Metrics and Turning Points of Cycles 1660–2018

Abstract

This chapter provides a summary of business cycle metrics for the UK under the different statistical and algorithmic approaches discussed in Chapter 3 and the historical GDP data discussed in Chapter 4. The range of different business cycle metrics that can be derived from the available techniques is very wide. This highlights the need to assess these metrics in the context of the historical narrative of UK output fluctuations.

In this chapter we apply some of the methods discussed in Chapter 3 to the composite GDP data series discussed in Chapter 4. This is to draw out some basic metrics on business and credit cycles based on the existing data. We first consider some of the key metrics using classical business cycle analysis, drawing heavily on Chadha et al. (2019), before going on to look at growth cycles under various methods of de-trending discussed in Chapter 3. We look at annual data from 1660 and quarterly data from 1920 with the break-in World War 2 that was discussed in Chapter 4.

5.1 Classical Cycle Metrics

We first consider classical business cycle dating on annual data from 1660, adopting the simple algorithm from Chapter 3 where we identify expansions and contractions in GDP and GDP per capita. Table 5.1 summarises the annual turning points in chronological order. Chart 5.1 shows this graphically. It charts log levels of GDP over the period with contraction periods marked in grey.

Table 5.1 Classical cycle peaks and troughs

Chart 5.1

Expansions and contractions in GDP

The chart suggests that for GDP there have been 72 cycles between the peak of 1663 and the trough of 2009 using a simple rule based on annual turning points. For GDP per capita there have been 78 cycles. A comparison of Charts 5.1 and 5.2 shows that many of the differences occur during the mid-late C19th when population growth rates were relatively large and positive implying many more contractions in GDP per capita.

Chart 5.2

Expansions and contractions in GDP per capita

Tables 5.2 and 5.3 ranks these cycles in terms of the size of the contraction in GDP from peak to trough and looks at the frequency and amplitude of cycles over time. Prior to 1825 the economy was in contraction for just under half of the time. After 1825 this drops to around a quarter of time for the next century or so before falling to around 10%. This can be seen visually in Charts 5.1 and 5.2. So it is the infrequency of large contractions that underpins the underlying shift in the growth rate of per capita incomes noted in Chapter 4. Contractions however have lengthened over time, with C20th recessions lasting longer than those in earlier centuries. Expansions have generally lengthened and increased in size during the C20th. The length of the classical cycle as a whole, measured as the sum of expansion and contraction periods, has increased fivefold since the late C17th.

Table 5.2 Ranking of individual annual contractions

Table 5.3 Summary statistics on cycles

Table 5.2 ranks individual annual contractions in terms of output loss. The worst historical contractions largely occurred in the late C17th and early C18th. However the worst fall in output occurred after the end of World War 1 from a peak in 1918 to the trough in 1921, when GDP fell by a quarter over three years. Another large fall occurs at the end of World War 2 when output falls by 14%. By contrast the Great Depression and the Great Recession rank 15th and 25th on the all-time list of contractions. The recession after the South Sea Bubble in 1720 ranks 29th on the list while that in the early years of Mrs. Thatcher’s government is 44th.

Table 5.4 provides a summary of recovery periods following recessions documenting how long it takes for output to recover to its previous peak. The length of recovery is measured from peak to peak rather than trough to peak given that many recoveries were interrupted by ups and downs in output. So it is defined as the length of time it takes output to recover from the start of the recession in that year. The table also documents the cumulative loss in output (relative to its previous peak) in percentage terms.

Table 5.4 Contractions ordered by length of time taken to recover to previous peak

The recovery from the 1704–1705 recession represents the longest and most costly length of time that output took to return to its previous peak. So on this metric it outscores the fall in output at the end of WW1 in terms of cumulative loss, even though it took 16 years in both cases for output to recover. The third row of the table shows that no sooner had output returned to its 1704 peak in 1720 then another recession occurred around the same time as the South Sea Bubble and again it took another 16 years for the level of output to recover. Note that in all these 16 year periods, the recovery was interrupted by several contractions in output most notably by the Great Depression in the case of the recovery following the contraction in output at the end of World War 1. Output in 1929 was still 3% below its 1918 level when the Wall Street Crash hit.

Charts 5.3 and 5.4 together with Table 5.5 show quarterly turning points over the 1920–1938 and 1955–2018 periods based on the rule that a technical recession should involve at least two consecutive quarters of negative growth. It reveals subtleties about certain recessions that are masked by the annual data. In particular it reveals the double-dip recessions in the Great Depression and in the mid-1970s which we will return to in the narrative chapter. There is also an issue about the timing of the trough in 1921 which is affected by the miner’s strike between 3rd of April and 28th June of that year as discussed in Mitchell et al. (2012) and can be seen clearly in Chart 5.3 with a large dip and recovery in 1921Q2 and Q3. This also affects the assessment about the size of the contraction in 1921 which is based on total output produced over the year. Note that in this case, where we have no quarterly data for 1918 and 1919, the 1930s recovery would be separate from that after 1920Q3 where output had returned to its previous “peak” by mid-1924. So the treatment of World War 1 matters quite a bit for this type of metric.

Chart 5.3

(Notes Recession periods are shaded)

Quarterly expansions and contractions (2 quarter rule) 1920–1938

Chart 5.4

(Notes Recession periods are shaded)

Quarterly expansions and contractions (2 quarter rule) 1955–2018

Table 5.5 Quarterly turning points in the United Kingdom, 1920–1938/1955–2018

To complete our analysis of classical economic cycles we also estimate a simple two-regime Markov Switching model in order to determine contraction periods, using Hamilton’s (1989) method that was discussed in Chapter 3. The results on annual and quarterly data are shown in Tables 5.6 and 5.7. The annual model suggests an expansion growth regime of just under 2% a year and a contraction regime of a 9% fall in output. As Chart 5.5 shows the model is able to detect turning points in large recessions but some contractions, such as the Great Depression of 1931, shows a probability of under 0.5 of being such a regime reflecting the relative mildness of that recession in output terms (although as we will see not in unemployment terms). The quarterly model shown in Chart 5.6 is able to pick out the key C20th recessions very well with all the major contractions showing a conditional probability of >0.5 of being in a contractionary state with the exception of the early 1990s recession.

Table 5.6 Markov-Switching model results—annual data 1660–2018

Table 5.7 Markov-Switching model results—quarterly data 1955–2018

Chart 5.5

Annual turning points 1660–2018: Markov-Switching model

Chart 5.6

Quarterly turning points 1955Q1 to 2018Q4: Markov-Switching model

5.2 Growth Cycle Metrics

For growth cycle metrics we derive de-trended measures using the various methods discussed in Chapter 3. We estimate the following models on annual data:

• Hodrick Prescott filtered (HP) estimates using the “standard” lambda parameter of 100.

• A Band-pass filter (BP) based on the Christiano-Fitzgerald asymmetric approach where the lower and upper bands are set at 2 and 8 years.

• An Unobserved Components (UC) model based on the local-linear trends model of Chapter 3. The cycle is modelled as an AR(2) process so that the data can determine whether the roots are complex or not, rather than impose the complex roots via specifying an explicit trigonometric cycle.

• A segmented -trend model (ST) where the cycle is backed out by removing a series of split-deterministic time trends. We use GDP per capita for the data here so implicitly the trends relate to labour productivity and the employment ratio. The time trends are linear.

• A Beveridge-Nelson (BN) decomposition derived from an ARIMA(2,1) model.

For each model we chart the implied cycles in Charts 5.7, 5.8, 5.9, and 5.10. In each case the Hodrick Prescott filter is used as a benchmark for comparisons. We then derive peak and trough points under each approach based on the deviation of each cycle from trend. As discussed in Chapter 3, we apply censoring rules to ensure that troughs represent negative deviations from trend and peaks are positive, in order to avoid mini-peaks and troughs. We also ensure that peaks and troughs alternate making judgements about where the peak or trough lies depending on the pattern of observations. This allows us to derive the metrics about the timing, length and amplitude of cycles which are shown in Tables 5.8, 5.9, 5.10, 5.11, 5.12, and 5.13.

Chart 5.7

Cycles based on Hodrick Prescott filter and band-pass filter

Chart 5.8

Cycles based on Hodrick Prescott filter and unobserved component model

Chart 5.9

Cycles based on Hodrick Prescott filter and segmented trend model

Chart 5.10

Cycles based on Hodrick Prescott filter and Beveridge Nelson decomposition

Table 5.8 Classical versus growth cycle dating

Table 5.9 Growth cycles—HP filter (λ = 100)

Table 5.10 Growth cycles—band-pass filter

Table 5.11 Growth cycles—unobserved components model

Table 5.12 Growth cycles—segmented trend

Table 5.13 Growth cycles—Beveridge Nelson decomposition

The results of applying the different de-trending methods are largely what would be expected from our discussion in Chapter 3. Upturns and downturns are more symmetric than classical cycles. The Band-pass filter delivers cycles that are slightly less volatile than the HP filter and slightly shorter, though peaks and troughs are fairly coincident.

The UC model filters out more of the fluctuations in output as noise and delivers fewer and longer, more persistent cycles. However the roots of the estimated AR(2) component are real rather than complex so there is no periodic cycle underlying the generated cycle. Charts 5.11, 5.12, and 5.13 summarise the AR(2) trend, cyclical and noise components.

Chart 5.11

Unobserved components model—trend

Chart 5.12

Unobserved components model—slope of trend

Chart 5.13

Unobserved components model—noise and AR(2) cycle

The segmented trend model has the least volatile trend and unsurprisingly leads to cycles that are generally larger in amplitude, although again the turning points in the growth cycle are very similar. The Beveridge Nelson has the most volatile trends and leads to very noisy cycles with little amplitude. The predicted turning points are also very different.

After applying the censoring rules most of the approaches suggest a narrowed-down set of turning points (Table 5.8) and, overall, they suggest that the length of growth cycles increases after 1870 (Tables 5.9, 5.10, 5.11, 5.12, and 5.13). The HP and BP models suggest that the business cycle lengthens from around 4–5 years to between 6 and 9 years. The UC model however appears to show that cycles mostly increase in length after World War 2, with a total cycle duration of 11–13 years between 1663 and 1943. The interwar periods and the 1660–1720 period show the greatest amplitude which is unsurprising given these contain the deepest recessions.

Overall the tables show quite a range in business cycle metrics, suggesting deriving stylised facts on the business cycle is difficult and very dependent on the method used. The BN decompositions in particular suggest that most of the fluctuations in GDP can be attributed to the trend component and that the cyclical component is noisy with low duration and amplitude. That would imply that many shocks lead to permanent shifts in output either because they reflect supply shocks as in the real business cycle model or demand shocks that have hysteretic effects on potential supply as discussed earlier in Chapter 2. The HP and BP models tend to reflect the “conventional wisdom” of a lengthening cycle over time but one that lies within traditional business cycle territory of between 2 and 10 years. The UC model results are particularly interesting in that they suggest that the duration of cycles are, on average, very much in the range of what modern consensus would deem to be credit cycle territory—a duration of between 8 and 20 years. As we show in Chapter 6 many of the peaks and troughs in the UC model bookend financial crises. On post-WW2 data the annual UC model suggests a long upswing of almost 25 years between 1948 and 1973, once censoring is applied.

We also apply some of the de-trending methods to the quarterly GDP data available from 1920–1938 and from 1955. Charts 5.14, 5.15, 5.16, and 5.17 consider the peaks and troughs for both the interwar and post-WW2 periods and a comparison is made between the HP filter (HP), Band-pass filter (BP(CF)) and an AR(2) cycle from an unobserved components model applied to quarterly data. Once again the BP and HP filters show similar patterns although the BP filter is smoother as it excludes high frequency movements that the HP filter lets through. The UC model exhibits more significant differences particularly in the post-WW2 period. The UC model suggests a more persistent boom in the build-up to the Great Financial Crisis in 2008 and a more persistent contraction relative to trend thereafter. Also note that applied to quarterly data from 1955, the UC model shows more peaks and troughs over the post-WW2 period than the annual UC model (with censoring rules applied). Clearly the development of quarterly GDP data over the 1938–1955 period would be beneficial so a longer quarterly assessment of growth cycles can be made.

Chart 5.14

Interwar growth cycles using quarterly data—HP and BP models compared

Chart 5.15

Interwar growth cycles using quarterly data—UC and BP models compared

Chart 5.16

Post-war growth cycles using quarterly data—HP and BP models compared

Chart 5.17

Post-war growth cycles using quarterly data—UC and BP models compared

Overall the results reaffirm the conclusion that, although many of the peaks and troughs derived from the various statistical methods show similar patterns, the business cycle metrics can vary quite a lot. None of this is surprising given the discussion of Chapter 3 and it is clear statistical methods alone are not sufficient to uncover the nature of business cycles. A key test is whether these metrics when combined with the historical narrative from contemporary and secondary sources can tell a consistent story over time. This is the focus of Chapter 6.