Have you, as a result of your frenetic activity since Christmas, got a bit of a peer review backlog? I can help. Let me be the scheme actuary you’re temporarily short of. With a 10% discount on the rates shown here until the end of the UK 2013/14 tax year, and a further 10% reduction for type 2 peer reviews.

Peer review cartoon

The Pensions Regulator has a consultation on the go. In fact they have two: regulating defined benefit pension schemes and regulating public service pension schemes. Both started in December and are due to wind up in February. The defined benefit pension schemes one alone runs to over 160 pages across the four documents published. All at the busiest time of the year for most pensions actuaries, caught between the 31 December 2013 accounting disclosures and the looming deadlines for submitting the 31 December 2012 scheme funding assessments. Could it be that they are rather hoping to limit the feedback they get?

Because the changes that are being proposed to the funding regime known as scheme specific funding which has run for 8 years are dramatic. Under the pretext of only making changes to allow the introduction of the Regulator’s new objective to “minimise any adverse impact on the sustainable growth of an employer” (see my previous post on this), they have effectively announced the death of scheme specific funding and proposed a system which looks very much like the Minimum Funding Requirement (or MFR – the previous discredited funding regulations) mark two to me, although the Regulator insists that it will be completely different this time.

The main problem with the MFR was that it was a one-size-fits-all approach (although it did vary in strength depending on how far on average members had to go until benefits were paid – known as the duration of the scheme), which encouraged an inappropriate level of contributions for many schemes (the minimum funding requirement effectively became a maximum funding requirement in many cases).

Fast forward to now, and the new proposed funding approach based around something called the Balanced Funding Outcome (BFO). This calculates a required level of assets for each scheme on an “objective liability measure, independent of the scheme’s funding assumptions”. The actual assets will be compared with the required amount and a recommended level of contributions to get up to the required level will then be calculated by the Regulator. The contributions the scheme trustees have agreed with the scheme’s employer will then be assessed to see if they measure up. Where MFR varied by duration, BFO will vary by duration and covenant (how likely the employer is to stick around to pay the last pensioner). So, as you can see, completely different!

At the end of Appendix G of the 50 page draft funding policy, we finally find the problem that I think the Pensions Regulator really wants to solve:

TPR graph

Look at all those dots. They’re all over the place. There is currently absolutely no correlation between the deficit reduction contributions (DRCs) employers are paying and the funding level in their schemes. The Regulator is determined to change that, by giving trustees and employers sight of their preferred contribution number during their negotiations. The contribution number won’t be compulsory of course, but if you use it then the Regulator will leave you alone. It is almost as if they have never heard of Daniel Kahneman or behavioural economics.

What will happen? Well who knows but here’s a guess. Schemes to the bottom left of the chart above (ie low assets and contributions) are already being subjected to extra scrutiny and generally have employers in such a poor financial state that there is very little they can do about it. But those in the top right will effectively have been given permission to swoop down to the blue line with a whoop of “Pensions Regulator’s new objective”. It will be like the 90s all over again when pension schemes took contribution holidays because they were measuring their funding in an unrealistic way. It will be seen as financially stupid to be in the top right of the Regulator’s graph. Group think will be in charge once more. But, to use another quote from Yogi Berra, the baseball icon, “If you don’t know where you are going, you might wind up someplace else”.

If we agree to this we will be making the pensions system more fragile. The model used by the Regulator will not anticipate the next defaulting economy or other Black Swan that throws currency and financial markets into meltdown (no one was suggesting Argentina would default a month ago) and reduces everyone’s level of funding, so when that happens everyone will be in trouble rather than just the proportion of schemes in difficulties we have now. The overall funding risk of defined benefit pension schemes will be inflated so much that the system may not easily recover.

It gets worse. There is a lot in this consultation about governance, and also references to asset liability modelling, due diligence, reverse stress testing, scenario testing and covenant advice. These are all things which are likely to be a problem for small schemes, which I pointed out previously when they were proposed by EIOPA (because, let’s be clear, it is compliance with prospective EU legislation which has driven many of these proposals). But guess which group are going to see an almost total reduction in the scrutiny they get from the Regulator under the new regime? That’s right: small schemes.

There is still time to register your opposition to reliving the last 15 years of defined benefit pensions all over again: the consultation runs until 7 February.


We are only six months into the Bank of England’s new regime of giving forward guidance about what circumstances might lead them to adjust the Base Rate and they are already in a bit of a mess with it. Whether forward guidance is abandoned or not is still in the balance, amid much confusion. However, much of this confusion seems to be due to the challenge that events have provided to the assumption that the Bank of England could make reasonably accurate economic predictions.

It turns out that not only did the Bank not know how fast unemployment would fall (not a surprise: the Monetary Policy Committee (MPC) minutes from August make clear that they suspected this might be the case), but neither did they know, when it did fall, what a 7% unemployed economy would look like. The Bank has been very surprised by how fragile it still is.

Back in August 2013, when unemployment was still at 7.7%, the MPC voted to embrace the forward guidance which has now fallen on its face. This said that: In particular, the MPC intends not to raise Bank Rate from its current level of 0.5% at least until the Labour Force Survey headline measure of the unemployment rate has fallen to a threshold of 7%, subject to the conditions below.

The “conditions below” were that all bets would be off if any of three “knockouts” were breached:

1. that it would be more likely than not that CPI 18 to 24 months ahead would be at 2.5% or above (in fact it has just fallen to 2%);

2. medium-term inflation expectations no longer remained “sufficiently well anchored” (the gently sloping graph below would suggest it hasn’t slipped that anchor yet); or

3. the Financial Policy Committee (FPC) judged monetary policy posed “a significant threat to financial stability”. More difficult to give an opinion on that one but, looking beyond the incipient housing market bubble, it is difficult to see that monetary policy is causing any other instability currently. Certainly not compared to the instability which would be caused by jacking up interest rates and sending mortgage defaults through the roof.

Source: Bank of England implied spot inflation curve

Source: Bank of England implied spot inflation curve

So it seems that there has been no clear knock out on any of these three counts, but that the “threshold” (it was never a target after all) of 7% is no longer seen as significant a sign of economic recovery as it had been believed it would only last August.

Fun as it is to watch the illusion of mastery of the economy by the very serious people flounder yet again, as what is an intrinsically good piece of economic news is turned into a fiasco of indecision, I think the Bank is right to believe that it is far too early to raise interest rates. I say so because of two further graphs from the Office of National Statistics (ONS) latest labour market statistics, which were not included in their infographic on the left.

The first is the graph of regional unemployment, which shows very clearly that large areas of the UK are still nowhere near the magic 7% threshold: the variations are so wide and, in austerian times, the resources to address them are so limited that it makes sense not to be overly dazzled by the overall UK number.

Regional unemployment

The second is the graph of those not looking or not available for work in the 16-64 age group since the 1970s. As you can see, it has recently shown a very different pattern to that of the unemployment graph. In the past (and borne out by the data from 1973 to around 1993) the number not available to work has tended to mirror the unemployment rate as people who could manage without work withdrew from the job market when times got tough and came back in when things picked up. However in the early 90s something new started to happen: people withdrawing from the job market even when unemployment was falling. There has been a steady increase in their number until it finally started to fall only last year. So what is happening?

Not in labour force

One of the factors has been a big increase in the number of people registered as self employed, rising from 4.2 million in 1999 to 5.1 million in 2011. However, many of these people are earning very little and I suspect that at least some of them would have been categorised as unemployed in previous decades. There must therefore be some doubt about whether 7% unemployed means what it used to mean.

The Bank of England have shown with their difficulties over forward guidance that it is very hard to look forward with any degree of precision. It should be applauded for admitting that it doesn’t know enough at the moment to start pushing up interest rates.

We are certainly living longer than ever before. But within that statement lie a number of interesting stories neatly summarised by the Office of National Statistics (ONS) report on average life span in England and Wales, which came out around a year ago.

The first graph below has been constructed by first devising a rather artificial thing called a life table. This starts with 100,000 people at birth for each year and then, based on the probability of dying in the first year of life, works out how many are expected to survive to age 1. Of those, the probability of dying in the second year is applied to the number at year 1 in the table to work out the expected number of deaths during the second year. These are then deducted from the year 1 entry to arrive at the year 2 entry. And so on. Skip the next paragraph if that explanation is enough for you.

So, for example, taking the data from the England & Wales interim life tables 2009-11, we have 100,000 males at age 0, 99,508.2 at age 1 and 99,475.2 at age 2. This is because the probability of death for males in the first year of life over the 3 year period 2009 to 2011 was 0.004918, so 100,000 x 0.004918 = 491.8 expected deaths and 100,000 – 491.8 = 99,508.2 expected to be left in this imaginary population to celebrate their first birthdays. The probability of death in the second year of life was 0.000331 (notice this is much smaller, we will return to the significance of this later) so that the number of boys getting to blow two candles out on a cake is expected to be 99,508.2 – (0.000331 x 99,508.2) = 99,475.2. This table is nothing like real life of course, as we all move through time as we get older, so that our chance of death at age 20, say, would not be the same as the chance of a 20 year old dying 20 years earlier. However such a table does allow us to illustrate the patterns of deaths in any given year, and then compare these with other years.

The three measures used are based on the three averages you learned at school: the mean, median and mode.

The life expectancy at birth is a form of mean. The probability of reaching each age can be calculated by looking how many people you have at that age in your imaginary life table and dividing that number by the 100,000 you started with. Then each of these probabilities is multiplied by the age reached and then the probability of dying in that year (strictly the ONS life tables are constructed by taking the average probability for each year as the mid point between the start of the year and end of year probability, with a further adjustment in the first year when the probability of death is very much concentrated in the first 4 weeks). This can be shown to be same as all the entries (from year 1, year 2, year 3, etc) in the life table added up and divided by the 100,000 you started with.

The median is the age at which we expect half the population to have died. The mode is the age at which we see the highest number of deaths. The mode here has been adjusted in two further ways: the deaths below age 10 have been removed (otherwise it would have been 0 in a number of years and it is the old age mortality we are looking to compare) and it has also been smoothed to take out year on year fluctuations caused by wars and flu pandemics (again this would lead to modes in the 20s and 30s in some years, which are not the ages we are focused on).

life expectancy

There are many features to this graph, as set out in the ONS paper. The closing down of the gap between the mode on the one hand, and the median and life expectancy at birth on the other, is especially striking. This was mainly due to the massive improvement in survival rates in the first year in birth in particular. It also demonstrates that, contrary to what we might have believed about Victorian England, plenty of people were living into their 70s in the 1840s.

However I want to focus on the race to live longer between men and women because, armed with these three numbers (or six as we are looking at men and women separately) for each year, we can see that men and women have had a rather different journey since 1841.

As we can see the experience was fairly similar in the 1840s, although even then women lived 2 or 3 years longer on the mean and median measures than men. The modal age at death was more variable due to the relatively small numbers at advanced ages in the early years, but was between 25 and 30 years in excess of the median and life expectancy at birth due to the relatively high level of infant and child deaths at the time. The median and life expectancy then steadily advanced on the mode (interrupted by two downward spikes: in the mid 1840s a combined assault of typhus, flu and cholera, and a much larger one in 1919 from the flu pandemic).

In 1951, the female median age at death moved above the male modal age for the first time, marking the start of a 20 year period where life expectancy increases on all measures for women exceeded those of men. While the commonest age of death for men stayed in the mid 70s over this period, that for women increased from 79.5 to 82.5, leading to a peak difference in commonest age of death between men and women of 8.5 years in 1971. A graph of the differences in all three averages is shown below.

Differences life expectancies

Since 1971 the tide has turned, with all six lines steadily, if very gradually, converging. In 2010 the male modal age at death finally crossed back over the female life expectancy at birth, and all three differences fell below 4 years for the first time since 1926. As the Longevity Science Advisory Panel’s second report points out, the average differences between life expectancy by gender at birth of 4.15 between 2005 and 2009 represent, in terms of the percentage of female life expectancy (5.1%), a return to the levels seen at the start of the journey in 1841. In 2010 this percentage fell to 4.7%. It has only fallen below that level four times since 1841, and not since 1857.

So we may be entering a new phase in the expected longevity differences between men and women. And, as the history shows us, those differences can change with surprising speed.

The latest figures (January 2014) from the European Central Bank (ECB) statistics pocket book have just been issued, providing comparisons between European Union (EU) countries, both in the Eurozone and outside it, on a range of measures. And some of these comparisons are not quite what I expected to see.

For instance, perhaps surprisingly in view of the current hysteria in the UK about economic migrants from Bulgaria and Romania, we find that unemployment was lower in Romania (7.3%) than it is in the UK (7.4%) for the latest month (September 2013) for which data on both was available (it’s the UK’s that is missing for October and November for reasons unknown).

I have graphed a selection of the data below, Euro countries are to the left:

ECB country data labelled

First to note, which may also surprise some, is that private sector debt in the UK is not particularly big in EU terms: Denmark and Sweden both have considerably higher private sector debt as a percentage of GDP than the UK, as do 7 countries in the Eurozone with Ireland and Luxembourg heading the list.

Government expenditure as a percentage of GDP is the most evenly distributed of all the measures. I have graphed the 2012 data, as the Q2 2013 data omitted France and Germany. The range across all countries is between 36.1% (Lithuania) and 59.5% (Denmark), with the UK’s 47.9% only a little below the Eurozone average of 49.9%. This suggests to me, for all of the political rhetoric we hear, that it is not the total spend which tends to alter much but the distribution of it. Certainly in the UK, there appears to have been a focus on a relatively small section of the welfare budget to make the savings from.

Government debt is much higher as a proportion of GDP in the Eurozone than in the rest of the EU, with no one outside the Eurozone reaching the Eurozone average of 93.4% (although the UK comes closest at 89.8%). There are 5 countries in the Eurozone with debt above 100%: Belgium (perhaps surprisingly), Ireland, Greece, Italy and Portugal. Spain’s debt is actually below the Eurozone average at 92.3%.

Unemployment statistics are unsurprisingly dominated by Greece and Spain, whose unemployment rates are around 50% higher than the next country. Unemployment rates average 12.1% in the Eurozone and 10.9% for the EU as a whole, perhaps demonstrating the advantage of keeping control of your exchange rate during an economic downturn.

The population statistics remind me what an unusual decision it was for the UK to stay out of the Euro. All the other big countries (by which I mean those with populations over 45 million) are in the Eurozone, with the next biggest EU country outside the Euro being Poland at 38.5 million (with the prospect of their joining the Euro receding somewhat last year). Most of the richer countries are too, illustrated by a much higher proportion of GDP (see below) held in Eurozone countries than their relative populations would lead you to expect.

Finally we come to GDP. This looks very differently distributed according to whether you look at amounts in Euros, or per capita, or by capita adjusted for the purchasing power in each country. The first of these is dominated as expected by the big countries of Germany, Spain, France, Italy and the UK. However, the outstanding performer when looking at GDP per capita with or without the purchasing power adjustment is Luxembourg. Eurozone countries have a higher GDP per capita than those outside (€28,500 compared to €25,500, with the gap narrowing slightly when adjusted for purchasing power).

A final thing strikes me about these statistics. As has been pointed out elsewhere, Francois Hollande is having a hell of a time considering that France’s economic performance is not that bad. In fact it is incredibly average: its Government debt sits at 93.5% compared to the Eurozone average of 93.4% and its GDP per capita when adjusted for purchasing power is bang on the Eurozone average of €28,500. France are much more representative Euro members than Germany (remarkable when you consider that the Euro was once referred to as the Deutsche Mark with a few disreputable friends) and, if Hollande’s approval ratings are any indication, the French people seem to hate that.

I recently came across this post from 2009, showing how total returns companies achieved and the remuneration packages of their CEOs had no obvious relation between them. This kind of article, showing a correlation does not exist, is relatively unusual in my experience.

Far more common are articles like this one, by Eugenio Proto and Aldo Rustichini, purporting to show new evidence about the link between life satisfaction and GDP. Even if you accept whatever methodology they have used to derive their life satisfaction index (I don’t think we can get no satisfaction currently, see my previous blog), you have then to accept them defining a feature of the data entirely created by their regression analysis tool (the so-called “bliss point”) before going on to discuss what the implications of it might be.

The article’s references are stuffed with well-known economists’ papers and I am sure that one of its conclusions in particular, that increases in GDP beyond a certain point may not increase life satisfaction in developed countries, will lead to the research paper underlying the article to be widely cited as this is a politically contentious area. However this kind of thing is really nothing more than an economic Rorschach test: the meaning of the ink spots often depend on what you want to see.

But such studies are not often treated in this way. Why? Well what if one of the interpretations of the ink spots was backed up by some mathematics which could be run very quickly on any ink spot pattern by anyone with a computer? There is nothing biased about the mathematics, after all. This is what regression tools give us.

Regression is taught to sixth formers (I have taught it myself) as a way of finding best fit lines to data in a less subjective way than drawing lines by eye. The best fit straight line in a scatter graph is arrived at by looking at differences between the x and y coordinates of specific points and the average x and y values respectively. For y on x (ie assuming y is a function of x, you usually get a different gradient if you assume x is a function of y), the gradient of the line is the sum of each x value less its average times the corresponding y value less its average, all divided by the sum of the squares of the x values less their average. Or as a formula (the clumsiness of the preceding sentence is why we use formulae):

Correlation formula

Now let’s focus again on the graphs in the Proto and Rustichini article (the second graph has excluded Brussels and Paris, on the basis that they are both very rich and very miserable) and their regression-generated lines of best fit.

GDP life satisfaction

If we look long enough at these graphs we can almost persuade ourselves that the formula driven trend line (not a linear one this time) shown actually represents some feature of the data. But could you draw it yourself? And, if you did, would it look anything like the formula-generated one? If your answer is no to either of these questions, there is a possibility that the feature identified by Proto and Rustichini would be entirely absent from your trend line. The formula will always give you some sort of result. The trick is identifying when it is rubbish.

As an illustration of this, I constructed a graph where I was confident there was absolutely no correlation between the two things, and then set Excel’s regression tools to work on it.

Correlation obsession

As you can see, none of the options, starting with the linear regression we discussed earlier and getting more complicated, result in the kind of #DIV/0 and #N/A messages we get to see regularly elsewhere in Excel. By setting the polynomial option to a quintic, Excel is quite prepared to construct a best fit polynomial of order 5 (it has a fifth power in it – the purple wavy curve) to my array of dots. These lines and curves are merely the inevitable result of the mechanistic application of formulae that in this case have no meaning.

There may be nothing biased about the mathematics, but, as Bernard says In Yes Minister, when questioned by Jim Hacker about the impartiality of an enquiry: “Railway trains are impartial too, but if you lay down the lines for them that’s the way they go.”

Many economic research papers contain graphs which are similarly afflicted.

For those people who are not pensions geeks, let me start by explaining what the Pension Protection Fund (PPF) is. Brought in by the Pensions Act 2004 in response to several examples of people getting to retirement and finding little or no funds left in their defined benefit (DB) pension schemes to pay them benefits, it is a quasi autonomous non-governmental (allegedly) organisation (QUANGO) charged with accepting pension schemes who have lost their sponsors and don’t have enough money to buy at least PPF level benefits from an insurance company. It is, as the PPF themselves appear to have acknowledged with several references to the schemes not yet in their clutches as the “insured” in a talk I attended last week, a statutory insurance scheme for defined benefit occupational pension schemes, paid for by statutory levies on those insured. As a scheme actuary I have always been very glad that it exists.

The number of insured schemes has dwindled since it was named the 7800 index in 2007 (with not quite 7,800 members at the time) to the 6,300 left standing today. As you can imagine, the ever smaller number of schemes whose levies are keeping the PPF ship afloat are very nervous about how that cost is going to vary in the future. They have seen how volatile the funding of their own schemes is, and seemingly always in the worst case direction, and worry that, when their numbers get small enough, funding the variations in PPF deficits could become overwhelming. Particularly as the current Government says whenever it is asked (although no one completely believes it) they will never ever bail out the PPF.

So there has been keen interest in the PPF explanations of how those levies are going to change next year.

PPF levies are in two parts. The scheme-based levy, which is a flat rate levy based on the liability of a scheme, and the normally-much-bigger-as-it-has-to-raise-around-90%-of-the-total-and-some-schemes-don’t-pay-it-if-they-are-well-funded-enough risk-based levy. The risk-based levy depends on how well funded you are, how risky your investment strategy is and the risk your sponsor will become insolvent over the next 12 months.

It is this last one, the insolvency risk, which is about to change. Dun and Bradstreet have lost the contract to work out these insolvency probabilities after eight years in favour of Experian. However, unfortunately and for reasons not divulged, the PPF has struggled to finalise exactly what they want Experian to do.

The choices are fairly fundamental:

  • The model used. This will either be something called commercial Delphi (similar to the approach D&B currently use) or a more PPF-specific version which takes account of how different companies which run DB schemes are from companies which don’t. The PPF-specific version looks like it was originally the front runner but has taken longer to develop than expected.
  • The number of risk levels. Currently there are 10, ie there are 10 different probabilities of insolvency you can have based on the average risk of the bucket you have landed in. One possibility still being considered at this late stage is not grouping schemes at all and basing the probability on what falls out of the as yet to be announced risk model directly. This could result in considerable uncertainty about the eventual levy. Even currently, being in bucket 10 means a levy 22 times bigger than being in bucket 1.

So reason for nervousness amongst the 6,300 perhaps? The delay will mean that it won’t be known by 1 April (an appropriate date perhaps) when data starts to be collected for the first levies under the new system next year. Insolvency risk is supposed to be based on the average insolvency probability over the 12 months to the following March, but the PPF will either have to average over a smaller number of months now or go back and adjust the “failure scores” (as the scale numbers which allocate you to a bucket are endearingly called) to the new system at a later date. Again, the decision has yet to be made.

All of this suggests an organisation where making models is much easier than making decisions. And that is in no one’s interest.

Perhaps surprisingly in the audience I was in, the greatest concern expressed was about the fact that the model the PPF uses to assess the overall risk to their future funding (and therefore used to set the total levy they are trying to collect each year) was different from either the current D&B approach, or either of the two possible future approaches, to setting failure scores, ie the levies they pay are not really based on the risk they pose to the PPF at all.

There are obviously reasons why this should be the case. Many of the risk factors to the PPF’s funding as a whole would be hard to attribute, and therefore charge, to individual sponsors. For instance the PPF’s Long-Term Risk Model runs 1,000 different economic scenarios (leading to 500,000 different scenarios in total) to assess the amount of levy required to ensure at least an 80% chance of the PPF meeting its funding objective of no longer needing levies by 2030. Plus it plays to sponsors’ basic sense of fairness that things like their credit history and items in their accounts (although perhaps not including, as now, the number of directors) should affect where they stand on the insolvency scale, rather than things that would impact more on PPF funding, like the robustness of their scheme deficit recovery plans for instance.

It is rather like the no claims discount system for car insurance. This has been shown to be an inefficient method for reallocating premiums to where the risk lies in the car driving population, and this fact has been a standard exam question staple for actuarial students for many years. However it is widely seen as fair by that car driving population and would therefore be commercial madness for any insurer to abandon.

So there we have it. The new PPF levy system. Late. Not allocating levies in accordance with risk. And coming to a pension scheme near you soon.

There has been the usual flurry of misleading headlines around the Prime Minister’s pledge to maintain the so-called triple lock in place for the 2015-20 Parliament. The Daily Mail described it as a “bumper £1,000 a year rise”. Section 150A of the Social Security Administration Act 1992, as amended in 2010, already requires the Secretary of State to uprate the amount of the Basic State Pension (and the Standard Minimum Guarantee in Pension Credit) at least in line with the increase in the general level of earnings every year, so the “bumper” rise would only be as a result of earnings growth continuing to grind along at its current negative real rate.

However, the Office for Budget Responsibility (OBR) is currently predicting the various elements of the triple lock to develop up until 2018 as follows:

Triple lock

The OBR have of course not got a great track record on predicting such things, but all the same I was curious about where the Daily Mail’s number could have come from.

The Pensions Policy Institute’s (PPI’s) report on the impact of abandoning the triple lock in favour of just a link to earnings growth estimates the difference in pension in today’s money could be £20 per week, which might be the source of the Daily Mail figure, but not until 2065! I think if we maintain a consistent State Pensions policy for over 50 years into the future a rise of £20 per week in its level will be the least remarkable thing about it.

The PPI’s assumption is that the triple lock, as opposed to what is statutorily required, would make a difference to the State Pension increase of 0.26% a year on average. It is a measure of how small our politics has become that this should be headline news for several days.

It’s a relatively new science, and one which binds together many different academic disciplines: mathematical modelling, economics, sociology and history. In economic terms, it is to what economists in financial institutions spend most of their time focusing on – the short to medium term – as climate science is to weather forecasting. Cliodynamics (from Clio, the Ancient Greek muse or goddess of history (or, sometimes, lyre playing) and dynamics, the study of processes of change with time) looks at the functioning and dynamics of historical societies, ie societies for which the historical data exists to allow analysis. And that includes our own.

Peter Turchin, professor of ecology and mathematics at the University of Connecticut and Editor-in-Chief of Cliodynamics: The Journal of Theoretical and Mathematical History, wrote a book with Sergey Nefedev in 2009 called Secular Cycles. In it they took the ratio of the net wealth of the median US household to the largest fortune in the US (the Phillips Curve) to get a rough estimate of wealth inequality in the US from 1800 to the present. The graph of this analysis shows that the level of inequality in the US measured in this way peaked in World War 1 before falling steadily until 1980 when Reagan became US President, after which it has been rising equally steadily. By 2000,inequality was at levels last seen in the mid 50s, and it has continued to increase markedly since then.

The other side of Turchin’s and Nefedev’s analysis combines four measures of wellbeing: economic (the fraction of economic growth that is paid to workers as wages), health (life expectancy and the average height of native-born population) and social optimism (average age of first marriage). This seems to me to be a slightly flaky way of measuring this, particularly if using this measure to draw conclusions about recent history: the link between average heights in the US and other health indicators are not fully understood, and there are a lot of possible explanations for later marriages (eg greater economic opportunities for women) which would not support it as a measure of reduced optimism. However, it does give a curve which looks remarkably like a mirror image of the Phillips Curve.

The Office of National Statistics (ONS) are currently developing their own measure of national well-being for the UK, which has dropped both height and late marriage as indicators, but unfortunately has expanded to cover 40 indicators organised into 10 areas. The interactive graphic is embedded below.

Graphic by Office for National Statistics (ONS)

I don’t think many would argue with many of these constituents except that any model should only be as complicated as it needs to be. The weightings will be very important.

Putting all of this together, Turchin argues that societies can only tolerate a certain level of inequality before they start finding more cooperative ways of governing and cites examples from the end of the Roman civil wars (first century BC) onwards. He believes the current patterns in the US point towards such a turning point around 2020, with extreme social upheaval a strong possibility.

I am unconvinced that time is that short based solely on societal inequality: in my view further aggravating factors will be required, which resource depletion in several key areas may provide later in the century. But Turchin’s analysis of 20th century change in the US is certainly coherent, with many connections I had not made before. What is clear is that social change can happen very quickly at times and an economic-political system that cannot adapt equally quickly is likely to end up in trouble.

And in the UK? Inequality is certainly increasing, by pretty much any measure. And, as Richard Murphy points out, our tax system appears to encourage this more than is often realised. Cliodynamics seems to me to be an important area for further research in the UK.

And a perfect one for actuaries to get involved in.