce wrote: Sat Jul 31, 2021 11:01 pm
    Lee_WSP wrote: Sat Jul 31, 2021 10:39 pm The textbook does not actually support your position. The formula is Delta of good. Delta means "change in". The change could be one good or ten goods. Further the second two pages make absolutely no mention of "small".

    Furthermore, a small change in income could be fifty thousand dollars, five dollars, or half a million dollars, it's all relative.
    All three of those pages have the word "small" in the accompanying text. The proper way to indicate a small change with the math symbols is to use a d instead of an upper-case Delta, but this was not a calculus-based class so they did not apply calculus notation. Notice, in that third page they actually took the derivative of f(x)=x^2 but avoided using the "proper" calculus notation of a limit and d/dx. But, there is no ambiguity that they are talking about small changes there.

    "Small" is indeed relative, but not in the way you describe. $1,000 may be a "small" amount of money to some forum members in a way it's not to me. It doesn't mean in a personal sense, it means in an analytic sense - does it make sense to divide this quantum of [whatever] further? When tax rates are considered, the answer becomes "no" at $100 most of the time, irrespective of one's income or personal utility for more money.
    Put it to a vote. I do not seek to convince you. Words mean what everyone thinks they mean. The wiki should reflect the majority opinion.
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    Re: Proposed Change to Marginal Tax Rate Page

    Post by fyre4ce »

    Again, small is not the same as single dollar. Small is the most common definition.

    Of the four additional links you provided, #2 actually does explicitly say "small." #3 and #4 don't say "small", but they are talking about tax brackets, so the implication is that the change is small enough to be contained entirely within a bracket - it wouldn't make sense otherwise.

    Along similar lines, the first link suggests a $10,000 change, and then gives a $1,530 change (15.3%) and $1,500 change (15%) in payroll and income tax respectively. Those are both entirely within a "bracket" and are therefore implied to be small. For sure, those rates wouldn't apply to, say, a $500k increase in income. So while they are not being perfectly precise with their terminology, they are able to get away with it by still looking at a change with a constant marginal rate.

    None of these sources say, or imply, that the term should be applied to any arbitrarily large amount of money.
    Lee_WSP wrote: Sat Jul 31, 2021 11:04 pm Put it to a vote. I do not seek to convince you. Words mean what everyone thinks they mean. The wiki should reflect the majority opinion.
    This is sort-of correct. As far as I can tell, the substance of the page isn't in dispute at all. The only question is, what is the definition of the term "marginal"? Marginal is a term of art that has a specific meaning we need to adhere to. The top five Google pages, a relevant textbook, my formal training, and the often-used PFT all explicitly support a "small" definition, and the latter even uses a different term for what you're describing. The links you provided are more ambiguous but are still consistent with this interpretation. Unless I've missed something here, I don't think there's much doubt about how the term is used out in the world. The wiki (really, any published work) needs to stick to the terms and definitions that are generally accepted in that field. Even if we, the editors, feel that the existing terms are inconvenient/misleading/whatever, it will cause more confusion for readers to use non-standard terminology.

    So about your vote proposal - if we are voting on the point of fact of how the term is most commonly used in relevant publications, sure. If you want to vote about whether we should adhere to this definition, or make up our own, that's more an editorial issue that I do not think should be put up to a vote. In forum posts, a personal blog, etc maybe that would be appropriate.
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    Re: Seeking comment on proposed revisions to Marginal Tax Rate and Traditional v. Roth wiki articles

    Post by Lee_WSP »

    I don't care if you use the word small. Just get rid of the notion that it only refers to the last dollar.

    Put another way. The last dollar is not the only way to measure marginal tax rate.

    I used a search in page and did not find small on the cbo page, BTW. I also cannot find it. Some help please.
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    Re: Seeking comment on proposed revisions to Marginal Tax Rate and Traditional v. Roth wiki articles

    Post by fyre4ce »

    Lee_WSP wrote: Sun Aug 01, 2021 12:16 am I don't care if you use the word small. Just get rid of the notion that it only refers to the last dollar.

    Put another way. The last dollar is not the only way to measure marginal tax rate.

    I used a search in page and did not find small on the cbo page, BTW. I also cannot find it. Some help please.
    When I check this link I see:
    The effective marginal tax rate for individuals is the percentage of an additional dollar of earnings that is unavailable because it is paid in taxes or offset by reduced benefits from government programs. [emphasis added]
    They are using "additional dollar" as a stand-in for "small." May I make a suggestion? I think it would be worth reviewing my earlier post on tax rates where I drop the definitions to avoid any confusion, and just refer to tax rates with numbers. I just want to make sure we're not talking past each other. There is no doubt that the "next/last dollar" terms are commonly used, but is technically inaccurate for the reasons I gave. But, the wiki tip-toes around this by saying...
    To emphasize the "change" calculation, the marginal rate is often described as the tax rate on the "next dollar" or "last dollar" of income.
    ...and then goes on to describe rounding errors. As-written, I think the current page is both technically correct and also instructional with respect to a "last dollar" / "small" distinction.

    If you're more concerned about applying the term "marginal" to arbitrarily large changes in income (#3 in my earlier post), that's a bit different. Again, most people will know what you mean if you say "marginal tax rate on $500,000 of additional income", but this is not the way the term is most commonly used. It definitely goes against the "small" and "next/last dollar" definitions, which are overwhelmingly the most common. It also causes a conflict, because each of those dollars (or $100 increments if accounting for rounding) has its own marginal rate, and using "marginal" to refer to the rate on each $1/$100 within that interval, and also the rate on the whole interval, is confusing. It's better to use a different term; PFT uses "cumulative" and that's as good as any other suggestion I found, so that's what I tend to use.
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    Re: Seeking comment on proposed revisions to Marginal Tax Rate and Traditional v. Roth wiki articles

    Post by Lee_WSP »

    All three definitions are used to define the concept. Usually when you are describing the concept you start with one more candy bar or some such.

    You can even use all three

    It's the small additional cost of producing one additional unit.

    The problem I have with the current definition is that it's too narrow. One additional unit need not me just one dollar. One small measure need not be one dollar.

    edit
    The problem is that when we tell someone to look at the marginal tax rate today vs tomorrow, and then they go read the wiki because they don’t have a good understanding of the term marginal, they get confused. Such that I’ve started telling them to compare the tax rate if they do the conversion vs the tax rate if they don’t. I should just be able to say look at the marginal rate on the conversion vs the marginal rate if you do nothing.
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    Re: Seeking comment on proposed revisions to Marginal Tax Rate and Traditional v. Roth wiki articles

    Post by trueblueky »

    For someone using the IRS Tax Tables, $100 is the smallest useful unit in many cases. For those above the tax tables, $1 works.

    For some cliffs in the tax law, e.g., IRMAA, the concern is the cliff. $1 additional income can lower spendable income by hundreds of dollars.

    What is the marginal rate on reaching IRMAA? Does it matter? It costs $59.40/month whether you measure the marginal rate over $1 or $100. If you are unfortunate enough to reach that while MFS, the single dollar over the MAGI limit costs $326.70/month.

    All that to say, there is no perfect way to describe "marginal" with our discontinuous tax law.
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    Re: Seeking comment on proposed revisions to Marginal Tax Rate and Traditional v. Roth wiki articles

    Post by Lee_WSP »

    trueblueky wrote: Sun Aug 01, 2021 11:46 am All that to say, there is no perfect way to describe "marginal" with our discontinuous tax law.
    Agreed, but the better way is to describe it as one additional unit of measured income, which allows the user to define the measured unit as $100 or up the the IRMAA cliff or whatever the person is measuring.
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    Re: Seeking comment on proposed revisions to Marginal Tax Rate and Traditional v. Roth wiki articles

    Post by FiveK »

    Back to the t vs. R article, it’s past time to include the “more complicated situation” of invested RMDs discussed in Why Roth conversions always pay off—if you can hold on long enough and How do RMDs affect Roth conversion choices? so I’ll do that.

    While there, a few other edits seem appropriate, including
    - Outline the “more complicated situations” section to make it easier to reference in forum discussions.
    - Maintain the introductory focus on “understanding one’s current and expected future marginal rates” as the suggested way to make the t vs. R choice and defer most “rules of thumb” to a later section.
    - Provide a “simplest” estimate approach for future income from traditional accounts, in addition to the more complicated approach currently described.

    Any other philosophical (or tactical) suggestions?
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    Re: Seeking comment on proposed revisions to Marginal Tax Rate and Traditional v. Roth wiki articles

    Post by FiveK »

    FiveK wrote: Thu Jul 28, 2022 3:42 pm Back to the t vs. R article, it’s past time to....
    Done. Well, not that it's ever "done".... ;)

    Main intent is to simplify things as much as practical for the "getting started ordinary investor" by putting simpler concepts up front. The overall article may still be too complicated, but the more complex parts do have their place, and if we can tell the new folks "just read ____ for now" that should be useful.
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    Re: Seeking comment on proposed revisions to Marginal Tax Rate and Traditional v. Roth wiki articles

    Post by fyre4ce »

    FiveK wrote: Thu Jul 28, 2022 3:42 pm Back to the t vs. R article, it’s past time to include the “more complicated situation” of invested RMDs discussed in Why Roth conversions always pay off—if you can hold on long enough and How do RMDs affect Roth conversion choices? so I’ll do that.

    While there, a few other edits seem appropriate, including
    - Outline the “more complicated situations” section to make it easier to reference in forum discussions.
    - Maintain the introductory focus on “understanding one’s current and expected future marginal rates” as the suggested way to make the t vs. R choice and defer most “rules of thumb” to a later section.
    - Provide a “simplest” estimate approach for future income from traditional accounts, in addition to the more complicated approach currently described.

    Any other philosophical (or tactical) suggestions?
    A few comments on these changes:

    1) The wiki already has a formula for the performance of a taxable account (here and the break-even rate for maxing out here, with derivations for both, and already in pretty-print on the wiki. I checked the formula you reference here, and found one mistake: the value for f is given as T2 * g/e when I believe it should be T2 * (1 - d/i) / (1 - (d/i) * T2). But, in that example you arrive at the correct value for f which gives the correct break-even rate. In any case, I slightly prefer the formulas already on the wiki, both because they're already there with derivations, and also because they calculate the basis explicitly, and then apply the actual capital gains tax rate; the equations you reference calculate an effective capital gains rate to correct for basis growth, but don't give the correct basis, which could be useful. I think we should pick one formula and use it consistently.

    That said, I think it's great to add the concept that [T vs R when not contributing the max] is analogous to [Roth conversions when paying the tax from the conversion] and [T vs R when contributing the max] is analogous to [Roth conversions when paying the tax from taxable assets] and this definitely deserves mention. Probably the same for Roth conversions that would reduce RMDs that would be reinvested in a taxable account. But, whether to Roth convert is a separate (albeit closely related) topic to T vs R contributions, and that topic already has its own wiki page. The T vs R page is already very long (and getting even longer) and I caution that we add more material that would better go elsewhere. I suggest only brief mentions of conversion-specific topics and follow them with links to the conversion page. Also, the bulk of this discussion should go in the "Maxing out retirement accounts" section further down the page, and keep the material in that "Calculations" section to a couple lines or so, with a link to the lower section. Keep in mind, by this point in the page, readers haven't even had current and future marginal rates explained.

    2) Last revision, feedback was positive on having the "typical cases" toward the top of the wiki; lots of reviewers said it made the page more accessible to readers who didn't want to wade into the more dense math. I agree that simpler concepts should be up front, but the typical cases is a simple concept, no? Readers who don't want to deal with any numbers can match their situation to one of the ~10 common cases and decide which is best. But that section has been removed completely, and I worry we cut out the part most likely to help readers who don't want to do any math. Why do you think this will help make the page more accessible? A change like this is large enough to deserve a separate discussion/forum poll on the question, in my opinion.

    3) While I like the idea of adding simplified content to help more novice readers, I worry that the added "Simple method" in "Estimating future marginal tax rate" section made things worse, and I'll explain why. Let's back up and think about this problem from first principles. The goal should be to maximize the amount of spendable income in retirement, and our range of control to meet this goal is some split of T/R contributions each year we're working. The lower bound on our future pre-tax balance is FV(r, 0, -[current balance]) = [current balance] * (1 + r)^t (ignoring conversions, which should be discussed separately) and the upper bound is FV(r, [maximum annual contribution], -[current balance]). (I know from prior discussions you don't like including future contributions in estimates for conservatism, but let's put that aside for now; we both agree if those contributions get made then the larger future balance will result.) If we made a plot of future spendable income vs. this maximum range of choices, and then the global maximum would be the optimal split of T/R contributions. Last year I created a tool that produces this exact plot, and recently updated it for 2022, so this wiki update is very timely.

    Running a single estimate with a single number of traditional contributions is like checking one point on this curve. It's not going to get the right answer every time, but it might get you close, if you get lucky. The slope of that curve is positive if current MTR > future MTR, negative if current MTR < future MTR, and flat if current MTR = future MTR. Checking with a FV with zero future traditional contributions will check the case of 100% Roth all the way at the left side of the curve. If you check this point and find that future MTR > current MTR, that means the objective function is sloping down to the right, which means you're at least at a local maximum, and this may be good enough for your "simplified" approach. BUT, if you check this point and find current MTR > future MTR, you've found a local minimum and this is not the right answer; you should not contribute 100% Roth.

    Likewise, if you check with a FV assuming maximum traditional contributions and find current MTR > future MTR, this means the curve slopes down to the right, so you are at a local maximum and you can go with this as a "simplified" answer. But again, if you check this point and find current MTR < future MTR, then that's not the right answer. If you check BOTH extremes and find they are both local minima, then the optimal answer is somewhere in the middle and you need more work to find the right split.

    Suggestion: go into the User Guide in the Excel file here and look at the plots; I think it will add clarity into how to approach this problem. After looking at this for years I'm convinced a software tool is the best way to solve this problem for most readers. For ~19 relatively easy inputs into a spreadsheet, readers will get as accurate an answer as they can, and all the math gets done for them.

    I'll post more back on this when I have time.
    Last edited by fyre4ce on Mon Aug 08, 2022 10:26 pm, edited 1 time in total.
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    Re: Seeking comment on proposed revisions to Marginal Tax Rate and Traditional v. Roth wiki articles

    Post by FiveK »

    fyre4ce wrote: Thu Aug 04, 2022 3:25 am 3) While I like the idea of adding simplified content to help more novice readers, I worry that the added "Simple method" in "Estimating future marginal tax rate" section made things worse, and I'll explain why.
    <snip>
    For ~19 relatively easy inputs into a spreadsheet, readers will get as accurate an answer as they can, and all the math gets done for them.
    Excellent discussion in the snipped section about mathematical modeling concepts, and I enjoyed it because I'm familiar with it. The general population, however, is not so enlightened. ;)
    Using only 3 inputs (rate of return, time, and withdrawal ratio) is simpler than using 19 inputs and, given the uncertainties involved, deferring to Occam and not multiplying entities seems best.
    2) I agree that simpler concepts should be up front, but the typical cases is a simple concept, no?
    No, not really, because most of those rules of thumb are based on assumptions about current and future tax rates. The article has good content discussing why people's actual marginal tax rates often differ from what one might guess, and thus why some math is recommended. The "for most people traditional is best and if you really can't decide then use 50/50" suggestions cover the "won't do any math" folks pretty well. The "typical cases" section has not been removed completely, and the link to it remains where it has been, so if people really want to use it they can.
    ...whether to Roth convert is a separate (albeit closely related) topic to T vs R contributions, and that topic already has its own wiki page. The T vs R page is already very long (and getting even longer) and I caution that we add more material that would better go elsewhere. I suggest only brief mentions of conversion-specific topics and follow them with links to the conversion page. Also, the bulk of this discussion should go in the "Maxing out retirement accounts" section further down the page, and keep the material in that "Calculations" section to a couple lines or so, with a link to the lower section. Keep in mind, by this point in the page, readers haven't even had current and future marginal rates explained.
    Thanks for the reminder that the "invested RMD" issue should appear on the Roth IRA conversion page. The purpose of this page, as stated at the top, includes "when you consider leaving money in a traditional account or converting some to Roth."
    1) The wiki already has a formula....
    Adding a footnote reference or two should be fine. The historical references should remain, both to acknowledge dodonnell's original contribution (to this forum) in 2014 and how it was decided that TFB's tool was correct. If we want to go far down the rabbit hole, we could bring User:FiveK/Taxable account after-tax balance - Bogleheads into the main wiki and reference it, because periodic compounding, not continuous compounding, is the lingua franca of personal finance - but leaving things as is seems fine.
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    Re: Seeking comment on proposed revisions to Marginal Tax Rate and Traditional v. Roth wiki articles

    Post by fyre4ce »

    FiveK wrote: Thu Aug 04, 2022 1:17 pm
    fyre4ce wrote: Thu Aug 04, 2022 3:25 am 3) While I like the idea of adding simplified content to help more novice readers, I worry that the added "Simple method" in "Estimating future marginal tax rate" section made things worse, and I'll explain why.
    <snip>
    For ~19 relatively easy inputs into a spreadsheet, readers will get as accurate an answer as they can, and all the math gets done for them.
    Excellent discussion in the snipped section about mathematical modeling concepts, and I enjoyed it because I'm familiar with it. The general population, however, is not so enlightened. ;)
    Using only 3 inputs (rate of return, time, and withdrawal ratio) is simpler than using 19 inputs and, given the uncertainties involved, deferring to Occam and not multiplying entities seems best.
    Sure, most readers will not have the background to understand how an optimization algorithm works. But if they are using a tool that does the math for them, they don't have to - they just need to input the right data and be able to understand the results. It's our job as editors (and potential tool publishers) to do the complex thinking, and to give readers the best balance of results and ease of use that we can.

    I'm still concerned about your proposed "simplified method". It takes in 4 inputs (the 3 you list, plus current aggregate pre-tax balance) but I worry the answer is so inaccurate as to be useless. For example, it ignores all other forms of income, which nearly all readers will have. Sure, readers can add those in themselves, but that just increases the number of inputs closer to what a full-function tool would take in. Readers would have create their own their own Social Security phase-in code (not simple) and estimate their income from a taxable account. And, the method ignores potential future contributions. A couple of 1099 earners can put away $122,000 per year ($135,000 if age 50+) pre-tax, which could add millions to the future balance. After all these tweaks are added, you’re basically back to the standard method of tallying up all expected income and comparing that to existing tax brackets, which is the method that’s already in the wiki and coded in my proposed tool. Also, if you’re going to check a single point on the range of traditional withdrawals, it’d be better to check the middle, which would be the FV function with half the maximum annual pre-tax contributions.

    It's clear to me that readers need some sort of tool to help them through the math of this complex problem. The only alternatives I see are a set of pre-calculated typical cases readers can match to (which you don’t seem to like), or laying out all the equations like a textbook and letting readers build their own spreadsheets. While that appeals to some readers, most can’t/won’t/don’t, which is why T vs R is still such a common question. I’d prefer to keep detailed discussions of my proposed tool in that thread, but maybe you can clarify for us, because you don’t seem enthusiastic about the tool – do you dislike the concept of an automated tool in general, or is there something wrong with that tool in particular?
    FiveK wrote: Thu Aug 04, 2022 1:17 pm
    2) I agree that simpler concepts should be up front, but the typical cases is a simple concept, no?
    No, not really, because most of those rules of thumb are based on assumptions about current and future tax rates. The article has good content discussing why people's actual marginal tax rates often differ from what one might guess, and thus why some math is recommended. The "for most people traditional is best and if you really can't decide then use 50/50" suggestions cover the "won't do any math" folks pretty well. The "typical cases" section has not been removed completely, and the link to it remains where it has been, so if people really want to use it they can.
    All methods to solve this problem will make some assumptions about future tax rates. The “typical cases” section was added in the last revision, where it was peer-reviewed and there was a consensus it improved the page. It should not be removed or shrunk to a link by a single editor.
    FiveK wrote: Thu Aug 04, 2022 1:17 pm
    1) The wiki already has a formula....
    Adding a footnote reference or two should be fine. The historical references should remain, both to acknowledge dodonnell's original contribution (to this forum) in 2014 and how it was decided that TFB's tool was correct. If we want to go far down the rabbit hole, we could bring User:FiveK/Taxable account after-tax balance - Bogleheads into the main wiki and reference it, because periodic compounding, not continuous compounding, is the lingua franca of personal finance - but leaving things as is seems fine.
    To be clear, the reason the derivation of the taxable account performance here uses continuous compounding is so the integration can be done much easier. But, the main page has both continuous and periodic compounding to satisfy readers of either taste, and other uses of that formula (eg. here, here, here) all use annual compounding, which I agree is the industry standard (for better or worse).

    It's okay to add an alternate formula to the wiki, but it should not be simply linked from a forum post. It should go through a peer review process to catch mistakes like the one I found, put into the wiki so there is a revision history, and some context (maybe a couple sentences) should be added to explain the differences between the two formulas.

    -----

    Per forum policy, please revert the changes, create a draft page with the proposed edits, and publish them for comment. Then changes can be made if there is a consensus (not necessarily unanimity) that they are an improvement. There are some good ideas here, but they need some wordsmithing, and some of the edits undid changes that were made by forum consensus last year. Maybe that consensus has changed, but these changes are too large to be made without peer review.
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    Re: Seeking comment on proposed revisions to Marginal Tax Rate and Traditional v. Roth wiki articles

    Post by LadyGeek »

    fyre4ce wrote: Wed Aug 10, 2022 1:29 pm It's okay to add an alternate formula to the wiki, but it should not be simply linked from a forum post. It should go through a peer review process to catch mistakes like the one I found, put into the wiki so there is a revision history, and some context (maybe a couple sentences) should be added to explain the differences between the two formulas.
    Linking to forum posts is fine as long as it's a credible source. In this case, additional review and rationale is suggested.
    fyre4ce wrote: Wed Aug 10, 2022 1:29 pm Per forum policy, please revert the changes, create a draft page with the proposed edits, and publish them for comment. Then changes can be made if there is a consensus (not necessarily unanimity) that they are an improvement. There are some good ideas here, but they need some wordsmithing, and some of the edits undid changes that were made by forum consensus last year. Maybe that consensus has changed, but these changes are too large to be made without peer review.
    (It's actually Wikipedia policy to get a consensus.) We have a disagreement on content, so let's get it resolved. Creating a second draft page is a good idea.

    If anyone needs help reverting changes and creating a draft page, post here and myself or another wiki editor will take care of it.

    Revision history is in the "View history" tab of every wiki page (desktop view). Supply the page and date / time you'd like the page to revert to.
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    Re: Seeking comment on proposed revisions to Marginal Tax Rate and Traditional v. Roth wiki articles

    Post by FiveK »

    It's unfortunate that trying to help people understand how their individual situation affects the likelihood of traditional or Roth contributions working better for them in the long run has become so contentious.

    Trying to consider all possibilities and make a very accurate prediction of one's finances 30+ years into the future is, unfortunately, a fool's errand, regardless of what tool one uses. Currently the wiki describes both simple and complex methods. As with most things in life, simpler is usually better, but for the smaller fraction who can benefit from a more complex, it's there.

    "Rules of thumb" are great when the rule of thumb and exact answers are close for a wide range of situations. E.g., "your money doubles every 72/(interest rate) years" is a good rule of thumb for estimating how long that takes. There are so many moving parts in the t vs. R choice (e.g., age, career prospects/choices), however, that most t vs. R rules of thumb are only narrowly applicable.

    The intent of the most recent changes was
    - include the “more complicated situation” of invested RMDs that McQ's and others' work had highlighted
    - Outline the “more complicated situations” section to make it easier to reference in forum discussions.
    - Maintain the introductory focus on “understanding one’s current and expected future marginal rates” as the suggested way to make the t vs. R choice and defer most “rules of thumb” to a later section.
    - Provide a “simplest” estimate approach for future income from traditional accounts, in addition to the more complicated approach currently described.

    Based on the assumption that those are all "good things", to the extent the changes accomplished those ends nothing should be reverted. If someone thinks those are not "good things" it would be interesting to hear that rationale.
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    Re: Seeking comment on proposed revisions to Marginal Tax Rate and Traditional v. Roth wiki articles

    Post by fyre4ce »

    FiveK wrote: Wed Aug 10, 2022 2:25 pm It's unfortunate that trying to help people understand how their individual situation affects the likelihood of traditional or Roth contributions working better for them in the long run has become so contentious.

    <snip>

    "Rules of thumb" are great when the rule of thumb and exact answers are close for a wide range of situations. E.g., "your money doubles every 72/(interest rate) years" is a good rule of thumb for estimating how long that takes. There are so many moving parts in the t vs. R choice (e.g., age, career prospects/choices), however, that most t vs. R rules of thumb are only narrowly applicable.

    The intent of the most recent changes was
    - include the “more complicated situation” of invested RMDs that McQ's and others' work had highlighted
    - Outline the “more complicated situations” section to make it easier to reference in forum discussions.
    - Maintain the introductory focus on “understanding one’s current and expected future marginal rates” as the suggested way to make the t vs. R choice and defer most “rules of thumb” to a later section.
    - Provide a “simplest” estimate approach for future income from traditional accounts, in addition to the more complicated approach currently described.

    Based on the assumption that those are all "good things", to the extent the changes accomplished those ends nothing should be reverted. If someone thinks those are not "good things" it would be interesting to hear that rationale.
    You're a really smart, knowledgable, and enthusiastic editor, and we both agree on the ultimate goal - to provide the best and most accurate advice, at the lowest "cost" (time, complexity, required background knowledge, etc.) to as many readers as possible. I just disagree that these edits are the best way to achieve that goal. Rather than duke it out here in an old thread, I think it would be best to start a fresh thread with these proposed edits on a draft page and collect other opinions. I'll weigh in, but hopefully many others will too, there will be a chance to wordsmith the draft page, and if there is a consensus that the new edits improve the page, they can be made then. I want to be the wiki edit police about as much as I want to be the HOA president issuing parking warnings (that is, not at all) but I suggest the live page be reverted to 19:34, 20 April 2022 (the last version before these changes).
    FiveK wrote: Wed Aug 10, 2022 2:25 pm Trying to consider all possibilities and make a very accurate prediction of one's finances 30+ years into the future is, unfortunately, a fool's errand, regardless of what tool one uses. Currently the wiki describes both simple and complex methods. As with most things in life, simpler is usually better, but for the smaller fraction who can benefit from a more complex, it's there.
    If I could change one thing here, it would be to convince you that a software tool would add value to readers. Remember, not all T vs R analysis is looking out 30+ years. There are plenty of readers who are ~5-10 years out, trying to decide whether to go over or under the Social Security taxation spike, or other tax spikes (capital gains phase-in, IRMAA) and I think there is real value in a software tool that will check all these cases automatically. I wrote my tool to automate as much of the calculations currently on the wiki page as possible; besides numerical inputs, the user just has to tell the tool whether they will be contributing the maximum, not getting the full match, or neither. The alternative to a tool is that a reader will have to read and understand the entire wiki page, correctly pick out which of the special cases apply to them, and build their own spreadsheet to stitch together the relevant equations. I would love to collaborate with you on a tool, and you are welcome to post any constructive criticism of the tool in that thread.
    Last edited by fyre4ce on Thu Aug 11, 2022 3:05 pm, edited 1 time in total.
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    Re: Seeking comment on proposed revisions to Marginal Tax Rate and Traditional v. Roth wiki articles

    Post by LadyGeek »

    fyre4ce wrote: Thu Aug 11, 2022 2:09 pm I want to be the wiki edit police about as much as I want to be the HOA president issuing parking warnings (that is, not at all) but I suggest the live page be reverted to 19:34, 20 April 2022 (the last version before these changes).
    OK, I'll be the wiki edit police. :wink: More appropriately, I'm a wiki admin and will follow Wikipedia:Dispute resolution.

    We have two editors in disagreement, which is fine. Numerous concerns are in the previous posts. Here's what we'll do:

    1. I have resurrected FiveK's prior draft page. User:FiveK/Traditional versus Roth The wiki software knows there was an earlier draft page and restores the prior revisions.

    2. Next, I updated FiveK's draft page with the revision as of 19:34, 20 April 2022 (what we have a consensus on).
    3. Next, I updated FiveK's draft page with the revision as of 20:57, 3 August 2022‎.

    FiveK now has a working draft which can be used to directly compare his changes against the baseline version (what we have a consensus on).

    4. I have reverted the changes in the "Live" page back to the version we have a consensus on (19:34, 20 April 2022).

    FiveK - Please start a new thread to discuss your proposed updates. Link to the new thread from here so everyone posting here will see the new thread.
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    Re: Seeking comment on proposed revisions to Marginal Tax Rate and Traditional v. Roth wiki articles

    Post by FiveK »

    LadyGeek wrote: Thu Aug 11, 2022 3:03 pm 4. I have reverted the changes in the "Live" page back to the version we have a consensus on (19:34, 20 April 2022).
    While that does seem a step backward for the reasons noted below (that had been composed in reply to fyre4ce before seeing the quoted post), admins do get the big bucks for such work. ;)

    There are plenty of examples in forum discussions (both here and in other personal finance forums) where "rules of thumb" either don't work or are hotly debated. For perhaps the most recent example, see Traditional or Roth 401K - Bogleheads.org. There is not even consensus regarding that one specific situation, let alone consensus on a broad range of typical situations. That lack of consensus is usually driven by people bringing different (not "wrong", just "different") assumptions to the discussion. It's not worth trying for consensus on which of the plausible assumptions is "most correct".

    Yes, a really good software tool could add value. The apparent demise of I-ORP: Optimal Retirement Planner has left a hole in the "automated multi-year optimization, including reasonably accurate tax calculation" space. That space isn't completely empty, because free tools such as the Retiree Portfolio Model and the personal finance toolbox spreadsheet, and commercial tools from companies such as Pralana (with which I have no experience) do exist, but it was nice to be able to suggest I-ORP to people with relevant questions.

    I don't recall offhand whether your tool does or could have I-ORP-like capability - what do you think? To the extent it could at least partially replace I-ORP as a suggested alternative, I'd be happy to look and comment.

    At the least, if you think your tool would be better for people than using the current More complicated method in the t vs. R wiki, why not either add a reference to it, or replace the "more complicated method" entirely with a reference to that tool?

    In any case, the simple method will still have a place because there are enough people in this country (in the world also, but t vs. R is a USA thing) who are willing to try something simple but not something that looks complicated.

    For the reasons above (i.e., there is no consensus on many "typical situations", and "simple methods have a place"), reverting the wiki to move the "typical situations" list to a more prominent location (note that it is still present, just not so prominently), and removing the simple method for future income estimation, is not called for.
    FiveK - Please start a new thread to discuss your proposed updates. Link to the new thread from here so everyone posting here will see the new thread.
    Will do.
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    Re: Seeking comment on proposed revisions to Marginal Tax Rate and Traditional v. Roth wiki articles

    Post by fyre4ce »

    FiveK wrote: Thu Aug 11, 2022 3:22 pm There are plenty of examples in forum discussions (both here and in other personal finance forums) where "rules of thumb" either don't work or are hotly debated. For perhaps the most recent example, see Traditional or Roth 401K - Bogleheads.org. There is not even consensus regarding that one specific situation, let alone consensus on a broad range of typical situations. That lack of consensus is usually driven by people bringing different (not "wrong", just "different") assumptions to the discussion. It's not worth trying for consensus on which of the plausible assumptions is "most correct".
    I wouldn't be so quick to dismiss the "typical cases" as applied to the thread you quoted. One missing piece is what the career trajectory and future income is likely to be. If the individual in question is probably near their peak earnings (adjusting for inflation), then at least some traditional is a really good idea. This is the first bullet in the traditional list. Maybe not this year with only 5 months of income, but next year I agree it makes sense to contribute traditional down to the top of the 12% bracket; below that, Roth is probably best. The current page recommends Roth at or below a 12% marginal rate, although that's in the "Current marginal rate" section, not "typical cases". If the person is likely to have income rise over time (doctor, engineer, etc.) then 100% Roth is the better choice. This is the first bullet under the Roth list. Tax-planning for what this new grad's financial situation will be in 50 years is extremely difficult but I think the typical cases hold up pretty well.
    FiveK wrote: Thu Aug 11, 2022 3:22 pm Yes, a really good software tool could add value. The apparent demise of I-ORP: Optimal Retirement Planner has left a hole in the "automated multi-year optimization, including reasonably accurate tax calculation" space. That space isn't completely empty, because free tools such as the Retiree Portfolio Model and the personal finance toolbox spreadsheet, and commercial tools from companies such as Pralana (with which I have no experience) do exist, but it was nice to be able to suggest I-ORP to people with relevant questions.

    I don't recall offhand whether your tool does or could have I-ORP-like capability - what do you think? To the extent it could at least partially replace I-ORP as a suggested alternative, I'd be happy to look and comment.

    At the least, if you think your tool would be better for people than using the current More complicated method in the t vs. R wiki, why not either add a reference to it, or replace the "more complicated method" entirely with a reference to that tool?

    In any case, the simple method will still have a place because there are enough people in this country (in the world also, but t vs. R is a USA thing) who are willing to try something simple but not something that looks complicated.
    I have heard i-ORP mentioned before but have never looked at it. I will when I have some time, likely not before this weekend. But I will say my tool does not have true multi-year capability. In my first draft, I had the capability to add years of Roth conversions at the end of a career (say, between age 67-72) that would reduce the pre-tax balance and also consume some taxable balance to pay the taxes. But it quickly got complicated. For those years, calculating the marginal rate is not enough; the entire tax bill must be computed accurately, with credits/deductions, which made the tax model much more complex. Living expenses would have to be subtracted, and assumptions would have to be made about capital gains tax on sold taxable investments to pay the taxes. So I removed that feature and made it more of a two-year (current and withdrawal) model.

    For the current year, users either enter a single number of a fixed marginal tax rate, or copy/paste a marginal tax rate table from the PFT (or another source). If you give it a table from the PFT, it will interpolate a cumulative marginal tax rate for the range of options of traditional contributions. I didn't bother to code up an accurate current-year tax model, because it would take more time than I have, and the PFT already does this very well, so why reinvent the wheel?

    Years between the current year and withdrawal, are assumed to be identical to the current year, although the tool takes an input of ST and LT capital gains tax rates, so dividends can be appropriately taxed the taxable account. Whatever T/R split the user looks at in the current year is assumed to apply to each year between now and withdrawal.

    For the withdrawal year, total income is calculated using pre-tax withdrawals, taxable yield, Social Security, any other income, and also tax-free interest (which is not directly taxed but can affect the amount of SS taxed. I was on the fence for adding this input but decided it's important for the readers who will be facing the SS tax spike). The 65+ standard deduction is subtracted, and the marginal tax rate is then looked up in the rate table. Rate bumps from SS taxation and CG phase-in are automatically included. There's an option to sunset the TCJA tax rates if the user wants. It also shows the future values if maxing out accounts and/or not getting the full match, if either situation apply. Users can also enable the IRMAA option, adding either the exact spikes, or an averaged tax rate over the most dense IRMAA range. Actually I think that's a great feature I haven't seen elsewhere, as IRMAA adds about a 5% extra rate.

    That sheet only looks at a single data point on the range of possible traditional contributions/future values. If a split contribution may be best, users can go to the second tab and hit the button to run a macro, which runs the same calculation for 41 possible combinations of T/R splits (with equal after-tax sizes) and puts the results into a chart. Users can optionally enable either contributing the max or not getting the full match options (but not both, as they are mutually exclusive). A chart of the future values of equivalent contributions today is, in my opinion, the most direct and intuitive output to give a user.

    So, the tool ended up being mostly a straightforward coding of the formulas on the live wiki page, and a run-through of the current "Estimate future marginal tax rate" method, with as many steps automated as possible. It's my current best attempt to balance simplicity and accuracy, but I'm happy to accept suggestions from you or anyone.
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    Re: Seeking comment on proposed revisions to Marginal Tax Rate and Traditional v. Roth wiki articles

    Post by FiveK »

    fyre4ce wrote: Thu Aug 11, 2022 4:42 pmI wouldn't be so quick to dismiss the "typical cases" as applied to the thread you quoted. One missing piece is what the career trajectory and future income is likely to be.
    Indeed, and this is a good example of why the "typical cases" don't belong up front: it takes too much space to add all the necessary qualifiers. Also, that thread exposes that there is not and hasn't been consensus within the BH community, even with regard to the now-reverted wiki. No problem keeping the "typical cases" section, just don't have it up where it is more likely to mislead the reader than if it occurs at a later place.
    I have heard i-ORP mentioned before but have never looked at it. I will when I have some time, likely not before this weekend.
    Unfortunately all you'll see is "The Optimal Retirement Planner is offline".
    But I will say my tool does not have true multi-year capability.
    Well, shoot - I was hoping it did. Again, if you want to include a reference to it, either in addition or instead of the current "more complex" section, I have no objection.
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    Re: Seeking comment on proposed revisions to Marginal Tax Rate and Traditional v. Roth wiki articles

    Post by Walkure »

    fyre4ce wrote: Fri Jul 02, 2021 11:28 pm Haha, I got a kick out of that :D I would extend your joke to include #4 though, because again, it's still a tax rate, just on a bigger interval. It's "marginal" relative to a baseline of not earning any income.
    I don't think it's correct to say that #4, which I've commonly heard described as the "effective tax," is marginal to $0 gross income, because the existence of refundable credits means that someone with literally no income could get a refund generating a negative marginal and effective rate.
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    Re: Seeking comment on proposed revisions to Marginal Tax Rate and Traditional v. Roth wiki articles

    Post by FiveK »

    FiveK wrote: Thu Aug 11, 2022 3:22 pm
    FiveK - Please start a new thread to discuss your proposed updates. Link to the new thread from here so everyone posting here will see the new thread.
    Will do.
    Done: Simplifying the Traditional versus Roth wiki articles
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