Central bank
How the central banks of non-player countries set their rate, and how all central banks gain or lose the public's trust. This page covers equations E7 and E17.
In plain words
Every central bank has an inflation target. When inflation rises, the bank raises its rate by more than inflation itself, which cools the economy (E7). It also has a reputation. As long as inflation stays close to the target, people trust it and expect the target, but if it lets inflation settle in, this trust wears away and inflation becomes harder to bring back down (E17).
In the game
In their own country, the player sets the policy rate themselves, between −1% and 500%, and the decision takes effect on the 1st of the following month. The Taylor rule therefore only steers the central banks of the other countries, which respond less to inflation when the head of government is strongly populist (E24). Credibility, on the other hand, counts everywhere, and the dashboard publishes it every month.
The basics
A country's central bank, such as the ECB for the euro area or the Fed in the United States, sets the policy rate, that is, the rate at which banks borrow from it. This rate then passes through to all loans, those of households, of firms and of the government.
Its main mission is to keep inflation close to a target. When prices run away, it raises its rate, and since borrowing then costs more, people spend less, the economy slows and prices calm down. When the economy runs out of steam, it lowers its rate to revive it.
To really slow things down, the rate must rise faster than inflation, because if inflation goes from 2% to 4% and the rate also rises by two points, the real cost of a loan has not changed. This is why the Taylor rule, named after the economist John Taylor, calls for raising the rate by one and a half points for each extra point of inflation.
A credible central bank does not need to hit hard, because people believe it will bring inflation back to the target. One that has lost people's trust, by contrast, sees each price rise feed the next one.
E7. The Taylor rule
In plain words
The rate the central bank aims for starts from the neutral rate, that is, the real rate that neither slows nor pushes the economy. Expected inflation is added to it, then half of the gap between expected inflation and the target and half of the output gap, but this response never exceeds 10 points, and the rate does not fall below a floor. The central bank does not jump to the rate it aims for in one go but covers half the distance in 269 days.
Taylor made his rule react to inflation over the past year. The studio makes it react to expected inflation, because, with a rule that looks at the past, Argentina, which is bringing 220% inflation back towards its target, would keep a rate far above the inflation to come and would pay real rates of a hundred points on its debt.
Take a country whose potential growth is 1.5%, which puts its real neutral rate at 1.5 − 0.92 = 0.58%. Its target is 2%, expected inflation is 4%, and the economy is running at its potential. The rate it aims for is then 0.58 + 4 + 0.5 × (4 − 2) = 5.58%, a real rate of 1.58%, above the neutral rate, and the central bank is braking. If the economy were running 2% below its potential, it would aim one point lower, at 4.58%.
In the formula:
| Symbol | What it is | In the example |
|---|---|---|
| \(i^{T}\) | the rate the central bank aims for | 5.58% |
| \(i\) | today's policy rate | |
| \(r^{*}\) | the real neutral rate, potential growth minus 0.92 points | 0.58% |
| \(\pi^e\) | expected inflation (E3) | 4% |
| \(\bar\pi\) | the target | 2% |
| \(a_\pi\), \(a_y\) | the response to inflation and to the output gap | 0.5 and 0.5 |
| \(\tilde y\) | the output gap (E1) | 0 |
| \(c\) | the cap on the response | 10 points |
| \(i_{\min}\) | the floor on the rate | −0.5% |
Show the full formula and its sourcesThe exact form at the daily step, every parameter with its source, and what the equation leaves out.
| Parameter | Value | Status | Source |
|---|---|---|---|
taylor_inflation a_π | 0.5 | Taylor 1993: 1.5 on inflation in total, i.e. 0.5 on its gap to the target | |
taylor_output a_y | 0.5 | Taylor 1993 | |
rate_smoothing | 0.79 per quarter | Clarida, Galí and Gertler 2000: the Fed under Volcker and Greenspan, 1979-1996 (half-life: 269 days); range of Berg et al. 2006: 0.50 to 1.0 | |
rate_floor i_min | −0.5 / 0 / 0% | ECB at −0.50% from 2019 to 2022 and Sweden at −0.50% in 2016; no emerging country below 0.1% since 2015 (BIS policy rate database, 49 economies) | |
neutral_rate_gap δ_r | −0.92 points | Holston, Laubach and Williams 2017, updated estimates (2026Q2): average gap between the neutral rate and trend growth, (1.01 − 2.41 + 1.76 − 1.94 + 0.09 − 1.27) / 3 for the United States, Canada and the euro area |
Why. The central bank raises its rate by more than inflation (1.5 times). This is what makes the real rate rise when inflation rises, and it closes the monetary loop. Taylor based his neutral rate of 2% on trend growth (2.2%); the model keeps this reasoning, corrected for the gap that Holston, Laubach and Williams measure between the two. It gives 0.90% for the United States (their estimate: 1.01%).
Two departures from Taylor (1993), to be validated. 1) The rule responds to expected inflation, like the estimated rules of Clarida, Galí and Gertler and the rule of the IMF model; Taylor used the last four quarters. The difference only matters when inflation falls fast. On past inflation, Argentina, which brings 220% back towards its target, would keep a policy rate far above future inflation, and would pay real rates of a hundred points on its debt. 2) The response is capped at c = 10 points, the cap of E1.
What it simplifies. There is no monetary union (each euro-area country has its own central bank here, §9). There is no response to the exchange rate, which emerging central banks practise (Mohanty and Klau 2004). The neutral rate of emerging and low-income countries is extrapolated from that of advanced countries. India, which starts from its observed rate of 6.5%, is brought by the rule towards 9.6%. The starting point: the December 2024 rate where the BIS publishes it (58 countries, euro area included), the rule's rate elsewhere.
E17. The central bank's credibility
In plain words
Every day, the model compares published inflation with two forecasts made three months earlier. The first is the forecast of a credible central bank, which brings inflation back towards its target, and the second is that of a central bank that has lost control and lets inflation drift towards 7 points above the target. The signal is close to 1 when inflation looks like the first forecast and close to 0 when it looks like the second. Credibility moves slowly towards this signal.
Since the second forecast lies above the target, inflation that is too high costs more credibility than inflation that is too low. The studio knows the limit of this mechanism, whose settings come from countries with moderate inflation. A country that starts from high inflation stays trapped there, since nothing in the game gives its credibility back at a stroke the way a stabilisation plan would, restoring it all at once in exchange for putting the budget back in order. Without shocks, Turkey and Nigeria are thus still at around 18% inflation after twenty years, against a target of 10%.
Take a target of 3%, with inflation of 6% three months ago. The credible bank then forecast 0.4 × 6 + 0.6 × 3 = 4.2%, and the one that has lost control 0.8 × 6 + 0.2 × 10 = 6.8%. Published inflation today is 5%, closer to 4.2 than to 6.8, so the signal is 0.84 and credibility rises. If inflation had reached 7%, the signal would have fallen almost to zero.
In the formula:
| Symbol | What it is | In the example |
|---|---|---|
| \(\pi^{L}\) | the credible bank's forecast | 4.2% |
| \(\pi^{H}\) | the forecast of the bank that has lost control | 6.8% |
| \(\pi^{12}\) | published inflation (E5) | 5% |
| \(\nu\) | today's signal, from 0 to 1 | 0.84 |
| \(\psi\) | credibility, which follows the signal |
Show the full formula and its sourcesThe exact form at the daily step, every parameter with its source, and what the equation leaves out.
Two forecasts are made one quarter earlier: that of a credible regime, which brings inflation back towards the target (πL), and that of a de-anchored regime, which takes it to 7 points above the target and leans more on the past (πH). Inflation close to the first forecast gives a signal ν close to 1, and inflation close to the second a signal close to 0; the stock of credibility ψ follows the signal. It modulates the anchoring of expectations (E3). At the start, ψ equals the signal of the starting inflation, compared with itself.
| Parameter | Value | Status | Source |
|---|---|---|---|
credibility_persistence | 0.75 per quarter | Chansriniyom, Epstein and Nalban 2020, table 1: calibrated by the authors for a half-life of about 2.5 quarters; 0.7 in Argov et al. 2007 | |
credibility_low_persistence | 0.4 | same source: the forecast of the credible regime | |
credibility_high_persistence | 0.8 | same source: the forecast of the de-anchored regime, which is more inert | |
high_inflation_gap | 7 points above the target | same source: the de-anchored regime converges to 10% for a 3% target in the Philippines (4.5% in Indonesia); the authors say it is set “somewhat arbitrarily” | |
pressure_on_central_bank | 0 | political pressure on the central bank, which Drechsel (2024) measures on expectations |
Why. This is the credibility channel of the IMF's semi-structural models (Argov et al. 2007; Alichi et al. 2009; Chansriniyom, Epstein and Nalban 2020), which are the closest to PREEMINENCE's gap model. Anchoring is no longer a given. It is earned by keeping inflation close to the target and lost by letting inflation slip. Because the de-anchored regime sits above the target, credibility is lost faster when inflation overshoots than when it stays below. The orders of magnitude are those of the literature: in the United States, the anchored share went from 0.06 to 0.81 around 1998 (Ball and Mazumder 2014); Argov et al. say it takes “1.5-2.0 years” to rebuild credibility, Alichi et al. “more than 4 years”.
What it simplifies. No study estimates the law of erosion. The parameters are IMF calibrations, for emerging countries with moderate inflation (Indonesia, Philippines, Israel). Applied to a country that starts from high inflation, they put it in a trap from the outset: credibility lost, backward-looking expectations, a disinflation lasting several decades. Without shocks, Argentina, starting from 118%, is still at 56% after ten years and only falls below 25% after nineteen years; Turkey and Nigeria are still around 18% after twenty years, for a target of 10% (§8.2). Nothing in the model restores credibility at a stroke, as a stabilisation plan would. Each regime's forecast is made on the published inflation of one quarter earlier, not in a full quarterly model; the expectations “bias” and its effect on demand, which Chansriniyom et al. add, are left out.