U.S. Credit-to-GDP Gap

USCGAP is the credit-to-GDP gap for the United States, the distance between credit to the private non-financial sector measured against output and a slow-moving trend fitted to that same ratio. It is neither an observation nor a published series carried through unchanged. The trend is estimated by KRED with a one-sided recursive filter, so each quarter's trend value is computed from the ratio up to that quarter alone and the published gap is the output of that filter rather than a measurement of anything (Hodrick and Prescott 1997; Borio and Lowe 2002). A positive gap says credit has grown faster than output relative to its own history and a negative gap says the opposite, and neither reading carries a statement about what happens next.

The object has a policy identity. Basel III names a gap of this construction as the reference indicator of its countercyclical capital buffer, and the work behind that choice reads a deviation of credit from trend as a summary of where an economy sits in its financial cycle rather than as a measure of anything observable (Borio and Lowe 2002; Drehmann, Borio, and Tsatsaronis 2011). The long cross-country record that motivates the interest is the one in which credit booms run ahead of banking crises and the recessions that follow them are deeper (Schularick and Taylor 2012; Jordà, Schularick, and Taylor 2017). None of that record is re-estimated here, and no part of this page is a forecast.

The endpoint problem is the first thing to read and not a footnote. The same ratio filtered with the whole sample in hand, which is the hindsight version of the same construction, agrees with the published one-sided series only loosely. Across the 274 quarters on which both are defined the correlation between them is 0.6344, the mean absolute difference is 4.5203 pp, the largest single-quarter difference is 14.6273 pp, and the two disagree about the sign of the gap in 84 of those quarters. A gap read at the end of the sample is therefore an estimate that later data can move and does move, which is the property Edge and Meisenzahl (2011) measure for gaps of exactly this construction and Orphanides and van Norden (2002) measure for trend and cycle estimates generally. The series does not identify a turning point.

The filter itself is contested. Hamilton (2018) argues that a Hodrick-Prescott construction produces cycles that are artifacts of the filter, and what is used here is the reference indicator's own definition rather than the uncontested way to separate a trend from a cycle (Ravn and Uhlig 2002; Baxter and King 1999). Measured against the alternative Hamilton proposes, at the 8-quarter horizon on 4 lags that is his own recommendation for quarterly data, the published gap correlates 0.5681 with that alternative and differs from it by 4.2247 pp on average and by as much as 17.2287 pp; at the 20-quarter horizon his text names for debt-cycle objects, on the same 4 lags, the correlation is 0.8852, the mean absolute difference is 3.9487 pp and the largest difference is 20.0441 pp. Both legs are reported together, neither is a threshold anything has to pass, and the early-warning evaluation that a published indicator would need is a separate exercise this page does not run (Drehmann and Juselius 2014).

(1) Input. The input is the quarterly ratio of credit to the private non-financial sector measured against output, used as it stands and with no transformation of its own, over 313 quarters from 1947-12-31 to 2025-12-31, and it is the aggregate around which the long-run record of credit expansions and banking crises is organized (Schularick and Taylor 2012; Jordà, Schularick, and Taylor 2017). Two compiled versions of that ratio exist and they are compared before anything is filtered. Over the 304 quarters they share, the largest single-quarter difference between them is 0.0499 pp and the mean absolute difference is 0.0252 pp, against a bar of 0.05 pp on the largest difference fixed before the comparison was run. That comparison is re-measured on every run, the two versions can stand one source release apart, and a run in which they differ by more than the bar is recorded and disclosed rather than withheld.

(2) One-sided trend. For each quarter the two-sided filter is applied to the sample that ends at that quarter and only its last trend value is kept, so the recursion re-walks the history quarter by quarter and no later observation ever reaches an earlier trend value (Hodrick and Prescott 1997). The smoothing parameter is 400000, far above the value a business-cycle reading of quarterly data would take, because the credit cycle is longer than the business cycle, and the principle that the smoothing parameter has to scale with the length of the movement being removed is the one Ravn and Uhlig (2002) formalize for the observation frequency (Baxter and King 1999).

(3) Burn-in and start. The first 40 quarters of the recursion are discarded, so trend and gap are both empty until the recursion has accumulated that much history, and the published gap begins at 1957-09-30 while the reference indicator's own published gap begins at 1957-12-31. That one-quarter difference is a property of the burn-in constant, which is carried unchanged rather than tuned to close it, and it carries no information of its own.

(4) Gap and anchor agreement. The gap is the ratio less its own recursive trend, stated in percentage points of output. Measured against the reference indicator's own published gap over the 273 quarters the two share, the mean absolute difference is 0.0240 pp and the largest single-quarter difference is 0.0555 pp, against a tolerance of 0.5 pp fixed in advance. That is agreement within a tolerance set before the comparison was run, not identity, and it is not a claim that this series reproduces or extends the published one (Borio and Lowe 2002; Drehmann, Borio, and Tsatsaronis 2011). The gap is written only when it agrees with the reference indicator's own published gap within the pre-registered tolerance, and a run outside that tolerance writes nothing and leaves the served series at its last good state.

(5) Disclosure comparisons. Two further comparisons are recorded as disclosures rather than as tests. Over the same 273 quarters the two gaps never disagree about the sign of the gap, and they never disagree about whether the gap stands above the 2 pp buffer-activation reference, a constant this component carries as its own disclosure and attributes to no source. Zero disagreements on either count is a statement about two independently computed series rather than a passed test, since no threshold governs either count.

(6) Robustness legs. The alternative regression filter of Hamilton (2018) is computed on the same ratio at both parameterizations and persisted as a disclosure, and the two-sided counterpart of the published construction is computed as well, so the endpoint disagreement quantified with the definition above is measured rather than asserted (Edge and Meisenzahl 2011; Drehmann and Juselius 2014). No leg carries a threshold and the published construction does not move under any of them.

(7) Revision. The recursion introduces no revision of its own, since the trend at each quarter uses only the ratio up to that quarter. The published history nevertheless changes, because the input ratio is restated at source and the load replaces the whole series whenever it is rebuilt, and no dated panel of earlier vintages is kept from which the size of that rewriting could be measured (Orphanides and van Norden 2002; Drehmann and Juselius 2012).

A credit-to-GDP gap is read as a summary statistic of the financial cycle. The deviation of credit from its own slow trend is the quantity Borio and Lowe (2002) put forward as a way of reading how far a credit expansion has run relative to the economy that carries it, and it is the aggregate whose calibration as a buffer anchor Drehmann, Borio, and Tsatsaronis (2011) study. The interest rests on a long record in which credit booms run ahead of banking crises and the recessions that follow them are deeper and longer (Schularick and Taylor 2012; Jordà, Schularick, and Taylor 2017), and on the related reading that the burden of servicing accumulated debt is itself a macroeconomic quantity (Drehmann and Juselius 2012).

The buffer framework is where the gap acquired its policy standing, and the reference it carries here is a disclosure rather than a rule. The gap is compared against a buffer-activation reference of 2 pp, a constant this component states as its own and attributes to no source, and the comparison exists so that a reader can see where the published series sits relative to it. A level of the gap is not an instruction, a crossing of that reference is not an event this page declares, and the evaluation of an indicator against the requirements a policy user would place on it is a separate exercise with its own standards (Drehmann and Juselius 2014).

What bounds any reading is the endpoint problem, and it is large. The hindsight version of the same construction, which reads every quarter through the whole sample, correlates only 0.6344 with the published series over the 274 quarters where both exist, differs from it by 4.5203 pp on average and by as much as 14.6273 pp, and takes the opposite sign in 84 of those quarters. Edge and Meisenzahl (2011) report the same property for credit-to-GDP gaps and Orphanides and van Norden (2002) report it for trend and cycle estimates generally, so the reading at the latest quarter is the least settled part of the series rather than its most informative part.

The construction carries a standing objection of its own. Hamilton (2018) argues that a Hodrick-Prescott filter manufactures cyclical movement that belongs to the filter rather than to the economy, and the answer this page gives is not that the objection fails but that the construction used is the reference indicator's own definition (Hodrick and Prescott 1997). The alternatives are computed and disclosed alongside it rather than folded into it, and the general question of how the smoothing choice and the band of movement retained interact is older than the credit application (Ravn and Uhlig 2002; Baxter and King 1999).

Three readings are therefore not supported. The series does not identify a turning point, since a quarter read at the edge of the sample is exactly where the disagreement above concentrates. The series is not a forecast, and the long-run evidence that motivates interest in credit gaps is evidence about a cross-country record rather than a statement about the next quarter of any one economy. And the level of the underlying ratio is not the object, since the published number is a deviation from a fitted trend and two economies with the same ratio can sit at opposite ends of their own credit cycles.

On a credit desk a gap of this kind is a low-frequency overlay rather than a signal. It says where credit stands relative to its own trend, which is the quantity bank capital frameworks reference and the quantity the crisis record is organized around (Borio and Lowe 2002; Drehmann, Borio, and Tsatsaronis 2011; Schularick and Taylor 2012), and it is read beside the higher-frequency stress gauges that move within a quarter rather than in place of them (Hollo, Kremer, and Lo Duca 2012) and beside the debt-service reading that asks what the accumulated stock costs to carry (Drehmann and Juselius 2012).

Three measurement facts bear on that use. The published number is a filtered estimate and not a price, so it inherits the assumptions of the construction that produced it and a different separation of trend from cycle returns a different number (Hamilton 2018; Hodrick and Prescott 1997). The history is rewritten whenever the input ratio is restated, since the load replaces the whole series, and no dated panel of earlier vintages is kept from which the size of that rewriting could be measured, 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 and van Norden 2002). And the quarter at the end of the sample is the least settled one, as the endpoint comparison records, where the hindsight version of the same construction correlates 0.6344 with the published series, differs from it by 4.5203 pp on average, and takes the opposite sign in 84 of the 274 quarters both cover (Edge and Meisenzahl 2011).

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 curve or the credit spread that actually prices it, and that pricing frame is a fitted construction with conventions of its own (Macaulay 1938; Fisher and Weil 1971; Hicks 1939).

Two uses are ruled out. A threshold read off the level of the gap alone is not supported here, because a level chosen after looking at the series is a selected level and the standard corrections for that selection are not applied anywhere on this page (White 2000; Lo and MacKinlay 1990). And the series is not an early-warning instrument on this surface, since the record that would establish such a use is built on cross-country panels rather than on this one series, and an evaluation against the requirements a policy user would impose is a separate exercise (Drehmann and Juselius 2014; Jordà, Schularick, and Taylor 2017).

USCGAP is the one-sided Hodrick and Prescott (1997) credit-to-GDP gap computed by KRED at a smoothing parameter of 400000, with the trend re-estimated recursively through each quarter from the ratio available up to that quarter, so the published level is a filtered construction and never an observation, and it is the credit-cycle gap the early-warning literature takes as its evaluation object (Borio and Lowe 2002; Drehmann and Juselius 2014). The stationarity of the gap follows from the filter that builds the trend rather than from the data, so 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 Hodrick-Prescott cycle of a driftless random walk is judged stationary in a large share of replications and a rejection would confirm the filter rather than discover mean reversion (Hamilton 2018; Hodrick and Prescott 1997). The battery is accordingly the persistence, amplitude, break and revision descriptives the construction admits.

Persistence and amplitude summarize the level. The first-order autoregressive coefficient of the gap is 0.993492 over 274 quarterly observations from 1957-09-30 to 2025-12-31, implying a half-life of about 106.155 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. That half-life is long relative to the sample it is measured on, so it summarizes the filtered path rather than pinning down a rate of decay. A level portmanteau such as Ljung and Box (1978), refining the form of Box and Pierce (1970), is not reported here, because on a recursively filtered gap it measures the gain of the filter rather than the process beneath it (Stock and Watson 1998). The gap has a standard deviation of 6.52215 pp and ranges from −16.9569 to 11.6469 pp, 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 five breaks in the mean of the level at 1968-03-31, 1979-09-30, 1989-12-31, 2000-03-31, and 2010-06-30. 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).

Revision behaviour has two channels that have to be stated separately. The recursion at each quarter uses only the ratio up to that quarter, so the one-sided filter at a smoothing parameter of 400000 introduces no revision of its own. The served history is nonetheless rewritten whenever the input ratio is restated at source, because the load replaces the whole series, and no dated vintage panel exists against which that rewriting could be quantified, so no revision statistic accompanies this field (Orphanides and van Norden 2002; Edge and Meisenzahl 2011). One further limit belongs with the verdict. The one-sided gap disagrees materially with the two-sided counterpart computed on the same ratio, a disagreement quantified in the narrative rather than here, so a reading taken at the end of the sample is the least settled part of the series and no turning point is identified from it (Ravn and Uhlig 2002; Baxter and King 1999).