U.S. Taylor-Rule Policy Stance Gap

USTAYLORGAP is the policy stance gap for the United States, the quarterly mean of the observed policy rate less a Taylor-rule prescription computed mechanically from three inputs, namely a constant real anchor, an assumed inflation target and an output gap measured against a potential-output trend produced elsewhere. It is published in percentage points at quarter-end dates over 265 quarters running from 1960-03-31 to 2026-03-31, and it is a construction rather than an observation of anything (Taylor 1993; Taylor 1999).

The centring of that construction is the first thing to read and it is not a footnote. The constant real anchor is 1.50 percent, which is the sample mean of the ex-post real policy rate over the same index, so the real-rate component of every stance gap is centred by the construction itself and the level of the gap carries no independent information. Only its variation does. The realized mean of the published gap over those 265 quarters is −0.51 percentage points, and that residual is the average contribution of the inflation-gap and output-gap terms, which the same construction does not centre. It is not a sign that the natural rate is mismeasured, and reading it as evidence about the average stance of policy would misread the object it describes.

The prescription is a benchmark and nothing more. It is a mechanically computed reference path, so the gap between it and the observed rate is a description of distance rather than a verdict on any decision, and no sentence here sets the rule up as an authority on what a rate was required to be. Over 34 quarters every month of which sat at the effective lower bound, and 38 quarters with at least one such month, the gap measures the bound binding on the observed rate rather than a discretionary choice. Those quarters are retained in display and never removed.

Three properties bound any reading. The constant real anchor is a sample mean, so it is recomputed as each new quarter arrives and the entire prescribed path shifts one-for-one with it, and across 67 expanding vintages it runs from 1.2462 to 2.6436, a range of 1.3975 percentage points. The inflation target of 2 percent is an assumption before 2012-01 and an announced longer-run objective from that month onward, and only 57 of the 265 quarters carry that announcement. And the output gap is measured against a trend produced elsewhere, a choice that moves the prescribed path by percentage points on its own (Orphanides and van Norden 2002; Hamilton 2018). Nothing on this page is a forecast.

(1) Inputs. The construction takes three inputs and transforms none of them, namely the quarterly mean of the observed policy rate, four-quarter inflation on the headline PCE price index, and an output gap measured against a potential-output trend produced elsewhere. The three are intersected into a single quarterly index of 265 quarters running from 1960-03-31 to 2026-03-31, and the projected portion of the potential-output series beyond the last actual output quarter is removed before anything is computed, so no projection enters a published gap (Orphanides 2001).

(2) Constant real anchor. The real anchor is a constant of 1.50 percent, set equal to the sample mean of the ex-post real policy rate over that same index, and it carries the construction's central caveat rather than an estimate of anything. Because it is a sample mean it is recomputed as each new quarter arrives and the entire prescribed path moves one-for-one with it. Over 67 expanding vintages the anchor runs from 1.2462 to 2.6436, a range of 1.3975 percentage points, which is the size of the shift the whole path inherits from the choice of sample alone.

(3) Inflation target. The target is 2 percent throughout. It is an assumption before 2012-01 and an announced longer-run objective from that month onward, and only 57 of the 265 quarters carry the announcement, so the label matters over most of the record. The sensitivity is stated analytically and never run as a grid, namely that a one-point change in the assumed target moves the prescribed path by exactly 0.5 percentage points (Orphanides 2003).

(4) Rule variants. Three anchor-free level rules are computed on the same inputs. The headline variant weights the inflation gap and the output gap equally, the balanced variant doubles the weight on the output gap, and the inertial variant smooths the prescribed rate toward its own previous value in the partial-adjustment form an estimated reaction function usually takes (Judd and Rudebusch 1998; Clarida, Galí, and Gertler 2000). Those weights are frozen construction constants of this component. Nothing is quoted from the text of Taylor (1993), which is cited as the rule's reference and for nothing else, and the historical rule-analysis line the balanced weighting belongs to is cited in the same way (Taylor 1999).

(5) Band and gap. The rule-range band spans the three level rules at each quarter, and the published gap is the observed rate less the prescribed rate in percentage points at quarter-end dates. Every prescribed path reproduces its closed form to zero absolute error and no quarter of any variant falls outside the band, so the arithmetic of the construction is exact rather than merely inside a tolerance.

(6) Reaction-function diagnostic. A reaction function with a lagged policy rate is estimated once on the same index as a sign diagnostic and for nothing more. The loading on the inflation gap is 0.1266 and the loading on the output gap is 0.1333 over 264 quarters, and both signs are positive, which is the whole of what the diagnostic asks. The implied long-run response to inflation is 1.42, which is not a gated quantity and is never read here as a Taylor principle result.

(7) Era split. The same reaction function estimated on the two sides of 1979-09-30 gives an implied long-run response of 0.85 on the 77 earlier quarters against 1.90 on the 186 later ones. The split is carried as a measured pattern and replicates no published finding, since the question it answers is the one posed by Clarida, Galí, and Gertler (2000) rather than a result of theirs reproduced here.

(8) Output-gap robustness. Two alternative trend constructions are computed on the same output series and compared on the resulting prescribed path. A one-sided filter at a smoothing parameter of 1600, which is this component's own robustness-leg constant and is attributed to no text, gives a path correlating 0.9567 with the headline one, differing by 0.8231 percentage points on average and by as much as 3.03 percentage points (Hodrick and Prescott 1997; Ravn and Uhlig 2002; Baxter and King 1999). The regression alternative of Hamilton (2018), at the 8-quarter horizon on 4 lags he recommends for quarterly data, correlates 0.9607, differs by 0.8053 percentage points on average and by as much as 4.41 percentage points. Neither leg is a threshold and neither moves the published construction, and both quantify the real-time unreliability of output-gap estimates that Orphanides and van Norden (2002) document and that Orphanides (2001) traces through rule prescriptions built on such estimates.

(9) Measure panel. The published prescription uses headline PCE inflation. Companions built on CPI-U and on core PCE inflation are computed and kept without being served, so that no single price measure reads as the measure. One quarter of the CPI-U companion is undefined because of a gap in the source's publication, and it touches nothing that reaches a published surface.

(10) Load and revision. Every rebuild replaces the whole series rather than appending to it, because the anchor is a sample mean that revises with each new quarter and the whole path moves with it. The trend against which the output gap is measured is also restated at source, and no dated panel of earlier vintages is kept against which either rewriting could be measured (Orphanides and van Norden 2002).

A rule benchmark is a way of setting the observed policy rate beside a number computed from a small set of macroeconomic inputs, and reading policy that way has a long practice behind it (Taylor 1993; Taylor 1999; Judd and Rudebusch 1998). What this series publishes is the distance between the two, quarter by quarter, in percentage points. The benchmark is mechanically computed and the distance is a description, so nothing here grades a decision or claims that a rate was required to take some other value.

The first thing that bounds the reading is the centring. The real anchor is the sample mean of the ex-post real policy rate at 1.50 percent, so the level of the gap is fixed by the construction and only its variation carries information. The realized mean over the 265 published quarters is −0.51 percentage points, which is the average contribution of the inflation-gap and output-gap terms rather than a sign that the natural rate is mismeasured. A reader who takes that residual as evidence about the average stance of policy has read the construction and not the economy.

The estimated reaction function is reported for its signs and nothing else. Over 264 quarters the loading on the inflation gap is 0.1266 and the loading on the output gap is 0.1333, both positive, and the implied long-run response of 1.42 is not a gated quantity and is never read here as a Taylor principle result. Estimated on the two sides of 1979-09-30 that same implied response is 0.85 on 77 quarters against 1.90 on 186, a pattern disclosed as measured which replicates no published finding, since the question it answers is the one the estimated-reaction-function literature poses rather than a result of that literature reproduced here (Clarida, Galí, and Gertler 2000; Judd and Rudebusch 1998).

The second bound is the output gap the prescription rests on. The path is built against a trend produced elsewhere, and replacing that trend with either standard alternative moves the path by percentage points rather than by basis points. A one-sided filter at a smoothing parameter of 1600 gives a path differing from the headline one by as much as 3.03 percentage points, and the regression alternative of Hamilton (2018) by as much as 4.41 percentage points, which is wider than most of the policy disagreements a chart of this kind is used to illustrate (Hodrick and Prescott 1997; Ravn and Uhlig 2002; Baxter and King 1999). Output-gap estimates are moreover unreliable in real time, so the gap a reader sees today is not the gap that was visible at the time (Orphanides and van Norden 2002; Orphanides 2001; Orphanides 2003).

Four readings are therefore not supported. The gap does not say what a rate was required to be, because the benchmark is a construction and not an obligation. Its level says nothing about the average stance of policy, for the reason set out above. Over 34 quarters every month of which sat at the effective lower bound, and 38 with at least one such month, the gap measures the bound binding on the observed rate rather than a choice, and those quarters stay in the display. And nothing here is a forecast, since the series carries no statement about the next quarter of anything.

On a rates desk a stance gap of this kind is a low-frequency frame rather than a signal. It sets the observed policy rate beside a benchmark computed from a small set of inputs, which is the frame in which rule-based readings of policy are usually discussed (Taylor 1993; Taylor 1999), and it is read beside the estimated reaction functions that describe how a policy rate has actually responded rather than in place of them (Judd and Rudebusch 1998; Clarida, Galí, and Gertler 2000).

Three measurement facts bear on that use. The real anchor is a sample mean, so it is recomputed every quarter and the entire published path shifts one-for-one with it, a shift worth 1.3975 percentage points across the 67 expanding vintages on record. The output gap inside the prescription is measured on revised data against a trend produced elsewhere, so a backtest that treats today's path as what was visible at each past date overstates what a desk could have acted on (Orphanides 2001; Orphanides 2003; Orphanides and van Norden 2002). And the choice of trend alone moves the prescribed path by as much as 4.41 percentage points under one alternative and 3.03 percentage points under the other, which is wider than the moves most positions in this space are sized against (Hamilton 2018; Hodrick and Prescott 1997; Ravn and Uhlig 2002; Baxter and King 1999).

A view formed on this reading is expressed through instruments the gap does not itself price, since the series is not tradable and carries no valuation of its own. Whatever position follows is measured in the space of the policy path or the curve that actually prices it, and the level of the gap is not the quantity being traded in either.

Two uses are ruled out. A threshold read off the level of the gap alone is not supported here, because the level is centred by the construction and a level chosen after looking at the series is a selected level. And the series is not an early-warning instrument on this surface, since it carries no forecast of a policy decision, of an inflation outcome or of anything else, and the quarters at the effective lower bound record a constraint rather than a decision.

USTAYLORGAP is a constructed policy stance gap, the quarterly mean of the observed policy rate less a rule prescription built from a constant real anchor, an assumed inflation target and an output gap taken against a trend produced elsewhere, so its level is an arithmetic construction and never an observation, and the rule whose form it instantiates is the one cited as its reference (Taylor 1993; Taylor 1999). The anchor is the sample mean of the ex-post real policy rate over the same index, so the mean reversion an integration test would look for is already half written into the definition of the series, and the augmented Dickey and Fuller (1979) regression, the Phillips and Perron (1988) test, the KPSS stationarity test of Kwiatkowski et al. (1992), the GLS-detrended test of Elliott, Rothenberg, and Stock (1996) and the modified statistics of Ng and Perron (2001) were deliberately not run, because a rejection would confirm that centring rather than discover mean reversion in the economy and because an integration verdict on the output-gap component would report which trend was subtracted (Hamilton 2018; Orphanides and van Norden 2002). The battery is accordingly the persistence, amplitude, break and revision descriptives the construction admits, and no order of integration is assigned here, by ruling rather than by an inconclusive test.

Persistence and amplitude summarize the level. The first-order autoregressive coefficient of the gap is 0.917709 over 265 quarterly observations from 1960-03-31 to 2026-03-31, implying a half-life of about 8.07155 quarters, reported as a descriptive property of the constructed gap rather than as an order of integration and read with the near-unity small-sample downward bias of Andrews (1993) in mind. Quarters in which the policy rate sat at its effective lower bound in every month are quarters where the gap measures the bound rather than a policy choice, so this single-regime persistence summary describes the published path and is never a statement about the stance of policy. A level portmanteau such as Ljung and Box (1978), refining the form of Box and Pierce (1970), is not reported here, because on a gap whose centring is set by its own construction it measures that construction rather than the process beneath it (Stock and Watson 1998). The gap has a standard deviation of 2.73878 percentage points and ranges from −10.8408 to 8.52825 percentage points, an amplitude that fixes the scale on which any movement in the level is read.

The multiple structural-break procedure of Bai and Perron (1998), computed by the dynamic-programming algorithm of Bai and Perron (2003) with the number of breaks chosen by information criterion (Yao 1988; Liu, Wu, and Zidek 1997), locates four breaks in the mean of the level at 1971-03-31, 1980-12-31, 1990-09-30, and 2002-12-31. That search is descriptive and carries no discovery status, since the dynamics of a constructed gap belong to the transform that produces it and break inference presumes a stable object to begin with (Perron 1989; Hamilton 2018). Spurious segmentation of a persistent constructed path is the standing risk such a search runs (Granger and Newbold 1974; Phillips 1986).

Revision behaviour is where the construction's dependence on its own sample shows most directly. The constant real anchor is a sample mean, so it is recomputed as each new quarter arrives and the whole published path shifts with it, and the expanding-vintage range of that anchor over 67 vintages is 1.39748 percentage points. The served history is replaced whenever the series is rebuilt and the trend against which the output gap is measured is restated at source, and no dated vintage panel exists against which either rewriting could be quantified, so the figure above is a pseudo-vintage diagnostic on today's data rather than a measured vintage panel (Orphanides and van Norden 2002; Orphanides 2001). One further limit belongs with the verdict. The persistence and break figures describe the published construction rather than an economy, so they support no order of integration, no turning point and no forecast of any kind.