The normalisation critique centres on how the nominal credit level is converted to a magnitude that is comparable both across time and across countries. According to the BCBS’s approach, nominal credit is divided by nominal GDP. In Switzerland, GDP revisions occur regularly and for several reasons^{Footnote 10}. These revisions can be significant and can extend backwards, affecting several years. Hence, any indicator that employs Swiss GDP in its function is subject to considerable volatility stemming from revisions and adjustments. A normalised measure of credit therefore runs the risk of being affected by movements that may or may not be directly relevant. In this section, we assess the relevance of the normalisation critique by comparing the BIS gap’s sensitivity to GDP volatility to an alternative gap measure that smooths the impact of GDP as it enters the denominator of the credit-to-GDP ratio.

### 3.1 Two ways of estimating the gap: BIS gap vs. modified BIS gap

The BCBS provides methodological guidance for calculating the BIS credit-to-GDP gap (BCBS, 2010). In this framework, the quarterly credit-to-GDP ratio \( {x}_t^{BIS} \) is computed as the ratio between the stock of domestic credit *c*_{t} and nominal GDP summed over the four previous quarters.

$$ {x}_t^{BIS}=\frac{c_t}{\sum \limits_{t^{\prime }=t-3}^t{GDP}_{t\prime }} $$

(1)

According to the BCBS guidelines, the BIS gap \( {y}_t^{BIS} \) is then estimated as the deviation of the ratio from its trend.

$$ {y}_t^{BIS}={x}_t^{BIS}-{HP}_{\left[1,t\right]}^{1s}\left({x}_t^{BIS}\right), $$

(2)

where \( {HP}_{\left[1,t\right]}^{1s}\left({x}_t^{BIS}\right) \) is the filtered value of *x* at time *t* using a one-sided HP filter with a smoothing parameter of 400,000^{Footnote 11} and where [1, *t*] is the time interval used to run the filter.

To assess the relevance of the normalisation critique for the Swiss case, we compare the BIS gap with an alternative gap: the modified BIS gap. The modified BIS gap accounts for the normalisation critique by smoothing GDP before it enters into the equation denominator. Smoothing is achieved by applying a two-sided HP filter to GDP, which is annualised by multiplying quarterly GDP by four. The SNB has considered the modified BIS gap as a relevant metric in the measurement of excess credit (SNB, 2018a).

$$ {x}_t^{ModBIS}=\frac{c_t}{HP_{\left[1,t\right]}^{2s}\left(4\ {GDP}_t\right)}, $$

(3)

where \( {HP}_{\left[1,t\right]}^{2s}\left({x}_t^{ModBIS}\right) \) is the filtered value of *x* at time *t* using a two-sided HP filter with a smoothing parameter of 1,600 and where [1, *t*] is the time interval used to run the filter.

As before, modified BIS gap \( {y}_t^{ModBIS} \) is then estimated as the deviation of the ratio from its trend computed using a one-sided HP filter with a large smoothing parameter (400,000 for quarterly data).

$$ {y}_t^{ModBIS}={x}_t^{ModBIS}-{HP}_{\left[1,t\right]}^{1s}\left({x}_t^{ModBIS}\right) $$

(4)

To compare the relative performance of the two gap measures, we assess the impact of GDP volatility on the gap measurement. We conduct assessments of point-in-time, and over time, signal volatility.

### 3.2 Point-in-time signal volatility

A point-in-time assessment considers how the signal provided by gaps estimated at time *t* evolves in reaction to (i) GDP revisions and (ii) the availability of new information (for the modified BIS gap). In other words, it is an assessment of how the gaps estimated at time *t* change once one-period ahead (*t* + 1) data are available. Therefore, it is by definition not an assessment of the gaps’ real-time signal but of how past gap signals change due to new data becoming available. The assessment is conducted using GDP vintages between 2005Q3 and 2018Q4^{Footnote 12} and considers both a quarterly and an annual perspective. The credit series is considered as of 2018Q4, as revisions for this series occur rarely and are generally of low amplitude.

#### 3.2.1 The impact of GDP revisions on signal stability

To assess the BIS gap’s signal sensitivity to GDP revisions, we compare absolute error levels for the gaps (Section 3.1). The error levels refer to signal differences resulting solely from revisions to GDP. For each quarter, the absolute difference (or absolute error level) is computed as:

$$ {\Delta}_t^{gap}=\mid {y}_{t,t}-\tilde{y}_{{t},t+a}\mid, $$

(5)

where *y*_{t, t} is the gap defined as in (2) and (4) using the GDP vintage at time *t* and where

$$ \tilde{y}_{{t},t+a}={x}_{t,t+a}-{HP}_{\left[1,t\right]}^{1s}\left({x}_{t,t+a}\right) $$

(6)

is the gap at time *t* based on the GDP vintage available at *t + a*, with *a* ∈ {1, 4} for the quarterly or annual perspective, respectively. \( {HP}_{\left[1,t\right]}^{1s} \) indicates that while the GDP vintage available at *t + a* is used, the estimation of the credit-to-GDP ratio’s trend is based only on data for the interval [1, *t*].

Figure 4 shows the absolute error distribution in gap estimates \( {\Delta }_t^{gap} \)resulting purely from GDP revisions for the two gap measures. On average, the modified BIS gap’s absolute errors display less error volatility than the BIS gap’s. The modified BIS gap’s signal therefore appears to be less sensitive to GDP revisions than the BIS gap’s. This finding holds true at both quarterly and annual frequencies. This is hardly a surprising finding since, by construction, the modified BIS gap smooths GDP fluctuations, thereby underplaying the importance of GDP movements (Section 3). However, it is important to note that at the quarterly frequency, significant outliers are observed for both gaps, suggesting that both measures have the potential to perform relatively poorly in certain quarters.

To shed some light on the above findings, we classify GDP revisions by size. Major revisions (Fig. 3, dark red and red rectangles) are those that either resulted in a parallel shift of the underlying series (e.g. 2012Q2 and 2014Q3)^{Footnote 13} or that mainly affected observations towards the end of the series (e.g. the last 5 to 10 observations, e.g. 2009Q2 and 2017Q2). The remaining revisions are minor and relatively insignificant (Fig. 3, yellow and orange rectangles). In classifying GDP revisions, we observe a certain degree of seasonality. In general, revisions occurring between Q1 and Q2 are large. This is the case for 2007, 2008, 2009, 2011, and 2015 and again most recently for 2016 (Fig. 3, red and dark red rectangles)^{Footnote 14}. This is an interesting but hardly surprising finding given that the release of Q2 data in early September generally^{Footnote 15} coincides with the release of annual estimates. It is therefore to be expected that quarterly estimates are affected by incoming annual data and that the impact on the signal, particularly when compared to other quarters, is considerable. Figure 5 plots the modified BIS gap’s absolute quarterly errors against those of the BIS gap based on the above classification. In line with the findings presented in Fig. 4, the modified BIS gap’s signal appears to be less sensitive to GDP revisions than that of the BIS gap. This holds true for all revision classifications. For the sake of brevity, we only present the quarterly results. However, a similar pattern is observed at the annual frequency. In fact, the effect is more pronounced at the annual frequency, reflecting the fact that up to four GDP revisions can take place over a one-year period.

#### 3.2.2 Effect of the end-point problem for the modified BIS gap

Gap signal sensitivity to new information works predominantly through the credit-to-GDP ratio’s denominator. More specifically, it depends on how GDP enters the credit-to-GDP ratio’s function and impacts the signal provided. As detailed in Section 3.1, GDP enters the BIS ratio’s denominator as the sum of GDP over the four previous quarters. As prescribed by the BIS, the long-term trend is obtained by applying a one-sided filter to the credit-to-GDP ratio. This means that the trend component is calculated recursively and consisting solely of end points^{Footnote 16}. This approach is beneficial in that the final point, and hence the gap’s signal, cannot change as information becomes available in the future. In contrast, our comparative measure (modified BIS gap), which focuses on dampening potential GDP volatility, adopts a smoothed GDP series in its denominator (Section 3.1). This is achieved by applying a two-sided HP filter to GDP before it enters the denominator of the modified BIS ratio (Eq. 2). The two-sided filter differs from the one-sided filter in that it uses all available information to provide more precise estimates. As such, trend GDP and therefore the modified BIS gap at time *t* may be revised each time new information becomes available (end-point problem). This is the case because the denominator of the ratio is revised backwards as new data become available, also affecting past values of the modified BIS gap.

To quantify the impact of new information on signal stability, we estimate the combined errors by combining the effects of GDP revisions and new information. We can then compare the results to those shown in Section 3.2.1 to isolate the impact of new information. For each quarter *t*, the absolute difference is calculated as

$$ {\Delta }_t^{gap}=\mid {y}_{t,t}-\tilde{y}_{{t},t+a}\mid, $$

(7)

where *y*_{t, t} is the gap at time *t* defined in (2) and (4) using the GDP vintage at time *t* and where

$$ \tilde{y}_{{t},t+a}={x}_{t,t+a}-{HP}_{\left[1,t+a\right]}^{1s}\left({x}_{t,t+a}\right) $$

(8)

is the gap at time *t* using the GDP vintage available at *t + a* with *a* ∈ {1, 4} for the quarterly or annual perspective, respectively. \( {HP}_{\left[1,t+a\right]}^{1s}\left({x}_{t,t+a}\right) \) is the credit-to-GDP ratio’s estimated trend for interval [1, *t* + *a*] evaluated at time *t*.

In line with expectations, our results show that new information does not affect the BIS gap in any way (red boxes, left and right panels, Fig. 6). This is the case because the gap is estimated recursively. For the modified BIS gap, however, the error distribution shifts upwards as new information is received. The mean of the distribution of absolute errors increases from 0.21 pp to 0.39 pp (+ 18 bp) while the median increases from 0.07 pp to 0.31 pp (+ 24 bp). Interestingly, the modified BIS gap’s errors are now higher than those estimated for the BIS gap: 0.30 pp (mean) and 0.13 pp (median).

Figure 7 plots the combined quarterly errors of the BIS gap against those of the modified BIS gap for different types of revisions. It is evident that for minor revisions, the modified BIS gap’s absolute errors are systematically higher than the BIS gap’s. This explains why we observe higher mean and median errors for the modified BIS gap than for the BIS gap in Fig. 6. From a policy perspective, this result has two implications. First, when taking the impact of new information into account, the total impact of GDP movements on the gap’s signal can be greater for the modified BIS gap than for the BIS gap. Second, as the modified BIS gap’s signal may move every time new information becomes available, past values of the modified BIS gap are also affected in the absence of GDP revisions. These frequent movements of past gap signals can complicate the interpretation and communication of the modified BIS gap considerably.

### 3.3 Signal volatility over time

In this section, we assess the evolution of the gap’s real-time signal to gauge how extreme GDP movements and GDP revisions affect its reliability over time. The real-time signal provided by the credit-to-GDP gap at time *t* is estimated using the most up-to-date information available at time *t.* Importantly, for this assessment, fluctuations that arise due to the end-point problem (modified BIS gap, Section 3.2) are excluded since the end-point problem does not affect real-time observations.

As in Section 3.1, our assessment considers GDP vintages between 2005Q3 and 2018Q4. To start, we estimate the BIS gap and modified BIS gap using the 2005Q3 vintage^{Footnote 17}. For each subsequent quarter, the gap is re-estimated using the GDP series that would have been available in real time in that quarter (e.g. 2005Q4, 2006Q1 etc.). Individual gap observations are then combined to derive an estimate for the series (Fig. 8).

Between 2008 and 2010, the BIS gap’s and the modified BIS gap’s signals differ considerably, by up to 3.5 pp. This period coincides with extraordinary GDP movement in Switzerland together with a significant upward revision of GDP in 2009Q2. Year-on-year Swiss GDP growth averaged approximately 6.1% between 2006 and end-2008 before turning negative and remaining negative for three consecutive quarters. The sharp slowdown in GDP growth accelerated the growth of the credit-to-GDP ratio, which in turn translated into a rapidly increasing gap. For the modified BIS gap, the impact of GDP growth (both the increase and decrease) was minor in comparison^{Footnote 18}. Trend GDP grew roughly 3.9% on average (year-on-year) between 2006 and end-2008 and slowed to 2.9% through 2009. Subsequent growth in the modified BIS credit-to-GDP ratio (Eq. 3) was moderate, resulting in a much more gradual increase in the modified BIS gap, as observed in Fig. 8. Importantly, signal differences remain considerable even when the 2009Q2 GDP revision is accounted for (Section 3.2.3).

A similar trend emerges towards the end of the sample period. Since the beginning of 2018, GDP has been growing steadily^{Footnote 19} following 6 years of subdued growth^{Footnote 20}. This dynamic has contributed to a slowdown in the credit-to-GDP ratio and a subsequent swift decline of the BIS gap. While the modified BIS gap tends towards the same direction, the GDP growth impact is again comparatively subdued resulting in a far more gradual adjustment of the modified BIS gap’s signal. Taken together, these findings suggest that over time, the BIS gap has been more sensitive to sudden and large GDP movements and that its volatility driven by GDP movements, which may or may not be policy relevant, is considerably greater.

However, from Fig. 8 we note that a trade-off between signal stability and early warning properties of the gap indicator may exist. It seems that the signal provided by the modified BIS gap tends to lag the BIS gap in the build-up phase. This is evident in the 2008-2010 high GDP growth period where the modified BIS gap lags the BIS gap by up to 6 quarters. The modified BIS gap continues to lag the BIS gap after 2010 despite more convergence in the signals. We observe a similar effect in the lead up to the 1990s crisis in Switzerland.

To summarise, our assessment thus far has shown that for the Swiss case, the BIS gap performs as well as the modified BIS gap against the normalisation critique. Hence, based on an assessment of the normalisation critique, we find no compelling evidence for a need to deviate from using the BIS gap as a reliable measure of excess credit in the Swiss credit market. Importantly, we note that the modified BIS gap tends to lag the BIS gap in the build-up phase, suggesting a trade-off between signal stability and early warning properties of the indicator. From a policy-making perspective, if confined to the use of one single indicator, a measure with superior early warning properties would likely dominate. The fact that the indicator provides a signal early ensures enough time for authorities and banks to react when credit excesses are building up. However, as shown above, both measures are prone to their own caveats. This highlights the importance of basing policy decisions on a broader set of information. As such, authorities should consider supplementing guiding indicators with additional metrics or plausible narratives based on a wide-ranging set of relevant indicators.