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Deficit and the public balance
One word, several numbers: which deficit are we talking about, and how does it become debt?
Balance = Revenue − Spending; Debt₁ = Debt₀ + DeficitProblem / motivation
“France is in deficit.” The phrase comes back every year — but it covers at least four different numbers, and the one quoted on the news is not the deficit of the state's budget.
The principle itself fits into one subtraction: on one side what the administrations collect (revenue), on the other what they pay out (spending); the difference is the BALANCE. If it is negative, we speak of a deficit. All the rest — and this is where the course really begins — consists in knowing WHO is being talked about (the state? social security? municipalities?), over which year, and how one year's hole becomes a stock of debt. Two writing conventions to start with: “€bn” reads “billions of euros”, and GDP is the value of everything produced in the country in a year (course “GDP”) — the yardstick everything is related to, because €150bn does not weigh the same in France as in Luxembourg.
This course works on REAL figures: the 2025 accounts of French general government, published by INSEE in March 2026. We shall do three things there that evening commentary rarely does out loud — break the deficit down between the four administrations that produce it, check that end-of-year debt really is start-of-year debt plus the deficit (it is not quite, and the gap can be explained), and understand why the debt/GDP RATIO can rise more slowly than the debt itself, or even fall while it rises.
Assumptions
In your view, which assumptions are needed for this model to hold? Jot down your ideas — no lead is wrong, this is your worksheet.
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0 idea(s) proposedFormalization
Before any subtraction, the perimeter has to be fixed. The national accounts file under “general government” four families: the STATE (the ministries, the budget voted in Parliament); the central government bodies the state funds and steers (universities, the CNRS, the meteorological office); LOCAL government (municipalities, departments, regions); and SOCIAL SECURITY bodies (health insurance, pensions, unemployment insurance). When a newspaper announces “France's deficit”, it means all four together — never the state alone. The public balance is the sum of their four balances, and the figure below shows how the €152.5bn of 2025 is split between them.
For each of them, and for the whole: Balance = Revenue − Spending. The official vocabulary speaks of net LENDING when the balance is positive and net BORROWING when it is negative: the same number, named after its sign. And that is where the subject's trap lies — France's balance in 2025 is −€152.5bn, while its deficit is +€152.5bn. In other words Deficit = −Balance: the shortfall is stated as a positive. A text that writes “a deficit of −152.5” counts the minus sign twice.
A hole in the year has to be filled: the state borrows what is missing. End-of-year debt is therefore start-of-year debt, plus the year's deficit: Debt₁ = Debt₀ + Deficit. This chaining — and it alone — turns a series of annual flows into a stock, and it gives the poll's answer: as long as the deficit is positive, we ADD, so the debt rises; halving it only slows the climb. In practice the equality is not perfect to the nearest billion, because a state also borrows for things other than filling its hole; that gap term has a name, the deficit-debt adjustment, and we shall put a figure on it for 2025.
That leaves making these amounts readable: we divide them by the same year's GDP. The deficit becomes a rate (152.5 / 2,994.7 = 5.1%), the debt a ratio (115.6%). A debt ratio above 100% is not absurd: we are comparing a STOCK accumulated over decades with one year's FLOW, exactly as a mortgage is compared with an annual salary — nobody is astonished at borrowing three times their annual income. And since the denominator moves too, the ratio can rise more slowly than the debt, or even fall while it rises. Here are the two relations, to be clicked term by term:
Solving / calculation
Let's take the 2025 accounts of French general government, published by INSEE on 27 March 2026. Eight stages: who digs the deficit, how much it is, what it weighs against GDP, what it becomes as debt, why the ratio rises more slowly than the debt (in two steps: the denominator, then the numerator), what deficit would have been enough to stabilise it, and what is left of it once interest is set aside.
- The perimeter: four administrations, four balances (€bn)
−128.1 (state) − 2.1 (central bodies) − 15.6 (local) − 6.7 (social security)public balance = −€152.5bn - The same thing through the narrative's subtraction (beat 2)
1,561.6 (revenue) − 1,714.1 (spending)−€152.5bn — both routes land on the same number - As a % of GDP (€2,994.7bn) — and the deficit is stated as a positive
152.5 / 2,994.7 × 100≈ 5.1% of GDP (European threshold: 3%) - From flow to stock: the debt expected at end-2025 (beat 3)
3,306.1 (debt at end-2024) + 152.53,458.6 expected against 3,460.5 observed → adjustment = +€1.9bn - The ratio moves at BOTH ends — first the denominator (GDP gained 2.0% in value)
the SAME end-2024 debt against 2025 GDP: 3,306.1 / 2,994.7 × 100110.4% — the ratio has already lost 2.2 points without a euro being repaid - Then the numerator: we add the year's deficit and the adjustment
110.4 + 5.1 (deficit) + 0.1 (adjustment)= 115.6% of GDP, that is +3.0 points in a year - What deficit would have left the ratio EXACTLY unchanged? (adjustment aside)
the debt merely has to grow at the same pace as GDP: deficit* = Debt₀ × g = 3,306.1 × 2.0%€66.1bn — against 152.5 in reality: there is the gap that cost 3 points of ratio - Once debt interest (€64.7bn) is set aside: the primary balance
−152.5 + 64.7−€87.8bn, that is −2.9% of GDP
One country, one year, and already four numbers: €152.5bn of public deficit (5.1% of GDP), of which 128.1 for the state alone; €87.8bn once interest is set aside — the primary balance, the one that steers the debt in the course “The dynamics of public debt”; and, according to the High Council of Public Finances, 4.7 points of STRUCTURAL deficit (measured against potential GDP), the part that will not disappear with the recovery (interpretation, point 1). On the debt side, keep stages 5 to 7: it gained €152.5bn, but the ratio only took 3 points, because GDP grew by 2.0% meanwhile — and €66.1bn of deficit would have been enough to leave it untouched. The deficit feeds the debt; growth dilutes it. The whole of the public debate sits in the race between those two forces.
Balance = Revenue − Spending; Debt₁ = 3,460.5 + Deficit; ratio₁ = Debt₁ / GDP₁The starting point is fixed on reality — debt €3,460.5bn and GDP €2,994.7bn at end-2025 — and the following year is yours to play (the sliders start from the 2025 accounts, rounded to whole numbers). The threshold of stage 7 is not fixed: push growth and watch the “deficit that would leave the ratio unchanged” move with it — at zero growth, it falls to zero, and only a balanced budget still stabilises the ratio.
Economic interpretation
Three readings so as not to have the wrong conversation: which deficit is meant, what Europe really requires, and how a state differs from a household.
The ACTUAL balance is the one in the accounts: −5.1% of GDP in 2025. The PRIMARY balance takes out debt interest: −2.9%. The STRUCTURAL balance takes out the effect of the cycle — because in a recession revenue comes in less and unemployment spending rises on its own (the automatic stabilisers); in France, that cyclical component is worth about 55% of the output gap, the gap between actual GDP and what would be produced at a normal pace. The High Council of Public Finances' verdict for 2025: the structural component is worth 4.7 points of potential GDP, against 5.1 points of actual deficit. In other words, the cycle and one-off measures explain only about 0.4 point: waiting for the recovery would close almost nothing, and the rest requires decisions. A fourth number, finally, the one heard in Parliament in the autumn: the state's BUDGET deficit, a narrower perimeter (the state alone) and different accounting — another figure, in another document.
The famous 3% of deficit and 60% of debt are written into a protocol annexed to the European treaty: two legal reference values, set at Maastricht in 1992. Contrary to what is often read, they are not independent of each other — and the rule of stage 7 shows it in one line. A deficit of 3% of GDP stabilises EXACTLY a debt of 60% of GDP as soon as GDP grows by 5% a year in value: 60 × 5% = 3. The two thresholds therefore form a coherent pair, on the assumption of 5% nominal growth — the rate considered normal in the early 1990s, when inflation was higher than today. What they are not, on the other hand, is a demonstrated optimum: nothing establishes that 60% is the right level of debt, and what theory says about sustainability is the subject of the course “The dynamics of public debt”. Since the reform that came into force in April 2024, steering is no longer done through these thresholds alone but through a NET SPENDING PATH each state commits to over four to seven years. And “excessive deficit” is not an arithmetic label awarded as soon as you hit 3.1%: it is a procedure opened by a decision of the Council, which also looks at debt and other factors. France has been under that procedure since 26 July 2024, with a return below 3% targeted for 2029. The fines provided for — up to 0.05% of GDP per half-year — have to this day never been applied to any country.
A household must have repaid everything by the end of its life; a state need not: it ROLLS its debt, issuing new securities to repay the ones falling due, indefinitely. The mortgage analogy of beat 4 therefore holds for the ORDER OF MAGNITUDE of the ratio — comparing a stock with an annual income — not for the constraint. The real constraint is the one in assumption 4: finding a taker, at a rate you do not set. And it has a cost that is already visible: in 2025, interest cost the administrations €64.7bn, up 11.2% in a year. That is 42% of the year's deficit: a little more than two euros in five of the hole go to paying for yesterday's borrowing. That euro is committed before any political arbitration, and it is what makes the interest rate central (courses “Bond prices and interest rates” and “The dynamics of public debt”).
Limits / critiques
Exercises
“France's deficit comes to €152.5bn in 2025.” Which perimeter is meant?
That same €48bn deficit for a GDP of €1,200bn: what percentage of GDP (in %)?
Debt €900bn, GDP €1,000bn (ratio 90%). The following year: a deficit of €20bn, and GDP in value grows by 4%. What is the new debt/GDP ratio (in %, one decimal)?
Public balance = −€60bn, debt interest paid during the year = €25bn. What is the PRIMARY balance, with its sign (in €bn)?
Revenue = €620bn, spending = €668bn. What is the public BALANCE, with its sign (in €bn)?
Debt at end-2029: €900bn. Deficit for 2030: €40bn. Neglecting the deficit-debt adjustment, what is the debt at end-2030 (in €bn)?
Starting debt €900bn, GDP growth in value of 3%. What deficit (in €bn) would leave the debt/GDP ratio EXACTLY unchanged?
True or false: if growth returned to its normal pace, the French public deficit would disappear.