Growth and demand
What a country produces, compared with what it could produce without overheating, and what makes the gap between the two change. This page covers equations E1 and E2.
In plain words
Every country has a potential GDP, which grows at its own pace (E2), and the output gap tells you how far the economy is running above or below this potential. Two things move this gap (E1). A high interest rate slows activity down, while a budget that has just become more generous pushes it up.
Almost everything else in the game depends on it, be it inflation (E4), unemployment (E6), the central bank's rate (E7) or the budget (E8).
In the game
Every month, the dashboard publishes real GDP growth over twelve months. This is where the player's decisions on the budget lines and on the policy rate take hold, and they take effect on the 1st of the following month or, for the budget, on the 1st of the month after parliament's vote (E25). For France played without shocks, after one year, cutting revenue by two points adds 0.68 points to the output gap and raising spending by as much adds 2.03, whereas raising the rate by two points takes away 0.36. The effect of the rate builds up slowly and reaches 1.26 points after five years (§7.3).
The basics
GDP measures everything a country produces in a year, and when it rises, we call it growth.
Every country has a cruising speed, set by its factories, its workers and its techniques, which matches what it can produce without overheating. The model calls it potential GDP. In some years, the economy runs faster than this pace, so firms hire to keep up with orders and prices rise. In other years, it runs more slowly, sales fall and unemployment rises.
The gap between actual output and potential, as a percentage, is called the output gap. When it is positive, the economy is overheating, and when it is negative, it is running below capacity. The model uses it as a thermometer.
The interest rate is the price of borrowed money. When it rises, households buy less on credit and firms invest less, so activity slows. But the rate that weighs on these decisions is the real rate, that is, the rate minus expected inflation, because borrowing at 5% when prices are rising by 5% costs almost nothing.
The budget works differently. A rise in public spending or a tax cut gives activity a boost that fades after a few years, even if the measure stays in place.
E1. Demand
In plain words
When the real rate is above its neutral level, the output gap falls, but not straight away, because the rate takes months to feed through to loans and projects. Output therefore keeps falling after the rate has stopped rising. In the long run, each excess point of real rate takes 0.64 points off the output gap, and this effect stops growing beyond 10 points above or below neutral. The studio has set this cap because the relationship is measured close to equilibrium, and because applying it to a real rate of 100 points, which a player who sets the policy rate at 300% would face, would call for a 64% fall in GDP.
The budget, for its part, acts through its changes and not through its level. In an advanced country, one extra point of GDP in spending adds 0.75 points of output on average in the first year, then the effect shrinks and output returns to its potential.
For example, in an advanced country, the central bank raises its rate by one point and keeps it there for a year, while expected inflation does not move. Output reaches its low point in the 18th month, at −0.26%, then recovers. Studies place this trough between 18 and 24 months without measuring the delay that produces it, so the studio has tuned this delay to make the trough fall within their range. If the government spends one point of GDP more and sticks to it, the output gap averages 0.70 points in the first year, then 0.89, 0.53, 0.26 and 0.12 in the following years (§7.2).
In the formulas:
| Symbol | What it is | Advanced country |
|---|---|---|
| \(i\) | the policy rate | |
| \(\pi^e\) | expected inflation (E3) | |
| \(r^*\) | the real neutral rate, which neither slows nor pushes activity | |
| \(\hat r\) | the real-rate gap as households and firms feel it, with a delay | |
| \(\tilde y\), \(\tilde y^{*}\) | the output gap, and the value it is heading towards | |
| \(\beta_{RR}/(1-\beta_{lag})\) | what one point of real rate takes away in the long run | 0.64 |
| \(G - \bar G\), \(T - \bar T\) | spending and revenue, minus their average over the past year | |
| \(k_G\), \(k_T\) | the coefficients that give the published multipliers | 2.57 and 0.86 |
| \(c\) | the cap on the real-rate gap | 10 points |
Show the full formula and its sourcesThe exact form at the daily step, every parameter with its source, and what the equation leaves out.
| Parameter | Value | Status | Source |
|---|---|---|---|
demand_persistence β_lag | 0.75 per quarter | Berg, Karam and Laxton 2006: 0.50 to 0.90 | |
rate_sensitivity β_RR | 0.16 points of output gap per point of real rate, per quarter | within the range of Berg, Karam and Laxton 2006 (0.10 to 0.25 for the sum of the effects of the real rate and the exchange rate): the value that, together with the lag ρ_r, puts the output trough at −0.25% per point of rate, the average effect corrected for publication bias (Enzinger et al. 2025) | |
rate_transmission_persistence ρ_r | 0.75 per quarter | the lag that places the output trough in the 18th month when the rate rises by one point for a year: studies put it between 18 and 24 months (Enzinger et al. 2025) | |
real_rate_gap_cap c | 10 points | see below | |
spending_multiplier | 0.75 / 0.2 / 0.2 | Batini et al. 2014: 0.75 in the first year for advanced countries (41 studies compiled by Mineshima et al. 2014); 0.1 to 0.3 for emerging countries (Ilzetzki 2011); low end, 0.1 to 0.3, for low-income countries | |
tax_multiplier | 0.25 / 0.3 / 0.2 | Batini et al. 2014: 0.25 (advanced); 0.2 to 0.4 (emerging, Ilzetzki 2011); low end (low-income) | |
fiscal_memory_years | 1 year | the impulse is the change in the budget over one year, as the IMF measures it |
Why. A real rate above the neutral rate slows demand; over the long run, each excess point of real rate removes β_RR / (1 − β_lag) = 0.64 points of output gap. It acts as it is felt. r̂ is the real-rate gap that reaches loans and spending plans, and it follows the central bank's gap with a delay. This gives a bell-shaped response, as in the studies. Output keeps falling for several months after the rate has stopped rising. The budget acts through its impulse. It is not the level of spending that supports demand, it is the change in spending. A lasting increase boosts activity while it is new, then output returns to its potential. The coefficients k_G and k_T are not parameters. They are computed so that the average output gap in the first year, per point of GDP of budget, is exactly the published multiplier (advanced: k_G = 2.57, k_T = 0.86). The resulting profile follows the one the IMF uses in its projections (Batini et al. 2014, table 9: 0.8; 1.0; 0.6; 0.3; 0 over five years). The model gives 0.70; 0.89; 0.53; 0.26; 0.12 for a multiplier of 0.75, which is the same shape to within one hundredth over the first four years (§7).
The cap c. The relation is estimated close to equilibrium. Applied to a real rate of 100 points (a player who sets the policy rate at 300%), it would call for a 64% fall in GDP. Beyond 10 points above or below the neutral rate, the real rate pushes no further. Ten points is a choice. The cap only bites in extreme situations (the Argentine disinflation, a policy rate of several hundred per cent set by a player). The same cap bounds the Taylor rule (E7) and the market rate (E10), so that the three stay consistent.
The transmission lag is not taken from a study that would estimate it in this form. It is a calculation, the value that places the trough where the studies measure it. The IMF model gets the same bell another way, through forward-looking expectations and a rate that stays high; a backward-looking model needs an explicit lag. With this lag, a one-point rise for a year removes 0.26% of output in the 18th month, and the price level falls by 0.065% after five years in advanced countries and by 0.13 to 0.15% in emerging ones, against 0.15% in the studies once corrected (§7.2).
What it simplifies. There is no exchange-rate channel. Advanced countries miss it most, because their Phillips curve is flat and the rate works through the currency as much as through demand (§8.2). The same multiplier applies whatever the cycle, the debt level or the exchange-rate regime, while the literature finds multipliers larger in recessions, at the lower bound of the policy rate and under fixed exchange rates (Batini et al. 2014; Ilzetzki, Mendoza and Végh 2013). Taxes do not change potential GDP.
E2. Potential GDP
In plain words
Potential GDP grows every day at the country's potential growth rate, which does not change, and real GDP equals this potential raised or lowered by the output gap. The player has no hold on their country's long-term growth, since nothing they do changes potential GDP.
France has potential growth of 1.1% a year in the model, which makes its potential rise by about 0.003% a day and by 1.1% in a year. If its economy is running 2% below, its real GDP equals 98% of potential.
Show the full formula and its sources
g* is the country's potential growth (§6): the IMF projection for 2029-2030, which assumes the gap has closed, or failing that the median growth over 2010-2019 (World Bank). What it simplifies: potential GDP depends on nothing the player does, neither public investment, nor reforms, nor hysteresis. These are increments (§9).