Discussing inequality requires precise language

When mathematicians discuss categories such as groups, rings and fields, they are all agreed about exactly what they discussing. Unfortunately, much political debate today degenerates into a dialogue of the deaf, because we fail to define our terms precisely enough.

This is particularly true with the subject of inequality in society. Let me illustrate.

Country A – an unequal dystopia

In country A, the top 1% own over 6% of total wealth, and the top 10% own almost 49% of total wealth.

This contrasts dramatically with the bottom 50% of the population. They own only 1.5% of total wealth.

Indeed, the bottom 30% of the population own absolutely nothing, while the 1.5% of wealth mentioned in the previous sentence is owned by those in the population range 31% – 50%.

Who could possibly justify such an unequal society? Isn’t Country A is rigged against the poor?

Country B – an egalitarian utopia

In country B, there is no inheritance. Everyone has the same life expectancy.

Everyone attends university until the age of 21, without incurring a penny of debt, and then starts work.

Country B is so equal that every person starting work at age 22 earns exactly the same salary. Each year they get an identical pay rise.

Everyone saves exactly the same proportion of their income. They also achieve exactly the same return on their investments.

Everyone works until the age of 70 when, they die, and the state takes 100% of their assets because no inheritance is allowed.

This society is so equal that only the most extreme socialists would envisage creating imposing such equality by government edict.

Concluding comments

Country A and Country B are, of course, the same country.

The reason they sound so different is that we regularly fail to define what we mean by equality.

In particular, very often we talk about inequality without specifying which part of the population we are talking about.

I have modelled this country using some simple assumptions:

  • Everyone saves 10% of their annual salary. While this is greater than the lamentable average UK savings rate, it is not excessive by international standards. The higher the savings rate, the greater the wealth owned by older people compared with younger people.
  • Everyone receives a return of 8% on their savings. This broadly corresponds to the long-term nominal rate of return on equities. Again, the higher the rate of return assumed, the higher the proportion of wealth owned by older people.
  • Everyone receives an annual, nominal, pay rise of 5%. Again, this is realistic for most economies with an assumption of 2% real growth and 3% inflation. The larger the assumed annual pay rise, the higher the proportion of wealth owned by older people.

I often encounter comments about inequality which fail to even clarify whether children (who of course do not earn in general) are being included in the population denominator.

The most serious error is to talk about equality as if we expected the average 25-year-old to have the same amount of wealth as the average 55-year-old. Such an expectation is completely nonsensical when you think about the relative amounts of time that the 25-year-old and the 55-year-old have had to earn, save, and grow their investments.

I have provided the Excel spreadsheet I used for my calculations if readers want to take a closer look at the figures. Readers can also flex the above assumptions to see how changing the assumptions alters relative wealth levels for each cohort.

Click here to download the spreadsheet.

One change to the spreadsheet, which would require amending the formulas, is to increase the savings rate as people become older and earn more. In practice, as people’s incomes rise, they can save a higher proportion of their income. In my 20’s, I managed to save very little, but by my mid-50’s I was saving about half of my income each year.

 

* Mohammed Amin left the old Liberal Party to join the Conservative Party. He stayed for 36 years, but joined the Liberal Democrats in October 2019.

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20 Comments

  • Laurence Cox 23rd Dec '19 - 1:12pm

    A good article and I am glad to see you back in the Party.

    In one sense, it is not income inequality per se that matters, but the inequality in disposable income. So I guess that Mohammed in his twenties was paying off a hefty mortgage, while in his fifties he was mortgage-free. That alone makes a massive diference to disposable income. Concentrating on disposable income also means that we become aware that even small improvements in it can have massive effects for those near the lower end of the income spectrum. This is one reason why I have called for many years for the lower income limit for paying NI contributions to be raised in line with increasing the income tax personal allowance (the latter was one of our flagship policies in coalition).

  • As Liberals isn’t it equality of opportunity that we are most interested in?

  • The biggest inequality between normal people is those who own and those who rent property. Mortgage free ownership of a house gives a huge boost to one’s finances, both in terms of disposable income and tax free capital gains. Worse yet, such equity can be used to finance offspring’s tuition fees and deposit on a place of their own. So even if a council estate lad makes it through uni, he is then faced with a massive debt to service, high tax rates if he starts earning serious money, eye watering rents, and by the time he has saved a deposit the cost of a property could well have doubled compared with someone who has had their deposit financed by a parent and is able to buy straight away.

  • The problem with “inequality” is it implies a belief that one group of people should have something taken from them and given to another group of people. This is rarely popular with the public who tend not to like the idea.

  • Mohammed Amin 23rd Dec '19 - 4:42pm

    @ Laurence Cox and @ Frank West

    Income inequality is a subject for another day. The article is about wealth inequality.

  • Christopher Maitland 23rd Dec '19 - 10:32pm

    I’m not sure what point you are making. It seems as though you are trying to downplay levels of wealth inequality by comparing like with unlike. What are you driving at?

  • Ed Shepherd 24th Dec '19 - 7:35am

    Vast numbers of workers are in insecure work with no worthwhile pension scheme. That will vastly change the balance of wealth amongst older people in the coming decades. Older people now benefitted from secure, unionised work with pension schemes. That was a post war anomaly.

  • Andrew Daer 24th Dec '19 - 8:09am

    Wealth is a poor proxy for a happiness index, but few of us like the idea of our children and grandchildren being financially poorer than us, and would be horrified to think of them living in abject poverty after we’ve gone, so the idea of leaving our personal wealth to be shared equally to the whole community might sound nice, but country B is never going to appeal to anyone who has any wealth to pass on. A more realistic political aim would be to promote greater equality of income, rather than state-enforced equality of wealth.

  • Andrew Daer 24th Dec '19 - 8:10am

    Wealth is a poor proxy for a happiness index, but few of us like the idea of our children and grandchildren being financially poorer than us, and most would be horrified to think of them living in abject poverty after we’ve gone, so the idea of leaving our personal wealth to be shared equally among the whole community might sound nice, but country B is never going to appeal to anyone who has any wealth to pass on. A more realistic political aim would be to promote greater equality of income, rather than state-enforced equality of wealth.

  • There is a problem with the analysis. If we look at what wealth can consist of then we find there is a range of differences which mean that we must be very careful in comparing different things. Housing for example. People need somewhere to live. This occupies land. The quantity of land is limited. And of course what it can be used for is decided by the state. Thus we have many people at present who are buying land and lobbying for changes in planning policies. Another example would be cars. There is a theoretical limit on how many could be built each year, but in fact as demand increases production increases.
    When discussing wealth, or anything else, we need to look at what the properties of the actual numbers we are using are.
    This is part of the problem with the use of maths. In the end it is the real lives of real people we should be concerned about.
    I suggest that trying to use maths without defining the properties of the numbers we are using is a common, almost universal, fault of our “western” culture.

  • Mohammed Amin 24th Dec '19 - 11:37am

    @ Christopher Maitland

    My point is that much of what is said about wealth inequality demonstrates imprecise, and indeed illogical, thinking.

    We hear all the time that X% of the population owns Y% of the total wealth, without any acknowledgement that large parts of the population (namely the very young) would be expected to own nothing, while others (young workers) would be expected to own little.

    What is much more logical to look at wealth inequality within cohorts, and then ask whether it is fair and reasonable or not.

  • Mohammed Amin 24th Dec '19 - 11:40am

    @ Tom Harney

    In my view the appropriate way of judging wealth is to look at the assets a person own at market prices. If the person wanted different assets, they could sell what they own and buy other assets.

    The real lives of real people are governed by mathematics, as is everything else.

  • The point is that prices are in the end decided by society. House prices will fall if more houses are allowed to be built. If no more houses can be built because all the land I’d built on in a particular area then prices will be high. Elsewhere the cost of the land depends on zoning. All of this builds uncertainty into the estimates. These estimates must be acknowledged.
    I do not understand the idea that our lives are decided by mathematics. Mathematics is a way of describing our lives – along with many others such as language.

  • Laurence Cox 25th Dec '19 - 9:31pm

    @Mohammed Amin

    If you except inheritance, which your model does, then the only way that anyone becomes wealthy is because they choose to save/invest some of their disposable income. If no one had disposable income then everyone would be living hand-to-mouth all the time. Hence your wealth inequality is nothing more than integrated disposable income (together with the capital gains arising from it). For example, you may choose to invest in the best house that you can afford, or in shares/bonds, or in collectables. All have risk/return profiles; some people choose to take big risks, like playing the Lottery where almost everyone loses their stake but a few win big sums; while others choose lower risks, like buying a house rather than renting (even if you are a forced seller, you should get nearly as much for your house as you paid for it).

  • Nonconformistradical 26th Dec '19 - 8:28am

    @Tom Harney
    “House prices will fall if more houses are allowed to be built.”
    Provided that the supply of money to buy houses is not being increased at the same time – i.e. provided that the definition of inflation – too much money chasing too few goods – is in force and and governments abide by it.

    “If no more houses can be built because all the land I’d built on in a particular area then prices will be high.”
    Unless density of dwellings can be increased…?

  • Nonconformistradical 26th Dec '19 - 8:37am

    @Mohammed Amin
    “Everyone attends university until the age of 21, without incurring a penny of debt, and then starts work.”
    If everyone attended university (a) I suspect you’d find there would be a very high proportion of drop-outs and (b) there would far too few people qualified to do all the every day work which we need badly – electricians, plumbers, carers etc. And given the seemingly prevailing attitude of the powers that be that you only get one chance in the education system (and tough if you made the wrong choice) there might be a serious lack of training opportunities for the drop-outs in order for them to be able to earn a living.

    And quoting from Tom Harney;_
    “I do not understand the idea that our lives are decided by mathematics. Mathematics is a way of describing our lives – along with many others such as language.”
    Agree – and there seem to be problems with the teaching of both maths and languages – not good enough to be useful to people in their everyday lives.

  • Mohammed Amin 26th Dec '19 - 3:40pm

    @ Laurence Cox

    I think we are agreed. Once inheritance is excluded, wealth inequalities are a function of:
    A) differential incomes
    B) differential savings rates
    C) differential rates of return on savings
    D) differences in the time over which wealth has been accumulated. i.e. age.

    The main point of my piece is that most discussions of inequality in political debate and in the media ignore D. (They also tend to ignore the personal decisions that give rise to difference in B, C, and also A.)

  • Mohammed Amin 26th Dec '19 - 3:42pm

    @ Nonconformistradical

    Mathematical models are built to aid thinking. The complete equality within cohorts is built into the model assumptions, because I want to illustrate the impact of D (in particular) in my reply to Laurence Cox above.

    D) differences in the time over which wealth has been accumulated. i.e. age.

  • @Mohammed Amin you omit outgoings.

    Person A – earns £45k p.a. Single. Lives in the north. Has considerable disposable income to invest.

    Person B – earns £45k p.a. Married, spouse doesn’t have paid employment, three children. Lives in the south. Has no disposable income once costs are deducted.

    Person A can have a a very enjoyable life spending their dispoable income on cheap holidays, consumer goods etc and/or save for retirement/invest in property or stocks.

    Meanwhile person B is investing in their children, who will have to support person B and their spouse with their future earnings, AND person A who has made no contribution to the upkeep of the children who will be paying their future pension.

  • Mohammed Amin 27th Dec '19 - 8:44pm

    @ TCO

    Have you downloaded and inspected the Excel model?

    Its purpose, clearly stated in my article, is to have perfect cohort equality, to bring out the impact of age and accumulation time.

    The Persons A and B you contrast are out of scope, since everyone in my cohorts is, be definition, identical.

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