Budget
What the government takes in, what it spends, line by line, and how non-player governments keep their debt under control. This page covers equations E8, E9 and E26.
In plain words
The budget has fifteen lines, eight for spending and seven for revenue, all as a percentage of GDP. Primary spending is the sum of the spending lines, and revenue is the sum of the revenue lines and of a few revenues that nobody sets (E26). Each revenue line gathers taxes whose rate the player sets (E35). The difference between revenue and spending is called the primary balance, and it also moves on its own when the economic cycle turns (E8). Non-player governments, for their part, follow a rule that aims for the balance that keeps their debt from drifting, correcting their course over several years (E9).
In the game
The player sets each spending line by its share of the budget and each tax by its rate. A spending line can range from 0 to 40 points of GDP, provided the total on its side does not exceed 80 points. In a democracy, parliament votes on each change, which takes effect on the 1st of the month after the vote (E25). If the country is shut out of the markets, it can no longer spend more than its revenue excluding the effect of the economic cycle, whatever the player decides (E16). France, left as it is, keeps its primary deficit of 4 points, so its debt enters the risk zone, where a confidence crisis drawn at random makes it default in February 2034, with debt of 156% of GDP. Non-player countries escape this, because their rule closes the deficit (§7.3).
The basics
Every year, the government collects revenue, mostly taxes and social contributions, and it spends money on schools, hospitals, pensions or the army. PREEMINENCE counts both as a percentage of GDP, the value of everything the country produces in the year. Revenue of 51% means that the government takes 51 euros out of every 100 euros produced in the country.
The primary balance is the difference between revenue and spending, not counting interest on the debt. When it is positive, the government runs a surplus. A negative balance signals a deficit, which the government has to cover by borrowing.
The budget also moves without anyone deciding anything. In a recession, taxes fall with activity while the spending that was voted stays the same in euros, so the deficit widens on its own, and a period of growth has the opposite effect. This mechanism is called the automatic stabilisers, because it cushions the ups and downs of the economy.
E8. The primary balance and automatic stabilisers
In plain words
The primary balance equals revenue minus spending, plus a term that follows the economic cycle. Each point of activity lost below the country's potential worsens the balance by about the share of spending in GDP, as it stood at the start.
With revenue of 51% of GDP and spending of 55%, the chosen balance is −4 points, and the share of spending gives a sensitivity of 0.55, which is France's. A recession that pushes activity 2% below its potential then takes away another 0.55 × 2 = 1.1 points, and the balance goes to −5.1 points without any decision having changed.
In the formula:
| Symbol | What it is | In the example |
|---|---|---|
| \(s\) | the primary balance, as a % of GDP | −5.1 |
| \(T\) | revenue | 51% |
| \(G\) | primary spending | 55% |
| \(\varepsilon\) | the sensitivity of the balance to the economic cycle, the share of spending at the start | 0.55 |
| \(\tilde y\) | the output gap (E1) | −2 |
Show the full formula and its sourcesEvery parameter with its source, and what the equation leaves out.
| Quantity | Value | Status | Source |
|---|---|---|---|
| ε, semi-elasticity of the balance to the output gap | the share of spending in GDP at the start, per country (France 0.55) | IMF, Fiscal Monitor of April 2015, chapter 2: the stabilisers are worth roughly the share of spending in GDP. Cross-checked: OECD average 0.44 (Girouard and André 2005), EU 0.50, from 0.30 (Bulgaria) to 0.63 (France) (Mourre, Poissonnier and Lausegger 2019) |
Why. Revenue follows GDP (elasticity close to 1: Belinga et al. 2014; Dudine and Jalles 2018), while voted spending stays fixed in euros. When activity falls by one point, the share of spending in GDP rises by as much, and the balance worsens by ε points. The model writes it this way: revenue stays a fixed share of GDP, and it is the share of spending that falls by ε points per point of output gap, G − ε ỹ. The balance is the same as if everything went through revenue. What changes is household income (E14). A tax that took a growing share of GDP in an expansion would take more from households than growth brings them. What it simplifies: unemployment benefits, which rise in recessions, are not distinguished from the rest of spending; they will come with the detailed budget.
E9. The budget of non-player countries
In plain words
A non-player government aims for a balance made of three pieces. The first keeps its debt from drifting, by paying what interest costs beyond what growth wipes out. The second adds an effort whenever the debt climbs back above the lowest level it has reached, while the third gradually corrects the gap the country had at the start. To reach this balance, the government adjusts only its spending, never its taxes, and it never lets spending fall below 5% of GDP.
Take debt of 110% of GDP, a long-term rate of 3.4% and nominal growth, inflation included, of 3.1%. For the debt to stay where it is, a surplus of (3.4 − 3.1) / 103.1 × 110 = 0.32 points is needed. If the debt has also climbed back 5 points above its low, the rule asks for 0.054 × 5 = 0.27 points more. A country that started with a balance 3 points too low corrects half of this gap in ten years. The studio chose ten years rather than five, because with five years all the non-player countries tightened their budgets at the same time, which caused a global slump around 2030.
In the formula:
| Symbol | What it is | In the example |
|---|---|---|
| \(s^{w}\) | the balance the government aims for | |
| \(i^{LR}\) | the long-term interest rate | 3.4% |
| \(\gamma\) | long-term nominal growth | 3.1% |
| \(d\) | the debt, as a % of GDP | 110 |
| \(\rho\) | the effort per point of debt above the low | 0.054 |
| \(d^{anc}\) | the lowest debt reached since the start | |
| \(\Delta_0\) | the starting gap, which halves in ten years | −3 |
| \(G_{\min}\) | the floor on spending | 5% |
Show the full formula and its sourcesThe exact form at the daily step, every parameter with its source, and what the equation leaves out.
with γ the long-term nominal growth, (1 + g*)(1 + π̄) − 1; iLR the long-term market rate (E10, with the policy rate at neutral), or, for a net lender state, the rate its savings actually earn; danc the lowest debt reached since the start; Δ₀ the gap, on the first day, between the country's balance and the balance that stabilises its debt. A country shut out of the markets (E16) spends no more than its structural revenue, whatever the rule says.
| Parameter | Value | Status | Source |
|---|---|---|---|
| stabilising term | — | Blanchard 1990: the primary balance that stabilises the debt ratio is (i − g) / (1 + g) × d | |
fiscal_debt_response ρ | 0.054 points of balance per point of debt | Bohn 1998, table I, United States 1916-1995 (0.028 to 0.054 depending on the period); Ghosh et al. 2013: 0.02 to 0.06 for moderate debts, 23 advanced countries | |
fiscal_half_life_days | 365 days | Bohn estimates on annual data: the balance responds to debt within the year | |
fiscal_consolidation_years | 10 years (half-life) | the horizon of a medium-term budget plan; the 2024 European framework spreads the adjustment over four years, extendable by three (Regulation (EU) 2024/1263). Five years would make all non-player countries tighten together and dig a synchronised global trough around 2030; ten years spread it out, which is what the studio chose | |
spending_floor G_min | 5% of GDP | the lowest share observed in 2024 among countries with more than one million inhabitants (Haiti, 5.2%, IMF): a debt that would require more is no longer serviced, and that is default |
Why. Bohn shows that governments raise their primary balance when their debt rises, and that this is what makes the debt sustainable; his coefficient alone does not stabilise the ratio when the gap between the interest rate and growth exceeds it. The rule therefore adds Blanchard's term, which exactly offsets the gap between the rate and growth. The debt of non-player countries no longer drifts, whatever this gap, and it returns towards the anchor at the pace ρ. On the first day, many countries are not at equilibrium (France has a primary deficit of 4% when 1% would stabilise its debt). They close this gap over a few years, not in one day. An adjustment of four points in one year would cause a recession that nothing in the data justifies.
The anchor. It is the lowest debt reached. A debt that inflation or growth has eroded is not borrowed again to return to the starting level. Without this, Sudan, whose 139% inflation eats its debt down from 263% to 86% in two years, would then borrow to push it back up, at the rates of a disinflation.
A lender state spends what its savings actually earn, as the Norwegian fiscal rule spends the expected return of its fund (a choice, argued this way). Planning on the long-term rate when savings earn more, as during a lasting high inflation, would make its assets grow without limit (Haiti at −900% of GDP in a hundred years).
What it simplifies. Governments adjust only spending, never taxes (real consolidations mix the two). The response does not weaken as debt grows, while Ghosh et al. (2013) find a “fiscal fatigue” from 90-100% of GDP, which turns negative around 150%; and many developing countries have a procyclical budget (Kaminsky, Reinhart and Végh 2004; Frankel, Végh and Vuletin 2012). Fiscal fatigue is not in the rule. Default (E16) came first, with its debt limit drawn from the same authors.
E26. The budget by lines
In plain words
The player does not set “revenue” and “spending” as a block. Primary spending is the sum of eight lines, from pensions to administration, and the player sets each of them by its share of the budget. Revenue is the sum of seven lines, such as income tax or VAT, together with revenue that nobody sets, such as oil rents, foreign aid, the government's own income and a few minor taxes. Each revenue line is the sum of what its taxes raise, and the player sets the rate of each of these taxes (E35). Because the rest of the model reads only the two totals, a point of GDP spent on pensions weighs on the economy as much as a point spent on education, and a point of VAT as much as a point of corporate tax. The studio knows this is a simplification, since studies measure different effects from one line to another. Interest on the debt is not a line, because the model computes it.
At the start, each country has the composition given by the data, scaled to its starting totals. If the player cuts VAT by one point of GDP and raises pensions by half a point, revenue loses one point, spending gains half a point, and the primary balance drops by one and a half points. Non-player governments do not touch their taxes, and when their rule changes their spending, each line follows the total in proportion.
The player reads and sets a spending line by its share of primary spending. When the player asks for a share, the other lines keep their amount, and the line receives what it needs to weigh that share of the new total. Say pensions make up 25% of a budget of 50 points, that is 12.5 points. If the player asks for them at 30%, the seven other lines keep their 37.5 points, pensions go to 0.30 × 37.5 / (1 − 0.30) = 16.07 points, and the budget to 53.57 points. The requested share waits for the vote and the 1st of the month, then turns into an amount on the day it applies.
In the formula:
| Symbol | What it is | In the example |
|---|---|---|
| \(G\) | primary spending, the sum of the eight spending lines | +0.5 |
| \(G_j\) | a spending line, such as pensions or health | pensions +0.5 |
| \(R\) | revenue | −1 |
| \(R_k\) | a tax, such as VAT or income tax | VAT −1 |
| \(A\) | other revenue, which nobody sets, held at its starting share | |
| \(\sigma'_j\) | the share of the budget requested for line \(j\) | 30% |
| \(G'_j\), \(G'\) | the line and primary spending once the share is applied | 16.07; 53.57 |
Show the full formula and its sourcesThe fifteen lines and their taxes, the start, the share of the budget, what non-player governments do, and what the equation leaves out.
The player does not set “revenue” and “spending” as a block. They set eight spending lines and the rate of fifteen taxes (E35, E38), and the two totals that the rest of the model reads (E8 to E11, E16) are the sums of fifteen lines.
| Side | Lines (name) |
|---|---|
| spending Gj | pensions (pensions), other social benefits (other_social), health (health), education (education), defence (defence), security and justice (security), economy and infrastructure (economy), administration and other (administration) |
| revenue Rk | income tax (income_tax), social contributions (social_contributions), VAT and general sales taxes (vat), excise duties (excises), corporate tax (corporate_tax), property taxes (property_tax), customs duties (customs); each one is the sum of what its taxes Rt raise (E35) |
| outside the levers A | other revenue: natural resource rents, foreign aid, the government's own income, and the minor taxes that no lever holds (taxes on exports, on services, on the use of goods, others); held at their starting share |
Interest on the debt is not a line, because the model computes it (E10). Once set, the pensions line follows the number of retirees and the rule for uprating pensions on every 1st of January (E59). What the player sets through it is each retiree's pension.
The start. The lines take the composition given by the data, rescaled to the model's starting totals, so the starting point does not move. On the spending side, each line equals its share of the measured lines, times primary spending. On the revenue side, each tax keeps its measured amount (VAT, which the data give as a single block, being shared out between its four rates, E38), a line is the sum of its own taxes, and the gap with total revenue forms the other revenue A. If the measured taxes exceed total revenue (sources with different scopes), they are scaled down in proportion and A is zero.
Non-player governments adjust their total spending through their rule (E9) and, during a default, cap it at their revenue (E16). Their lines follow this total in proportion. They do not touch their taxes.
The player sets each spending line between 0 and 40 points of GDP, and each tax by its rate (E35). A decision is refused if it takes the total on its side above 80 points, the former bound of the two totals. No player sets a revenue line. It comes from its taxes. A decision takes effect on the 1st of the following month, or after the vote in parliament (E25). A spending line follows the voting rules of spending, and a tax those of revenue.
The share of the budget. The player reads and sets a spending line by its share of primary spending, σj = Gj / G. Asking for the share σ′j leaves the other lines their amount and gives the line what it needs to weigh σ′j of the new total. Several shares asked for together (the set S) each take their share of the total that the other lines GO complete:
The sum of the requested shares stays below 100%. The order keeps the share. It waits for the vote and the 1st of the month as it was requested, and turns into an amount on the day it applies, on that day's budget, together with all the shares that apply on that day. The share requested is the share obtained, even when the player has given two orders in the same month. At the vote (E25), a share is weighed as the amount it would take on the day of the vote. Pensions at 25% of a budget of 50 points, requested at 30%, go from 12.5 to 16.07 points, the budget to 53.57, and each other line keeps its points. Non-player governments, which move their lines in proportion, do not change their shares.
What the screen shows. For a changed line or tax, what the change does to the budget balance over one year, in dollars: the gap in points of GDP, times current nominal output, positive when money comes in. It is a conversion, not a forecast. It does not count what the change will do to output.
What it simplifies. All the lines on one side have the same effect on the economy. A point of GDP of pensions weighs like a point of investment, and a point of VAT like a point of corporate tax. These are the spending and tax multipliers of E8 and E9. Studies measure different effects depending on the line. Telling them apart would be a new equation, which remains to be decided. The other revenue is frozen as a share of GDP, with no link to oil prices or aid.