# Appendix 1: Identification of Rate Cycles

Section II discusses the application of the BBQ algorithm in Harding and Pagan (2002) to identify local maxima and minima in policy interest rates and thereby define rate cycles. A simple application of this algorithm to the data on policy interest rates, however, can be problematic due to several characteristics of the interest rate data—particularly long windows when there is no change in it. To address this and more accurately identify the turning points of easing and tightening phases consistent with changes in central bank policy stances, we start with the dates identified in the BBQ algorithm, but then make several adjustments and add additional criteria for a month to qualify as a turning point. This appendix describes the process used to identify the easing and tightening phases in more detail.

First, we apply the BBQ algorithm in Harding and Pagan (2002) to the policy rate data, with one adjustment. Early in the sample, when the policy rate is market-determined in some countries, there are occasionally sharp spikes in the rate that appear to primarily reflect shifts in market sentiment, shifts that are quickly reversed. To avoid classifying these temporary market-based fluctuations as turning points in a cycle, we smooth across these spikes by replacing it with (it+1 + it−1)/2 if the policy rate changes by more than 500 basis points in one month.

Second, we set three parameters for the BBQ algorithm: (1) the window on each side of a local maxima and minima must be at least 18 months; (2) a full cycle (including both tightening and easing phases) must be at least 36 months; and (3) any individual phase of a cycle (either a tightening or easing phase) must last at least 7 months. The first two criteria require relatively long windows on each side of a turning point and for the full cycle in order to capture changes in policy which are not reversed quickly; this also avoids classifying changes in policy rates that largely reflect market movements as turning points in the policy cycle. The shorter window for individual phases in a cycle, however, still allows short periods when central banks adjust policy rates to qualify as an easing or tightening phase (such as a rapid reduction in rates over one month in response to a shock).

Third, we require it to increase or decrease for month t to qualify as the start of a tightening or easing phase, respectively. This requirement sounds obvious—but is necessary as the dating algorithm incorrectly identifies about 10 false “turning points” during long periods when there is no change in interest rates. This requirement is also needed to correctly date turning points when the exact month identified by the algorithm is slightly off due to substantial volatility in the data or the smoothing around spikes (as mentioned above). Also, if any of these adjustments causes a “false” phase to be dropped, then the subsequent phase must also be dropped as an easing phase must be followed by a tightening phase (and vice versa).<sup>77</sup> Fourth, we require that the change in the policy rate identified as a turning point must be “meaningful or lasting”. To qualify as “meaningful or lasting”, we require: (a) either a change in rates of at least 50 basis points over one month, or (b) at least one rate changes (of any size) over a year after the first change such that the policy rate is at least 30 basis points higher/lower one

> 77 For example, the algorithm initially identified Switzerland as starting a tightening phase in July 2016 and starting an easing phase in December 2020—despite there being no change in Switzerland’s policy rate from January 2015 (when the rate was lowered to -0.75) through May 2022. Therefore, we drop the falsely identified turning point in July 2016, as well as in December 2020, so that Switzerland remains in an easing phase from 2010 (when it started lowering rates) through May 2022 (when its first rate hike since before 2015 meets the criteria to start a tightening phase).

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