We have over 340 months of “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.

Table 1
Stats
for mom inflation 1993-2021
| |

average
| 0.17% |

median
| 0.22% |

Variance
| 0.000013 |

St. dev.
| 0.003552 |

skew
| -0.7028 |

kurtosis
| 0.5912 |

Table 2: Mom inflation by Decile and Quartile | |||

10
| -0.33% | Quartile | |

20
| -0.06% |
25
| -0.01% |

30
| 0.03% | ||

40
| 0.13% | ||

50
| 0.21% |
50
| 0.21% |

60
| 0.29% | ||

70
| 0.36% | ||

80
| 0.45% |
75
| 0.42% |

90
| 0.55% | ||

99
| 1.00% |

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.

Table 3: | mom inflation | Percentile | Annualised |

Mar-21
| 0.29% | 59 | 3.6% |

Apr-21
| 0.64% | 95 | 8.0% |

May-21
| 0.59% | 92 | 7.3% |

Jun-21
| 0.50% | 85 | 6.2% |

Jul-21
| -0.02% | 29 | -0.2% |

Aug-21
| 0.71% | 97 | 8.8% |

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.

Table 4: mom stats 1988-92 | |

Average
| 0.45% |

Median
| 0.38% |

Variance
| 0.000031 |

St dev
| 0.005546 |

Skewness
| 2.66 |

kurtosis
| 11.94 |

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.

Figure 2 gives the Histogram for Mom inflation 1988-1992.

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).

Headline Inflation is set to increase in the coming months: there are policy induced increases (reversal of VAT reduction for hospitality and Ofgem price caps) along side pressures from the supply chains and labour markets. However, the last 5 months have also been exceptional and very much on the high side historically. Whilst a “return to the seventies” may not be on the cards, a return to the period 1988-1992 may be a possibility.