Can We Grow Out of This?
Imagine you’re in charge of America’s money. Now What?
You just became U.S. Treasury Secretary. The Fed isn’t lowering rates for you. The government spends more than it collects, debt keeps growing, and borrowing is expensive.
Your job: make the math work.
So, what do you do?
Raise taxes? Cut spending? Change how the government borrows?
Hope inflation cools? Or simply wait …?
There are plenty of levers to pull.
But underneath almost all of them sits one surprisingly simple piece of math.
So, let’s see .⇩
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The Formula for Trouble.
The debt sustainability formula ↓
It looks intimidating. It really comes down to three things:
r → What does the debt cost?
The average interest rate the government pays.
g → How fast is the economy growing?
Nominal GDP growth — real economic growth plus inflation.
Primary Balance → Are we adding to the tab?
Government revenue minus spending, before interest payments.
Strip away the notation and you get a pretty simple race:
g > r → 👍 Debt gets easier to carry
r > g → 😬 Debt gets harder to carry
There is one important catch: r > g does not mean debt automatically rises even if the government spends nothing extra. The primary balance still matters. A sufficiently large primary surplus can offset the unfavorable r − g effect; a primary deficit makes it worse.
So the real assignment isn’t simply “get g above r.”
It’s: Grow faster. Borrow cheaper. Run a smaller primary deficit.
Preferably, all three. ↓
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Now, Let’s Run the Numbers.
One caveat before the arithmetic. These are rounded, illustrative estimates based on the figures we’ve covered — not an official CBO or Treasury forecast.
Step 1 — Start With the Scoreboard
→ Debt held by the public: ~$32T
→ Nominal GDP: ~$30T
→ Debt-to-GDP: ~107%
In other words, for every $1 the U.S. economy produces in a year, there’s roughly $1.07 of publicly held federal debt.
Now our three variables:
1) r ≈ 5% — our illustrative borrowing-cost assumption, roughly in line with current long-term Treasury yields.
2) g ≈ 5% — roughly 2% real growth + 3% inflation.
3) Primary deficit ≈ 3% of GDP — Washington is spending more than it collects even before interest enters the bill.
Which gives us an unusually neat starting point:
r ≈ g
The interest-growth part of the equation is basically a draw.
Unfortunately, the budget isn’t.
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Step 2 — Which One Is Winning: r or g?
Using our illustrative 5% assumptions:
r (5%) − g (5%) ≈ 0%
That little zero does a lot of work.
If r − g ≈ 0, then: (r − g) × Debt-to-GDP ≈ 0
In plain English, the debt burden isn’t getting meaningfully heavier or lighter from the interest-vs.-growth relationship alone.
So what determines which way the debt ratio moves?
The other half of the equation: the primary balance.
And unfortunately, that number isn’t zero.
Step 3 — Now Add the Deficit.
With r − g ≈ 0, that whole side of the equation essentially cancels out.
What’s left?
Change in Debt-to-GDP ≈ Primary Deficit
Using our illustrative 3% primary deficit:
0% + 3% ≈ +3 percentage points
So debt-to-GDP would rise by roughly 3 percentage points per year simply because the government is spending more than it collects before interest.
✱ Put differently: even if r and g behave perfectly, the debt ratio can still keep climbing.
Step 4 — Now Turn Up the Interest Rate.
Now let’s make borrowing more expensive.
If r rises from 5% to 6%, while g stays at 5%:
r − g = +1%
Apply that gap to our illustrative 107% debt-to-GDP ratio:
1% × 107% ≈ +1.1 percentage points
Then add the 3-point primary deficit from Step 3:
+1.1 + 3.0 = +4.1 percentage points
So instead of debt-to-GDP rising roughly 3 points a year, it rises about 4.1 points — nearly 40% faster in this simplified example.
✱ And that’s the uncomfortable part about higher rates:
A one-point move in r doesn’t sound like much. On a debt pile this large, it is.
Step 5 — What If Growth Wins Instead?
Now flip the experiment.
If g rises to 6% while r stays at 5%:
r − g = −1%
Apply that to our illustrative 107% debt-to-GDP ratio:
−1% × 107% ≈ −1.1 percentage points
This time, the math is working for the government.
Add the 3-point primary deficit:
−1.1 + 3.0 = +1.9 percentage points
Debt-to-GDP is still rising — but by roughly 1.9 points instead of 3.
Just one extra point of nominal growth.
✱ That’s the arithmetic behind all those productivity stories about AI, automation and investment. Faster sustainable economic growth doesn’t magically erase the debt.
But it makes the denominator considerably bigger.
Step 6 — The Lever Washington Actually Controls.
There’s another way to change the equation without hoping for faster growth or waiting for markets to lower borrowing costs:
Change the primary balance.
Suppose the primary deficit falls from 3% of GDP to 1%.
If r ≈ g, our simplified math becomes:
0 + 1% ≈ +1 percentage point
Instead of debt-to-GDP rising roughly 3 points per year, it rises about 1 point.
That’s a 2-percentage-point improvement without requiring r or g to move at all.
And unlike Treasury yields or economic growth, the primary balance is the part policymakers can influence most directly — through spending and taxes.
✱ The problem?
Those are also the two buttons everyone notices when you press them.
Three Ways Out.
At this point, the equation leaves you with three basic options.
1 Lower r — make the debt cheaper.
Lower borrowing costs make the math easier. That’s why lower rates are so attractive when the government is carrying trillions in debt. The catch: the Fed’s job is inflation and employment, not making Treasury’s interest bill smaller. And Treasury buybacks can improve liquidity in the bond market, but they don’t set the interest rate on new debt.
2 Raise g — make the economy bigger.
This is the nicest answer on paper. Faster real economic growth raises nominal GDP without requiring spending cuts or tax increases. It’s also the math underneath all those AI-productivity forecasts: if technology can sustainably make the economy grow faster, g gets a boost — and the debt gets a bigger denominator.
3 Improve the primary balance — spend less, collect more, or both.
This is the lever policymakers control most directly. Shrinking the primary deficit reduces the amount being added to the debt equation. Unlike hoping for lower yields or a productivity boom, Congress can legislate changes to spending and revenue.
Unfortunately, it’s also the option that requires someone to actually give something up.
Cheaper money. Faster growth. Smaller deficits.
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