Lifestyle inflation and Early Retirement: Nat is Wrong

Hi RIP readers,

I mentioned several times how much I like almost anything Nat Eliason writes or does.

I also liked his old post about Financial Independence. Nothing new, but seeing that Nat in on board with our “movement” made me feel in good company πŸ™‚

Ok, today I want to write a review of his latest post on the 75% Rule for Lifestyle inflation & Early Retirement.

Dear Nat, even if the message you want to broadcast is very good (telling people to not splurge all their salary raises), I think your math is wrong on so many levels. Motivated by my deep respect of your writings, I needed to spreadsheet things out immediately.

Here a short summary of Nat’s article:


Why don’t high-income people retire faster?

Because they increase their expenses every time they get a raise!

I have a solution for you: with every raise you get, 75% (at least) of it must be saved and invested, the other 25% (at most) can be spent.

Say you get a 10k yearly salary raise, you can allow yourself to expand your lifestyle by 2.5k per year. Not more.

If you do this, your Early Retirement date won’t change compared to “before the raise” scenario. If you expand your lifestyle by more than that, your Retirement date is moving away in the future. If – obviously – you increase your lifestyle by less than that (or don’t increase it at all after a raise) you can retire even earlier than expected. Because your saving rate would increase (same expenses, higher salary).


It seems intuitive. You get a raise, you can splurge a bit but you must still throw a good portion of your raise into savings and investments.

It actually seems depressing: why can’t I raise my spending by… I don’t know… 50% of the salary increase? I’d still be saving more money than before the raise, and I’d also increase the saving rate (if it was below 50% before the raise), right? Shouldn’t I retire earlier anyway?

Wrong.

And even Nat’s numbers are wrong. I’ll show you why.

Before we continue, the “Retirement Date” is based on the 4% Rule, i.e. on constant dollar (inflation adjusted) withdrawal method, with a 4% Safe withdrawal Rate – which we know it’s both risky and inefficient, according to Ben Felix.

Let’s deep dive into Nat’s post. Here again a link to it:

The 75% Rule for Lifestyle Creep & Early Retirement

Nat introduces the 4% rule:

Already a couple of errors:

  • The 4% rule is not based on 7% average nominal returns and 3% inflation. It’s based on the worst Sequence of Returns we observed in history (for a 75%/25% portfolio of US stocks/bonds) over a 30 years period. Actual historical S&P500 CAGR (with dividends reinvested) is ~7%, which is way more than 4%. Is Sequence of Returns risk that draws the SWR down to 4%.
  • If your salary is 100k per year, and you save and invest 25% of it each year, you won’t need a principal ofΒ  25*100k (2.5M) but 25*75k (1.875M) to keep sustaining your lifestyle forever. It’s 25 times expenses, not salary.

That’s a good news.

The bad news is that you need 1.875M of today Dollars.

Nat claims you’re going to need 31 years to reach your goal if you start from Zero Net Worth and keep saving and investing 25% of your income, assuming no salary raises and no spending increments.

I don’t know where Nat got the 31 years. Using Networthify I see it takes 35.3 years to FIRE with 25% Saving Rate, and 4% real return (after inflation – and fees and taxes btw)

To prove his point, Nat introduces a simulated scenario where you get a constant salary raise until Retirement date. Let’s use 5% yearly salary raise (like Nat’s example).

What happens is we increase our lifestyle by the entire raise amount?

What happens if we increase our lifestyle by 50% of the raise amount?

What about 25%? What about Zero, i.e. what if we don’t change our spending regime after a raise?

Of course we expect first case (100% of the raise) to be really bad. And in fact it is bad: you never reach Retirement.

But second case (adjust spending by 50% of the raise) maybe it’s ok, right?

Assuming I was saving 25% of my salary pre raise, my saving rate would be improving if I save 50% of the raise, right?

Right, your Saving Rate improves. But you’re going to retire later than pre-raise – no matter what the shockingly simple math says.

According to Nat you now need almost 40 years to retire if you adjust your spending level by half the raise you received.

Counterintuitive!

Ok what about 25% or less?

Nat graphs the change in your Retirement date based on the percentage of the raise you decide to use to increase your lifestyle:

Nat concludes that the sweet spot is at around 27%. If you increase your lifestyle by 27% (“let’s call it 25% to make things easier“) or more of your raise, you’re going to retire later that pre-raise scenario.

Nat also claims that this 25% Rule (or 75% Rule) holds true if we start from a 50% Saving Rate instead of 25%, or if your yearly salary raise is 10% instead of 5%.

Cool, we’ve found an invariant! A universal rule!

Or… did we?

While reading his article, my WTFs per minute counter spiked.

I had to create a spreadsheet, and math things out.

And I found that Nat is wrong.

Let’s verify it together. Here’s the link to my working spreadsheet:

Spreadsheet: Nat is Wrong

I also embed the spreadsheet here so you can follow me closer.

Btw, it took me literally 10 minutes to generate the spreadsheet. Being able to spreadsheet fast is a superpower you won’t regret learning πŸ˜‰

My spreadsheet has several sheets, with tables and graphs. I recommend you to use a desktop/laptop instead of your smartphone.

First of all: where is inflation in all Nat’s formulas and graphs? We can’t get rid of it, we can’t use “today dollars” in our formulas, it makes everything more complex. And it’s not how raises work. Raises are always in nominal dollars.

Second, where are taxes? In theory a constant 5% gross raise translate in a diminishing net raise percentage because marginal tax rate increases with the growth salary. And if you consider taxes as expenses you’re screwed: good luck keeping marginal tax rate below 25%. Ok, let’s simplify this by only using take-home pay, i.e. net salary. All salary raises will be net salary raises for simplicity here.

First sheet: No Salary Raise – Exp Adj INFL

If you never get a raise, your expenses are anyway going up with inflation. Assuming 100k salary and 75k expenses, going up with inflation you reach Retirement in…

Wait, where is the Yellow line?

Oh crap, total Net Worth goes negative in 27 years because at one point expenses are greater than income and… things go south.

Of course this is a weird scenario. A scenario where you NEVER get a raise, not even to preserve the purchasing power of your salary with inflation.

Not realistic.

Note that using “nominal” amounts for salary and expenses means that the target is moving (green line).

To Retire you need to accumulate 25 times (i.e. 1/SWR) current expenses, which are growing with inflation.

Ok, let’s now assume you do get a raise every year, and that raise is identical to the inflation rate.

Second Sheet: Salary Raise INFL – Exp Adj INFL

Now you get a 3% raise every year (assuming 3% inflation).

This is the inflation adjusted scenario, where your salary and your spending level stay constant over your entire life, they just get adjusted for inflation.

This scenario reaches Retirement after slightly more than 35 years, in line with what Networthify suggests

… and not after 31 years like Nat wrongly assumed.

Mind that this is the scenario where your purchasing power and your spending regime never get inflated EVEN THOUGH you’re getting raises!

After the raise, you tell yourself: “Ok, the boss gave me a 3% raise, so my purchasing power didn’t change compared to last year… I should spend exactly like last year, i.e. increase nominal spending by 3% to keep up with inflation

What if we use Nat’s 75% formula? Should we allow our lifestyle to increase by only 25% of the raise, i.e. 0.75% in nominal dollar (less than the inflation)?

Are we doomed to get 12% annual raises to be able to inflate our lifestyle by 3% which barely keeps up with inflation?

Something is wrong. Inflation messes up with Nat’s formula.

Let’s see what happens in the 5% raise that Nat used in his post.

Third Sheet: Salary Raise 8% – Exp Adj INFL

Now I’m raising the salary by 8% each year, which is 5% “real” raise plus 3% inflation, which is my best guess of what Nat meant in his scenario: he compared this 5% raise to a scenario with zero raise and zero spending increase, which I assume it was my previous scenario, i.e. salary raise and inflation spending adjustment equal to inflation rate.

So, we now have a 8% nominal dollar yearly salary raise, cool!

Let’s see that happens if we don’t inflate our lifestyle at all, just raise our spending level by 3% to keep up with inflation:

Awesome, we can retire in 18 years!

It’s expected, isn’t it? We started with a 25% Saving Rate, and by the end of year 10 the Saving Rate is more than 50%! We got yearly salary raises, but we chose to spend the same amount, inflation adjusted.

Cool!

But we’re still increasing our spending level by 3% per year, which is more than 25% of the raise!

Ok, this is true on the first year, then the formula gets more complicated because Nat is binding his analysis on the “fraction of the raise” that we need to save, not percentage of current spending…

As a tangent, let’s see the scenario where we increase the spending by the same percentage amount of the yearly raise. I mean, keeping the Saving Rate constant.

Fourth Sheet: Salary Raise 8% – Exp Adj 8%

I’m still saving 25% of my income every year, I’m doing great! I expect retirement date to not change much over time:

What the fuck? Never retire? But I’m saving 25% of my income every year!

That’s because I’m assuming a 5% real dollar raise (and 5% real dollar lifestyle inflation), i.e. a 8% nominal dollar raise and spending increase, while investment returns grow by only 7%.

I’m never going to reach the goal because the invested money are losing purchase power (by 1%) in my overinflated world of earning 8% more and spending 8% more.

This scenario is identical of a hypothetical one with no raise, no spending increase, no inflation and a -1% return on investments.

Which is exactly what’s shown in the next sheet.

Fifth Sheet: Salary 0% – Exp 0% – INFL 0% – Returns -1%

A world with no inflation, no salary raise, no lifestyle inflation, a 25% saving rate… and a -1% return on investments:

And you’re never going to be FI even if you’re saving 25% of your income every year.

[You can see that the “ratio”, i.e. FIRE% (col I) is growing like the ratio in the previous spreadsheet]

Let’s move back to the main thread.

Sixth Sheet: Salary Raise 8% – Exp Adj 100% Salary Raise

Now we copy Nat’s scenario “5% annual raise, no savings increase“, which translates in 8% nominal raise, and only 25k USD saved each year.

Of course this means that the Saving Rate shrinks over time. After 30 years, 25k USD is just 3% of yearly income! You’re going nowhere. It’s much worse than scenario Four, where both salary and spending grow by same percentage.

Yeah, after 30 years we’re still at 10% FIRE, and a Saving Rate of 3%. Goodbye retirement.

Nat’s original analysis was also not rosy for this scenario, but reality is much much worse than Nat depicted.

We’re finally ready to verify Nat’s 75% Rule now.

Seventh Sheet: Salary Raise 8% – Exp Adj 25% Salary Raise

Now we’re getting a 8% nominal dollar yearly raise, and we increase our spending by just 25% of the nominal dollar raise. A bit of math in the spreadsheet and voilΓ :

Awesome! It works! We’re retiring in… 20 years?

Wait, weren’t we supposed to just hold with pre-raise retirement horizon (which was 35 years)?

What happened?

It happened that if you mix pre and post inflation numbers you get a mess!

We’re now increasing our lifestyle by 25% of the nominal dollar raise, but this is not even enough to cover inflation! We’re spending less than the scenario where we adjust expenses with inflation (Third Sheet), i.e. a 5% real raise / 0% real spending increase (or 8% nominal raise, 3% nominal spending increase).

I don’t think Nat meant this when he claimed that “we can increase our lifestyle by up to 27% and not slowing down our Retirement plans“. We’re not increasing our lifestyle at all, our expenses are not even keeping up with inflation!

I do think that to call something “a lifestyle inflation” it has to be “after adjusting spending level by inflation”, right?

So… how do we proceed now?

Let’s just try this: increase spending by inflation rate plus 25% of whatever’s left of the salary raise (excluding inflation).

I know it’s getting very complicated… and it will require you to do a lot of math when your boss gives you a raise: “ok, I got 10% raise, but last year I didn’t get a raise, so let’s account for 6.09% inflation over two years (3% compounded for two years), so I should raise my expenses by 6.09% + 25% of the remaining 3.91%, which is 7.0675%! Cool!

Not cool.

Anyway, let’s see if this complicated formula is actually working.

Eight (and final) Sheet: Salary 5%+INFL – Exp INFL + 25% Salary

As stated above: 8% raise, 3% inflation, expenses adjusted for inflation plus 25% of the actual raise.

Now we’re FI in 25 years, which is not connected with the initial 35 years… this 75% or 25% rule doesn’t mean anything.

We can try to tweak the parameters to see if there’s a constant percent we can splurge (after inflation) of any raise, but I doubt it makes sense. I played a little bit and found that there’s no rule.

The amount of your raise you could use for lifestyle inflation depends on all the other factors like real inflation, current market returns assumption, actual percentage of the raise, saving rate and so on.

If we want to keep – just for fun – the 8% (nominal) raise, 3% inflation and 7% (nominal) investment returns we get same scenario of pre-raise with a lifestyle inflation of 44% of the annual raise.

Like shown in the last scenario (real last one, promised).

Ninth Sheet: Salary 5%+INFL – Exp INFL + 44% Salary

It’s the rule of 56%?

Nope it’s not a rule. This percentage changes based on all the parameters πŸ™‚

There’s no rule, Nat was wrong.

Have a nice day!

 

P.S. I just saw this after publishing:

So… Nick is wrong as well πŸ™‚

Here’s their original Spreadsheet used for this analysis, which is indeed lacking inflation numbers everywhere.

12 comments

  1. Hi Mr RIP,
    Onde again nice analysis and what a spreadsheet kung-fu you have shown. You have too much free time in your hands but knowing how to really use a spreadsheet is a craft not everybody has, I don’t. πŸ™‚
    Now that we have in the “discussion” also Nick from Off Dollars and Data that I also read and learn with his math, let me seat back to see where this is going to. I hope they pick up your post.
    πŸ™‚
    Regards,
    Luis Sismeiro

    1. I have too much free time on my hands? You joking? I started a new job in September πŸ˜€

      About Nick and Nat:
      Nat’s post dated back to September 9th (14 days ago). I only read it two days ago, and immediately dropped everything I was doing to write this post. That’s how addicted I am πŸ™‚
      I interacted with Nat on twitter, who acknowledged his mistakes and appraised my analysis. And retweeted my post. Good guy Nat!
      Yesterday (September 22nd), a day after my post, Nick wrote a post to address Nat’s errors, and essentially he got “closer to the truth”. He thanked Nat for having inspired him to write that post. No mention to my analysis, but it’s ok… No it’s not!

      Anyway, Nick’s post seems an attempt to save something from an analysis which is flawed in many parts. Guys, don’t fall in sunk cost fallacy. If a line of thinking goes nowhere, let it die! Nick’s conclusion is that the amount of a raise you must save depends on your current saving rate, which is better than the constant 75% found by Nat (and produces similar results of my analysis for a 25% Saving Rate).

      But this analysis is also flawed: it uses the “shockingly simple math of earl retirement”, which implies a 4% SWR, models 3% inflation and 7% average expected portfolio returns. Change one of these parameters and Nick’s table is wrong again.

  2. Wow, RIP on steroids, 7 posts in one month! Always a pleasure to read. Nice insight!
    Lifestyle inflation + exponential functions = FIRE skyrocketing πŸ™‚

    We often realize about lifestyle inflation too late on the way to FIRE…or at least we find it hard to resist it. It’s human nature. I try to resist it but you know…you have a life, a wife, 3 kids…my gosh! Nat is a wise man but I agree, his “formula” doesn’t take into account such a complex environment.

    I also love spreadsheets.. Apart from the total savings rate, which is the number one monthly goal to reach, I suggest to try to find a way to counterbalance lifestyle inflation in some areas, with some spending review and cutting expenses in other areas. I mean you can try to fight inflation in some ways… for example you can try to lower the utilities bills by changing provider and being more conscious, you can try to be more mindful at the supermarket and try to find more things on discount…you can refinance your mortagage now if you have one…not easy but possible to some extent…I’m doing it in some way, but I’m not perfect.

    Tracking every expense to the cent is sooooo important!!! But life happens, they say

    1. Haha yes, and I’m assumed to be working on my new job. This should tell you how I feel right now πŸ™‚
      I’m not complaining about Nat not taking into account the complexity of life and the desire to increase your lifestyle, this is a purely math problem.

  3. Excellent Pos
    I guess the answer to this problem is a variable value and it is based on multiple variables. Hence I agree NAT is wrong.
    But it can be calculated ..
    To make the discussion short and to the point, you want to maintain the same saving rate before and after the salary increase … that will make the answer not dependent on your Sequence of Return risk assumptions and your desire SWR (4%, 3%, 2% or even 0.5%) ..

    I would take the value of the maximum margin tax of the increase of the salary.. this variable depend on the income level and location.

    t : 1 – Margin tax rate and other deductions for the income increase
    x: The original expense
    y: The original net salary (After Tax and Other deductions).
    z: salary increase
    g: spending increase
    Saving rate = (y – x)/y = (y + zt – x – g )/(y + zt)
    g = zt(-x – y + 1) + (y – 1) (x – y)

    The answer will need to be calculated based on all the above variable.
    Thanks for this discussion Mr. RIP.

    1. I think you’re right that the value depends on too many variables, and maybe it can be calculated (even though you can’t calculate for very possible sequence of returns).
      But.. I think it’s useless to have a forward, predictive model πŸ™‚

      The best way to calculate what you can do with a raise or with the temptation of lifestyle inflation is: have a forecasting model (like my FIRE Metrics), plug your new numbrs, see what the model says, and tune your expected spending level until the FIRE date pleases you. Much easier than theoretical speculation πŸ™‚

      And you might not just want to increase your lifestyle to just keep your Retirement date constant! You might want to play with it and slightly change plans.

      “Cool, I got a huge raise! I was planning to retire in 10 years, but let’s see what happens if I don’t change my spending level… awesome, I can retire in 7 years! Well, I’d like to splurge a bit, but also retire earlier than previously planned. Say 8 years instead of 10. Great, I can increase my lifestyle by 10% and still retire in 8 years instead of 10!”

      See? Such advanced analysis can’t be done with a table that tells you how much you can splurge, but with a slightly more complex (not much more) model.

      And btw, getting exact numbers for when you reach 100% FIRE is also pointless in my opinion. I’ve written so many times that I don’t think FI is a sharp line.

  4. A question that would come to my mind after this post, is there indefinite lifestyle inflation possible? I feel like I spend a pretty comfy lifestyle with my ~100k CHF in expenses and sure while I could buy a boat, a bigger house, multiple cars etc. I’m probably not doing that so I’m somewhat optimistic the lifestyle inflation will diverge towards 0% over time instead.

    1. Yes. Marginal utility. If you have a 2 bedroom dwelling, then acquiring an extra bedroom has a marginal utility of 50%. Though that 8th bedroom is a MU of about 14%.

      Financial planners like to assume your expenses increase linearly with your income. If my salary doubled, I know I would allocate most of the increase towards savings and investments, not spending.

      1. That’s because we’re finance savvy people, but that’s not true for regular people.
        We’re already living an inflated lifestyle by living in Switzerland. If I consider my spending level today and 10 years ago, my lifestyle inflated on average 26% per year…

  5. Ciao MrRIP.
    This is not a question about your disquisition on Nat’s argumentation.
    I only want to ask you if you know the software named: Notion. I think is very similar to Roam tool that you mention in the first lines (I just took a look at your link), or anyway, they could be used for the same outputs/objectives that is increase productivy and basically manage your life.
    If the answer is yes, in what do you think one is better than the other ?

    1. Yes, of course I know Notion. I’ve linked a couple of videos in other posts in this blog about it. I’ve seen few Thomas Frank Notion videos and read about it from other people.
      it never convinced me. It’s still “siloed”, and hierarchical (folder) driven. Roam is note-centric. It’s more a PKM, while Notion is more productivity oriented. But Roam is moving toward heavy customization and querying, which is very interesting.
      I hope I answered your question somehow πŸ™‚

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