The core formula used throughout the platform:

i_t — prescribed OCR. r*_t — nominal neutral rate. π_t — year-on-year inflation. π*_t — inflation target midpoint at time t. gap_t — output gap as % of potential. α, β — policy response coefficients (Taylor's original: α = β = 0.5).

The optional Inertial Taylor Rule spreads adjustments over time:

The lag term uses the previous actual OCR, not the previous inertial rate. This anchors the inertial path to where the OCR actually was rather than where the rule said it should be, producing a smoother but history-grounded prescription.

The RBNZ's MPS publishes a nominal neutral OCR directly. Using this avoids the need to estimate a real neutral rate and add an inflation expectation, which would compound uncertainty.

Because r* is nominal, the formula has no separate inflation passthrough term. In the classical real-r* formulation, current inflation appears explicitly to convert to a nominal rate — with a nominal r* that conversion is already embedded. The decomposition chart reflects this: the neutral rate bar is r* itself, with the inflation gap and output gap contributions stacked on top.

The neutral rate series is manually compiled from RBNZ MPS statements. For quarters before the RBNZ began publishing explicit estimates, values are backfilled from the RBNZ's Finding Neutral research bulletin and earlier MPS commentary. Coverage extends to Q1 2000 but is denser from around 2010.

The r* override in the Parameter Playground accepts a real value and adds current inflation internally to convert to nominal before applying the formula — consistent with the nominal framework throughout.

The platform uses the historical midpoint of the RBNZ's inflation target band:

The π* override holds the target fixed at any value across all periods — useful for counterfactual analysis such as asking what the rule would have prescribed if the target had always been 2%.

The output gap is sourced from RBNZ MPS projections as a percentage of potential output. Using the RBNZ's own estimate is preferable to computing one independently — the Taylor Rule is then benchmarked against the same view of economic slack that informed the RBNZ's actual decisions.

The MPS output gap for the current quarter is technically an RBNZ projection rather than a finalised estimate. It is included because the RBNZ uses it in their own deliberations, and is labelled provisional where relevant.

Core inflation measures for the current quarter are not published in the MPS. When a core measure is selected, the Taylor estimate shown is from the most recent quarter for which that measure is available, with a data-pending note. CPI Headline is the only measure where the current quarter is always available.

Four measures are available. The default is the RBNZ Core Inflation Average — the RBNZ's preferred summary of underlying inflation, averaging the sectoral factor model, trimmed mean (30%), weighted median, and CPI ex food and energy. Using the measure the RBNZ actually monitors is the most defensible baseline for Taylor Rule analysis.

Trimmed Mean (30%) removes the largest price movements from the CPI basket before averaging, reducing sensitivity to one-off changes. Sectoral Factor Model estimates the common inflation component separately across tradable and non-tradable sectors. CPI Headline is included for completeness but is the noisiest measure and least suited to Taylor Rule analysis.

Changing the measure updates all Taylor calculations, charts, scatter plots, and OLS estimates simultaneously. Historical coverage varies — older quarters may be null for some core measures.

Historical mode (default) uses the RBNZ's published neutral rate path and the historical π* step series — the most realistic setting, reflecting the frameworks the RBNZ was working within at each point.

Override mode fixes r* or π* at a constant value across all periods, enabling counterfactual analysis. What would the Taylor Rule have prescribed throughout the 2000s under a neutral rate of 4%? How sensitive is the deviation series to the inflation target assumption? Overrides answer these directly.

α and β sliders control the rule's sensitivity to the inflation gap and output gap. Default 0.5 / 0.5 follows Taylor's original (1993) specification. R² fit statistics update live, showing how well the current specification tracks the actual OCR.

OLS estimation regresses (OCR − r*) on the inflation gap and output gap with no intercept, estimating the α and β that best describe actual OCR decisions over the selected window. The no-intercept specification is correct because subtracting r* already accounts for the baseline. The R² reported is uncentered, which is appropriate for a no-intercept model and will generally read higher than a standard centred R².

Deviation statistics summarise quarterly deviations (OCR − Taylor Rate) over the selected window. Positive = RBNZ more hawkish than the rule; negative = more dovish.

Rolling statistics show the four-quarter rolling mean and standard deviation of deviations — useful for distinguishing sustained policy stances from transient departures.

Scatter plots show contemporaneous correlations between deviations and three indicators: inflation, unemployment, and NZD/USD. Pearson r and an OLS trend line are shown. These are descriptive relationships, not causal ones.

Governor regime comparison runs separate OLS regressions for each governor's full term. α, β, R², and RMSE are computed over the complete regime and do not respond to the date range selector. Mean deviation is the only column that adjusts to the currently selected window.

Revised data. Historical estimates use the latest available MPS vintage. The RBNZ set rates with real-time data, which for the output gap and neutral rate can differ materially from revised figures.

Output gap uncertainty. Even the RBNZ's own output gap estimates carry substantial uncertainty. Different methodologies would produce different Taylor paths.

Rule scope. The Taylor Rule cannot capture financial stability concerns, unconventional tools such as the LSAP programme, effective lower bound dynamics, or global spillovers. Large deviations during COVID and the GFC partly reflect these constraints rather than pure discretion.

OLS coefficients. Estimated α and β describe historical co-movement, not intent. A low α may mean a governor was less inflation-reactive, or simply that inflation was near target throughout and offered little variation for the regression to detect.