I write this back in October 2021, a summary of the data.

We have over 340 months of month on month or “mom” inflation since January 1993, during which inflation has remained in the range 0-5% and most of the time in the range 1-3%. We can summarise the data with the following statistics: Table 1 gives the standard statistics, Table 2 the deciles and quartiles.

As we can see, the average is 0.17% (to two decimal places), which is consistent with the long-run average annual inflation of 2%. The median is quite a bit higher, indicating that there is a bit more of a “down” tail with more low values, as reflected in the negative skewness. The Kurtosis is Pearson’s measure which is zero for the normal distribution: the slightly positive value (leptokurtic) reflects the fat tails. The mom inflation is noisy, as reflected by the large value of the standard deviation relative to the mean (the standard deviation is over double the mean): the inter-quartile range is 0.43.

Figure 1 is the histogram for inflation in the period January 1993 to August 2021

Both the mean and the median are in the tallest column, which represents 24% of the total. However, the bottom decile lies below -0.33% and the top decile above 0.55%.

Given these general statistics of mom inflation, what can we say about the recent experience of inflation in 2021? We have seen a few months of very high inflation since March 2021, which we show in Table 3.

As we can see, three out of the months were in the top decile. So this is a “rare” event, since in general, mom inflation is not significantly serially correlated from month to month. Now, August was inflated by a clear policy induced “base effect”, the impact of the August 2020 “Eat out to Help out” and the hospitality VAT reduction which accounted for 0.4% of the increase. However, even the remaining 0.31% is still in the 62^{nd} percentile. This is clear if we take the annualised inflation rate, which represents the annual rate that would result if the mom inflation was repeated for 12 months (the figures allow for compounding). Apart from July, all of these are well above the Bank of England’s target rate of 2%.

We can look back at the last period of high inflation from the late 1980s to early 90s: the Lawson boom and crash. We can take the CPI data from 1988-1992.

As we can see, the stats look rather different: the mean mom inflation is 0.45% (an annualised rate of 5.6%). The skewness is positive and large indicative of a large up tail. (Excess) Kurtosis is also large, indicating a leptokurtic distribution with fat tails. These statistics are mainly due to the policy induced “Black Swan” of April 1991, when mom inflation was a stratospheric 3.4%. Since the period only has 47 months (Feb 1988 to December 1992), an outlier of this magnitude still shines through. The Budget of April 1991 was one of Norman Lamont’s emergency budgets with an increase in VAT from 15 to 17.5% along with increases on alcohol and Tobacco duty. The histogram for this period of 4 years.

If we compare the two histograms, we can see that the long left tail in 1992-2021 is absent. Instead, we see the long right tail and of course the April 1991 outlier. 7 out of the 47 inflation figures were above 1%: in the period 1993-2021, out of 343 months only one exceeded 1% (April 1993).

We depict the whole time series of mom inflation from 1988 to 2021 in Figure 3. The red dotted line is the twelve-month moving average. This represents the headline 12 month annual inflation in a miniature version (since the headline is closer to the *sum* of mom inflation rather than the average).

We can see that the big increase in inflation since February 2021 has resulted from a few large and unusual mom inflation figures. Base effects were present, particularly for August 2021. Looking forward, we can see some more policy changes that will tend to increase inflation: the reversal of the VAT cut on hospitality which will effect the October 2021 and May 2022, and Ofgem’s “price cap” which will effect the October 2021 and April 2022 inflation figures.

The exact size of the Ofgem price cap increase at the end of April is unknown as yet, but likely to be large. It is a backwar-looking cap based on inflation of wholesale prices over the previous months. Since the increase has already been substantial and unlikely to be reversed before April, it indicates a large increase in April 2022. These are policy induced changes. The prevalence of labour and supply shortages which seem likely to persist for longer than was expected earlier in the year indicates that inflation will probably remain elevated until 2023, peaking at over 5% in April 2022.

## Update April 2022.

Clearly, since I wrote this October 2021, quite a lot has happened. Prior to the invasion of the Ukraine, most commentators saw inflation peaking in April 2022 with the OFGEM price cap increase. The level of inflation remained high and so the “peak” of inflation was thought to be 7-8%. Post the Ukraine war and with the ensuing economic sanctions imposed by the “Collective West” (North America, Western Europe and close allies Australia, Japan, South Korea, Taiwan and New Zealand), inflation looks set to reach double digits and not to start to fall until the war is over and sanctions either end or cease to be effective. In the latest figures mom inflation was 0.8% in February and 1.1% in March. In terms of our histogram and Table 2 above, these are exceptional figures in the top percentile of the distribution 1993-2021. With the coming increase in the OFGEM price cap in September 2022 being at least as big as the one just witnessed in April 2022, it looks as if even if the war ends soon inflation cannot begin to fall significantly until September 2023.