Traditional vs Roth - Is this a factor?

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$tar-Lord
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Traditional vs Roth - Is this a factor?

Post by $tar-Lord »

For simplicity sake, assume a constant tax rate for all taxed dollars going in (Roth) or coming out (Traditional). As known, the commutative property of multiplication means that the investor's results are not different with Roth or Traditional.

Roth - P*(1-T)*G = Investor Result
Trad - P*G*(1-T) = Investor Result


However, are the government's taxation results the same?
Roth - P*T*I = Roth Government Result
Trad - P*G*T= Traditional Government Result

(P) - Principle
(T) - Tax Rate
(I) - Inflation over time
(G) - Investment gain over time


If G > I, then Traditional Government Result > Roth Government Result.
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JoMoney
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Re: Traditional vs Roth - Is this a factor?

Post by JoMoney »

$tar-Lord wrote: Mon Sep 28, 2020 3:43 pm...
If G > I, then Traditional Government Result > Roth Government Result.
Yes.. but only in some sort of adjusted purchasing parity terms, and it does assume G > I , which isn't guaranteed in anything but TIPS (and maybe not even there)... If your account is invested in stocks, it could easily lose money, and in that case you're still better off having not pre-paid taxes on it to put it in a Roth.

Roth accounts can be strategically used for an advantage, but I'm not a fan of them as a 'default' choice for every situation.
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David Jay
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Re: Traditional vs Roth - Is this a factor?

Post by David Jay »

I am not getting your point, why do I care about the Government's income? Are you concerned that the benefit to the government could affect Washington DC decision making with regard to inflation, etc?

That aside, here are a few points on your formulas:

1. There is no utility function for the time value of money, receiving the taxes immediately as they are earned (Roth) vs. waiting for 30-40-50 years to collect (Traditional).

2. With the Roth, there is no inflation factor. The taxes are paid immediately as they are earned, as follows:

P*T = Roth Government Result

3. It would seem that both Gain and Inflation are factors in the traditional calculation, like this:

P*(G/I)*T= Traditional Government Result

So the Government is really carrying all the risk of the Traditional IRA - delay in receipt of taxes, investment gains and inflation.
Prediction is very difficult, especially about the future - Niels Bohr | To get the "risk premium", you really do have to take the risk - nisiprius
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David Jay
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Re: Traditional vs Roth - Is this a factor?

Post by David Jay »

If the government wanted to increase receipts, they could eliminate all tax-deferred savings plans and only allow after-tax plans (Roth 401K, etc). That would result in a huge, immediate (but short term, perhaps 10-15 years) increase in revenue.
Prediction is very difficult, especially about the future - Niels Bohr | To get the "risk premium", you really do have to take the risk - nisiprius
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Re: Traditional vs Roth - Is this a factor?

Post by FiveK »

$tar-Lord wrote: Mon Sep 28, 2020 3:43 pm However, are the government's taxation results the same?
No, but as JoMoney and David Jay commented, who cares?

Using "amount of tax paid" as a guide is the second of two Common misconceptions in this arena.
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$tar-Lord
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Re: Traditional vs Roth - Is this a factor?

Post by $tar-Lord »

David Jay wrote: Mon Sep 28, 2020 4:25 pm I am not getting your point, why do I care about the Government's income? Are you concerned that the benefit to the government could affect Washington DC decision making with regard to inflation, etc?
If a person were small government minded and all other circumstances being the same they choose not to "feed the beast" this could matter.

That aside, here are a few points on your formulas:

1. There is no utility function for the time value of money, receiving the taxes immediately as they are earned (Roth) vs. waiting for 30-40-50 years to collect (Traditional).
Agreed, that is why there is not inflation factored in the investor outcome.

2. With the Roth, there is no inflation factor. The taxes are paid immediately as they are earned, as follows:

P*T = Roth Government Result

This is moving the future value of the Traditional taxes to today. The formulas I wrote move Roth taxes to the Traditional time. It works either way.

3. It would seem that both Gain and Inflation are factors in the traditional calculation, like this:

P*(G/I)*T= Traditional Government Result
This is moving the future value of the Traditional taxes to today. The formulas I wrote move Roth taxes to the Traditional time. It works either way.

So the Government is really carrying all the risk of the Traditional IRA - delay in receipt of taxes, investment gains and inflation.
They carry a risk that you won't invest in a manner that beats inflation. For a Boglehead following appropriate strategy, that is a safer bet.
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Re: Traditional vs Roth - Is this a factor?

Post by $tar-Lord »

FiveK wrote: Mon Sep 28, 2020 6:43 pm
$tar-Lord wrote: Mon Sep 28, 2020 3:43 pm However, are the government's taxation results the same?
No, but as JoMoney and David Jay commented, who cares?

Using "amount of tax paid" as a guide is the second of two Common misconceptions in this arena.
From the Link:
There are two common misconceptions, one that incorrectly favors traditional, and one that incorrectly favors Roth.

The second misconception is that "it's better to pay tax on the seed than the harvest."
This is addressed by the investor result equations (Traditional & Roth). Both equations are the same.
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$tar-Lord
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Re: Traditional vs Roth - Is this a factor?

Post by $tar-Lord »

David Jay wrote: Mon Sep 28, 2020 4:43 pm If the government wanted to increase receipts, they could eliminate all tax-deferred savings plans and only allow after-tax plans (Roth 401K, etc). That would result in a huge, immediate (but short term, perhaps 10-15 years) increase in revenue.
This question relates to existing rules, not future predictions.
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Re: Traditional vs Roth - Is this a factor?

Post by retire2022 »

Op

For traditional ira, pre tax 401, 457 & 403b.

What about an investor with pension?

And Social Security IRMMA rule as well as RMD how can someone incorporate those variables with math challenged investor?
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Re: Traditional vs Roth - Is this a factor?

Post by $tar-Lord »

retire2022 wrote: Tue Sep 29, 2020 9:31 am Op

For traditional ira, pre tax 401, 457 & 403b.

What about an investor with pension?

And Social Security IRMMA rule as well as RMD how can someone incorporate those variables with math challenged investor?
Those are very important questions to ask for someone performing a full evaluation of what is the most profitable approach for them.

For simplicity sake in this post, I chose to assume that the tax rate today and tomorrow (10,20, or 30 years from now, for example) is the same, after considering income and taxes today, tomorrow, all the factors that you mentioned, and everything else already considered. The reason for this is that this is typically considered the decision point between Roth and Traditional.

It's just a factor that came to my mind. The odds of many people being exactly on this decision point is probably low. It was more of a mental exercise and wondering if anyone had ever considered this.
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Re: Traditional vs Roth - Is this a factor?

Post by David Jay »

$tar-Lord wrote: Tue Sep 29, 2020 8:55 am
David Jay wrote: Mon Sep 28, 2020 4:25 pm 2. With the Roth, there is no inflation factor. The taxes are paid immediately as they are earned, as follows:

P*T = Roth Government Result

This is moving the future value of the Traditional taxes to today. The formulas I wrote move Roth taxes to the Traditional time. It works either way.
I believe that you are incorrectly conflating the cycle for the individual investor with the cycle for the government, which is my root issue with your formulas.

The investor will not utilize the funds until retirement, in which case the commutative property applies to the taxes. It doesn’t matter to the individual if the taxes come out at contribution or at distribution, only the net final distribution matters.

In contrast, it is a very real aspect of government revenue that Roth taxes are actually withheld from earnings today, whereas the tax revenue from the Traditional is deferred for decades. And the government has expenses on which it can spend that revenue today. You can’t arbitrarily delay the government’s collection of Roth taxes for decades without some factor for the time value of money for the tax revenue.
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$tar-Lord
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Re: Traditional vs Roth - Is this a factor?

Post by $tar-Lord »

David Jay wrote: Tue Sep 29, 2020 10:38 am
$tar-Lord wrote: Tue Sep 29, 2020 8:55 am
David Jay wrote: Mon Sep 28, 2020 4:25 pm 2. With the Roth, there is no inflation factor. The taxes are paid immediately as they are earned, as follows:

P*T = Roth Government Result

This is moving the future value of the Traditional taxes to today. The formulas I wrote move Roth taxes to the Traditional time. It works either way.
I believe that you are incorrectly conflating the cycle for the individual investor with the cycle for the government, which is my root issue with your formulas.

The investor will not utilize the funds until retirement, in which case the commutative property applies to the taxes. It doesn’t matter to the individual if the taxes come out at contribution or at distribution, only the net final distribution matters.

In contrast, it is a very real aspect of government revenue that Roth taxes are actually withheld from earnings today, whereas the tax revenue from the Traditional is deferred for decades. And the government has expenses on which it can spend that revenue today. You can’t arbitrarily delay the government’s collection of Roth taxes for decades without some factor for the time value of money for the tax revenue.
Agreed, that is why my equation inflates the Roth tax dollars to future value:
Roth - P*T*I = Roth Government Result
For example I was assuming "I" would be something like I = 1.03^X where X is the number of years from Roth contribution to Traditional withdrawal.

On the conflating issue, that was exactly what I was attempting to avoid by saying that the investor result is no different in either circumstance.
Last edited by $tar-Lord on Tue Sep 29, 2020 10:50 am, edited 1 time in total.
fyre4ce
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Re: Traditional vs Roth - Is this a factor?

Post by fyre4ce »

Bottom line: we don't know what the discount rate / utility function is of the government for money now vs. later. Without treading too deeply into political philosophy, the purpose of the government should be to serve its citizens, not make money. So if money now is (for instance) able to prevent pandemic deaths, one could argue that's a more important objective than getting more tax revenue in several decades, even if the NPV would be higher using a reasonable discount rate.

If I remember correctly, that was explicitly part of the pitch for creating Roth accounts in the first place - it provided a similar, mirrored, tax structure to Traditional accounts, but brings in tax revenue now.

In an case, I wouldn't make a T vs R decision based on what's best for the government. Even if you're Jeff Bezos the amount of income taxes you pay isn't enough to make any meaningful difference. If you care about having a government that functions effectively and serves its citizens, the best thing you can do is VOTE, for every office from local to national, and convince everyone you know to do the same.
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Re: Traditional vs Roth - Is this a factor?

Post by frugalecon »

$tar-Lord wrote: Tue Sep 29, 2020 9:43 am
retire2022 wrote: Tue Sep 29, 2020 9:31 am Op

For traditional ira, pre tax 401, 457 & 403b.

What about an investor with pension?

And Social Security IRMMA rule as well as RMD how can someone incorporate those variables with math challenged investor?
Those are very important questions to ask for someone performing a full evaluation of what is the most profitable approach for them.

For simplicity sake in this post, I chose to assume that the tax rate today and tomorrow (10,20, or 30 years from now, for example) is the same, after considering income and taxes today, tomorrow, all the factors that you mentioned, and everything else already considered. The reason for this is that this is typically considered the decision point between Roth and Traditional.

It's just a factor that came to my mind. The odds of many people being exactly on this decision point is probably low. It was more of a mental exercise and wondering if anyone had ever considered this.
I had thought of this exact issue, but not really as a personal finance issue. It is more of a public finance issue. It could be optimal for a government to defer collecting taxes if it can borrow cheaply and have citizens invest on its behalf in the stock market. At present, there is a large embedded deferred tax bill in IRAs and 401ks. When thinking about government finances, that should probably be netted against the stock of government debt held by the public.
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$tar-Lord
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Re: Traditional vs Roth - Is this a factor?

Post by $tar-Lord »

fyre4ce wrote: Tue Sep 29, 2020 10:47 am Bottom line: we don't know what the discount rate / utility function is of the government for money now vs. later. Without treading too deeply into political philosophy, the purpose of the government should be to serve its citizens, not make money. So if money now is (for instance) able to prevent pandemic deaths, one could argue that's a more important objective than getting more tax revenue in several decades, even if the NPV would be higher using a reasonable discount rate.

If I remember correctly, that was explicitly part of the pitch for creating Roth accounts in the first place - it provided a similar, mirrored, tax structure to Traditional accounts, but brings in tax revenue now.

In an case, I wouldn't make a T vs R decision based on what's best for the government. Even if you're Jeff Bezos the amount of income taxes you pay isn't enough to make any meaningful difference. If you care about having a government that functions effectively and serves its citizens, the best thing you can do is VOTE, for every office from local to national, and convince everyone you know to do the same.
I appreciate your perspective and points. The main thought I have is when have you ever voted for a politician who wanted less government and made it happen? In my experience, the trend is to vote themselves larger salaries, vote to spend more, vote for more government control and oversight, etc.
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$tar-Lord
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Re: Traditional vs Roth - Is this a factor?

Post by $tar-Lord »

frugalecon wrote: Tue Sep 29, 2020 10:57 am
$tar-Lord wrote: Tue Sep 29, 2020 9:43 am
retire2022 wrote: Tue Sep 29, 2020 9:31 am Op

For traditional ira, pre tax 401, 457 & 403b.

What about an investor with pension?

And Social Security IRMMA rule as well as RMD how can someone incorporate those variables with math challenged investor?
Those are very important questions to ask for someone performing a full evaluation of what is the most profitable approach for them.

For simplicity sake in this post, I chose to assume that the tax rate today and tomorrow (10,20, or 30 years from now, for example) is the same, after considering income and taxes today, tomorrow, all the factors that you mentioned, and everything else already considered. The reason for this is that this is typically considered the decision point between Roth and Traditional.

It's just a factor that came to my mind. The odds of many people being exactly on this decision point is probably low. It was more of a mental exercise and wondering if anyone had ever considered this.
I had thought of this exact issue, but not really as a personal finance issue. It is more of a public finance issue. It could be optimal for a government to defer collecting taxes if it can borrow cheaply and have citizens invest on its behalf in the stock market. At present, there is a large embedded deferred tax bill in IRAs and 401ks. When thinking about government finances, that should probably be netted against the stock of government debt held by the public.
Agreed, interesting thoughts. Thank you
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Re: Traditional vs Roth - Is this a factor?

Post by fyre4ce »

$tar-Lord wrote: Tue Sep 29, 2020 10:58 am
fyre4ce wrote: Tue Sep 29, 2020 10:47 am Bottom line: we don't know what the discount rate / utility function is of the government for money now vs. later. Without treading too deeply into political philosophy, the purpose of the government should be to serve its citizens, not make money. So if money now is (for instance) able to prevent pandemic deaths, one could argue that's a more important objective than getting more tax revenue in several decades, even if the NPV would be higher using a reasonable discount rate.

If I remember correctly, that was explicitly part of the pitch for creating Roth accounts in the first place - it provided a similar, mirrored, tax structure to Traditional accounts, but brings in tax revenue now.

In an case, I wouldn't make a T vs R decision based on what's best for the government. Even if you're Jeff Bezos the amount of income taxes you pay isn't enough to make any meaningful difference. If you care about having a government that functions effectively and serves its citizens, the best thing you can do is VOTE, for every office from local to national, and convince everyone you know to do the same.
I appreciate your perspective and points. The main thought I have is when have you ever voted for a politician who wanted less government and made it happen? In my experience, the trend is to vote themselves larger salaries, vote to spend more, vote for more government control and oversight, etc.
Should the goal be to always have less government? That doesn't sound right to me. The government does certain things better than either private industry or individual citizens, like national defense. We'd be living in a very different world if FDR's Infamy speech had gone something like, "Citizens of Hawaii - grab your rifles and defend yourselves. Good luck!" (This should be non-controversial regardless of your political leanings.) The question we should be asking is, which functions are best handled by the government, corporations, and citizens? We will all have different lists. But saying less government is always better doesn't pass superficial scrutiny.

And yes I share your concerns about self-interested politicians, regardless of party.

Let's steer off this topic before the thread gets locked. Political discussions are prohibited.
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$tar-Lord
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Re: Traditional vs Roth - Is this a factor?

Post by $tar-Lord »

fyre4ce wrote: Tue Sep 29, 2020 11:12 am
$tar-Lord wrote: Tue Sep 29, 2020 10:58 am
fyre4ce wrote: Tue Sep 29, 2020 10:47 am Bottom line: we don't know what the discount rate / utility function is of the government for money now vs. later. Without treading too deeply into political philosophy, the purpose of the government should be to serve its citizens, not make money. So if money now is (for instance) able to prevent pandemic deaths, one could argue that's a more important objective than getting more tax revenue in several decades, even if the NPV would be higher using a reasonable discount rate.

If I remember correctly, that was explicitly part of the pitch for creating Roth accounts in the first place - it provided a similar, mirrored, tax structure to Traditional accounts, but brings in tax revenue now.

In an case, I wouldn't make a T vs R decision based on what's best for the government. Even if you're Jeff Bezos the amount of income taxes you pay isn't enough to make any meaningful difference. If you care about having a government that functions effectively and serves its citizens, the best thing you can do is VOTE, for every office from local to national, and convince everyone you know to do the same.
I appreciate your perspective and points. The main thought I have is when have you ever voted for a politician who wanted less government and made it happen? In my experience, the trend is to vote themselves larger salaries, vote to spend more, vote for more government control and oversight, etc.
Should the goal be to always have less government? That doesn't sound right to me. The government does certain things better than either private industry or individual citizens, like national defense. We'd be living in a very different world if FDR's Infamy speech had gone something like, "Citizens of Hawaii - grab your rifles and defend yourselves. Good luck!" (This should be non-controversial regardless of your political leanings.) The question we should be asking is, which functions are best handled by the government, corporations, and citizens? We will all have different lists. But saying less government is always better doesn't pass superficial scrutiny.

And yes I share your concerns about self-interested politicians, regardless of party.

Let's steer off this topic before the thread gets locked. Political discussions are prohibited.
Thanks for the interesting thoughts. Definitely don't want to tread controversial political waters.

This idea could also span Federal vs. State vs. Local responsibility/over-reach. A citizen's impact does progressively improve moving down the chain. Also the ability to change your governance improves down the chain and creates competition (e.g. people moving from the coasts to other areas). If government must grow, Local could be preferable.

The example of national defense is definitely worth considering as it is special as the only constitutionally mandated function of the federal government.
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Re: Traditional vs Roth - Is this a factor?

Post by fyre4ce »

$tar-Lord wrote: Tue Sep 29, 2020 11:24 am The example of national defense is definitely worth considering as it is special as the only constitutionally mandated function of the federal government. [/color]
Even a narrow reading of Article 1 is much more expansive than just national defense. Not saying what the gov't should or shouldn't do, just what the constitution says.
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Re: Traditional vs Roth - Is this a factor?

Post by $tar-Lord »

fyre4ce wrote: Tue Sep 29, 2020 12:21 pm
$tar-Lord wrote: Tue Sep 29, 2020 11:24 am The example of national defense is definitely worth considering as it is special as the only constitutionally mandated function of the federal government. [/color]
Even a narrow reading of Article 1 is much more expansive than just national defense. Not saying what the gov't should or shouldn't do, just what the constitution says.
Agreed, wasn't implying it was the only function allowed, just only function mandated to be performed.
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Re: Traditional vs Roth - Is this a factor?

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