Methodology and limits

This is a teaching model, not a forecasting engine. It is built to make the mechanisms of inflation visible. It is not calibrated to predict next year's CPI, and it never reports a forecast or a probability that inflation will be some number.

The backbone: a 3-equation New Keynesian model

The engine is a discrete-time version of the standard 3-equation New Keynesian model (IS curve, Phillips curve, monetary-policy rule) used to teach monetary policy, following Carlin and Soskice (2005) and Clarida, Galí and Gertler (1999). We use the backward-looking, inertial form so it runs tick by tick in your browser without solving a rational-expectations fixed point each step. One tick is one quarter.

1. Expectations (adaptive, with an anchoring pull to target)

πᵉ = cred · π* + (1 − cred) · [ πᵉ₋₁ + λ·(π₋₁ − πᵉ₋₁) ]

The bracket is textbook adaptive expectations; the credibility weight pulls expectations toward the 2% target, which is how we represent anchored expectations.

2. IS curve (real rates and demand drive the output gap)

y = ρ·y₋₁ − φ·(r₋₁ − r*) + fiscal + money + shock

A higher real interest rate lowers the output gap, with a lag. This is the dynamic IS relation of Clarida, Galí and Gertler.

3. Phillips curve (expectations + slack + cost shocks)

π = πᵉ + α·y + supply

The expectations-augmented Phillips curve (Friedman, Phelps). When expectations equal actual inflation and shocks are zero, it is vertical: there is no long-run trade-off.

4. Monetary rule (Taylor rule with smoothing)

i* = r* + π + 0.5·(π − π*) + 0.5·y, then smoothed and floored at zero.

Taylor (1993). Raising rates more than one-for-one with inflation (the Taylor Principle) is what stabilises it. You can switch to manual mode and set the rate yourself.

Supporting relations

Okun's law turns the output gap into unemployment. The quantity theory of money (MV=PY) is treated as an accounting identity, not a mechanical cause: when you print money and inflation does not move with it, the model shows it went into velocity or output instead. Velocity rises with expected inflation (people spend faster to avoid holding depreciating money), and central-bank credibility is an endogenous state, lost quickly and rebuilt slowly.

Default parameters and their sources

Values flagged est? in the app are modeling choices, not estimated facts.

Parameter	Default	Source / status
Inflation target π*	2%	Fed / ECB 2%
Taylor coefficients	1.5 / 0.5	Taylor (1993); smoothing ≈ 0.8 (Smets–Wouters 2007)
Neutral real rate r*	2.0	Taylor (1993); recent HLW ≈ 0.8
NAIRU	4.5%	CBO NROU
Okun coefficient	2.0	Ball, Leigh and Loungani; unstable over time
Phillips slope α	0.30	Pedagogically visible. Empirical κ on marginal cost is far smaller (≈0.02; Hazell et al. 2022) — the flat Phillips curve debate.
Expectations speed λ	0.25	est? learning studies use smaller gains; visible value for teaching
Velocity (baseline)	1.3	FRED M2V; not a stable constant

Full table and the estimated-DSGE sources (Smets and Wouters 2007) are in the project's methodology document.

What each scenario must reproduce

The model is not fit to data, but it is checked for directional correctness against real episodes:

Scenario	Must show
1970s stagflation	Inflation and unemployment rise together; expectations un-anchor. Peak CPI ~14.6% (1980)
Volcker tightening	Disinflation only after a sharp recession; cost larger when credibility is low. Funds ~19%, unemployment 10.8%
Post-pandemic	A supply spike that partly recedes plus a demand component needing tightening. Causation is genuinely contested.
High debt + monetization	Money-financed deficits give accelerating inflation that rate hikes alone cannot stop. Sargent (1982)
Productivity boom	Low unemployment with low inflation. Late 1990s
2008 financial crash	A demand collapse: output falls, unemployment jumps, inflation dips toward or below zero, rates hit the zero floor, then a slow recovery. Great Recession
Argentina 1989	Deficits financed by the printing press plus lost credibility: runaway inflation that also collapses output. ~5,000% in 1989

Supply, demand and helicopter shocks are modeled as fading impulses, not permanent changes. Whether the inflation they cause is transitory or persistent then depends on expectations and credibility, rather than being assumed.

Limits: what this model does not do

It is a teaching diagram, not a forecaster. No output is a prediction.
MV=PY is an identity, not a mechanical cause. Money maps to inflation only through velocity and output.
Expectations are backward-looking with an anchoring pull. They deliberately fail the way adaptive expectations fail at sharp regime changes.
There is no permanent inflation-unemployment trade-off. The long-run Phillips curve is vertical, and no control lets you buy permanently lower unemployment with permanent inflation, because that relationship does not exist.
It is a closed economy with a simplified exchange-rate channel, not a full open-economy model.
Several parameters are typical values and some are weakly anchored. Extreme regimes are shown qualitatively, not to scale.