An ‘ideal’ wealth distribution and the life-cycle

People have difficulty understanding distributions. This can be seen in the survey presented in the recent documentary by David McWilliams (which I haven’t seen yet, but am looking forward to watching). In an ‘ideal’ world survey respondents said the top 20% would get slightly more than 30% of net wealth, and the bottom 17%. But in this ‘ideal’ world the bottom 20% are actually richer than those in the middle 60%. Obviously this is impossible.

As pointed out by Seamus Coffey in a blog there is a relationship between aging and wealth as people save for retirement, and then draw down on their savings. It is useful to set out an ‘ideal’ world of saving and drawing down, and then see what wealth distribution emerges. This will show the limits of what can be achieved in a ‘fair’ world.

An “ideal” world

In this “ideal” there is no inheritance, no college debt (so everyone gets the same start), income for those of working age is equal, and everyone of the same age has the same net wealth. Each year people save one unit of their income, and then draw down on this when they retire. They leave no assets behind when they die. (I set working age at 23-67 to allow for new pension rules, and people now stay in education longer, and the rate of return on investment at 4%. Age of death is 78 because it is conveniently 60 years after 18.)

In this world the share of net wealth by age is remarkably similar to what we see in the data.

“Ideal” distribution by age remarkably similar to the data.

I was quite surprised when I saw this, so the Excel file is available here for people to play with (and alter assumptions).

Even in this “ideal” world roughly 45% of wealth would still go to the top 20% (as opposed to roughly one-third as respondents to the survey described as ideal).
However, there still space for a more equal world. Though the top 20% (aged 60-71) would get about 45%, this compares to roughly 72% at present. The top 10% would get a quarter of total wealth rather than half; and the top 5% would get roughly 13% of total wealth, rather than over 35%.

What drives this age based inequality?

Interestingly increasing the amount saved has no impact on measures of wealth inequality. If people double what they save over their life, the pie doubles, but they own the same share at each period. This is relevant as if pensions are provided by the state, and people only save a small amount as a top-up, it has no impact on wealth inequality statistics. (If this seems counter-intuitive, imagine if you saved in old punts rather than Euros; changing the scale doesn’t change dispersion.) Even in a communist country, so long as savings are possible, household wealth is likely to increase with age.

Increasing the rate of return on investment does increase the ratio of wealth of the old versus the young.


Obviously this is a simplified view of the world (and a proper paper rather than a blog would go into more detail, and fine-tune the share of total population of each group). There are two main caveats:

  1. Wages tend to increase with age, and people increase their savings over-time. This serves to increase the young/old wealth gap.
  2. Overall wages increase over time. People in older cohorts, such as those born in the 1950s, had far lower wages during their entire working life compared to someone born in the 1980s. This reduces the young/old wealth gap.


Although in this “ideal” world the top 20% still hold a large chunk of net wealth, there is still plenty of space for a more equal distribution. Much of aggregate net wealth inequality is due to inequality within age groups. Those who are starting out in their working lives will likely continue to have very low levels of wealth. It is within the top 20% that the largest extremes exist.

[EDIT: Now online, how transfers to the young (similar to large wedding presents in the past), can help reduce age based wealth inequality.]

Is Dublin Getting all the Jobs?

There has been some discussion recently as to where jobs in Ireland are being created, with the claim the notion that most of the jobs are going to Dublin. It is true that of the 8 regions in Ireland, Dublin is getting the most jobs, but this is to be expected given that Dublin is the biggest region.

Perhaps the best way to examine where the jobs are is to look at how the share of jobs in each region has changed. During the ‘real’ Celtic Tiger Dublin lost job share to the Mid-East region (the commuter belt). Overall these changes are relatively small.

Dublin's share of jobs fell during the 'real' Celtic Tiger.
Dublin’s share of jobs fell during the ‘real’ Celtic Tiger.

Between Q2 2008 and Q2 2015 Dublin’s share has risen by 29.7% to 30.2%. This isn’t particularly dramatic. If Dublin were to have the same job share in Q2 2015 as Q2 2008 the difference would be roughly 10,000 jobs. Not nothing, but not a huge change over seven years.

The table below shows that changes in the regional share of employment have not been dramatic either. Although proportionately the South-East was the second hardest hit region (after the Border region) from 2008 to 2012 (losing 22% of jobs) it subsequently gained the most, leaving it’s share roughly stable.

Shifts in regional job share have been minor.
Shifts in regional job share have been minor.

Overall, the regional story is best understood by examining long term trends rather than changes during the recession. Recovery is not complete, but the regions that lost the most jobs are the ones that subsequently gained the most.

Man shortage as ratio of men to women hits a historic low

In recent policy debates there has been a focus on the aging of Ireland’s population. However there has also be a substantial change in Ireland’s sex-ratio, and this shift has been most dramatic for the age groups of the late 20s and early 30s, leading to a shortage of men in Ireland.

The first graph show’s Ireland’s sex ratio by age. Following convention this is the ratio of men to women. As can be seen in 2014 there has been roughly 5% more boys born than girls (a sex-ratio of 1.05, or 105 baby boys for every 100 baby girls). This imbalance at birth is due to biological factors. If even numbers of boys and girls were born the ratio would be 1.00. In other countries sex-selective abortions occur where having a male heir is considered more desirable and baby girls aren’t appreciated, but this is not the case in Ireland.

Across the world boys and men have a higher mortality rate (due to both disease, accidents, and violence), meaning the sex-ratio declines with age, so by the age of 24 there is a roughly equal number of boys and girls.

sex-ratio by age
Sex-ratio by age

However, what is striking is how this has changed over time. The second graph shows an increase in the sex ratio for those in their late 20s and early 30s during the construction boom as men migrated into Ireland. Unsurprising, during the crisis men were also more likely to leave. However, sex-ratios have now reached historic lows meaning a shortage of men aged 25 to 34. There are now roughly 10% fewer men than women in this age group.

Ireland's changing sex ratios
Ireland’s changing sex ratios

As I am not a sociologist I will not try predict what the implications for these changing ratios will be for society. In the past (such as in France after the First World War) such changes were a catalyst for the economic independence of women. Of course, unlike France’s war dead there is a chance of these Irish men returning.

Economically this is of concern as women tend to earn less, leading to a lower tax take for the government in the future. These changes make achieving gender pay equality a more pressing issue. However, a lack of male labour may increase employment opportunities for women, helping Ireland achieve gender pay parity.

The original CSO data is available here.

Ireland’s 20 somethings

In today’s Irish Independent, Dan O’Brien has an interesting article looking at how the number of those in Ireland aged in their 20s has declined compared to five years ago. This is due to a mix of trends, migration, and birth rates. It compares people who were born from 1980 to 1989 with those born from 1985 to 1994.

The below graph instead looks at people who in 2014 were in their 20s (i.e. those born from 1985-1994). Jack Charlton’s children rather than the Popes. This isolates the effects of migration, and removes changes due to changes in birth rates. Unsurprisingly, during the recession there is a fall in those born from 1990 to 1994 due to migration (these people are now aged 20 to 24).

There is also a jump during the boom of those born from 1985 to 1989 (during 2007, the peak of the boom these people were aged 18 to 22), which is likely due to inward migration.

For biological reasons more boys than girls are born. However, as men seem more likely to migrate than women (but only slightly), the gender imbalance for those born in the late 1980s has shifted, with more women in this age group than men.

Ireland's 20 somethings

The original CSO data is available here.

An example of why contract manufacturing affects Irish GDP figures

In national accounts the main way to decide whether a transaction took place was a transfer of ownership. Though with ESA 95 there were some exceptions.

Suppose I made a table, but it needs to be professionally painted. Suppose I live on the French side of the French/Belgian border, but the painter is in Belgium. If I bring my table to the painter in Belgium there is no change of ownership (I still own the table). However with ESA 95 a change of ownership was imputed. The statistics agency pretend I sold the table to the Belgian painter (an export) and then bought back the table (an import). Under ESA 95 I manufactured a table, and then pretend that I sold it to a Belgian firm, and bought it again when it was painted.

Under ESA 2010 such changes of ownership are no longer imputed. Instead I am not considered to have exported the table, but just to have imported the painting service.

Assuming there is no transfer pricing there should be no change to GDP from the new classification.

As a more extreme example, now assume that instead of making the table myself I buy the wood and screws (I own them) and send them Belgium to be made into a table (following my design). As there is no change in ownership of the wood and screws, under ESA 2010 there is no transaction. So I began with raw materials, ended with a finished table, and merely imported some services from Belgium (though of course in reality the services are the manufacture of an entire table). The table is considered French output (though with a considerable service input from Belgium).

Again, assuming no transfer pricing this should not affect aggregate GDP, just it’s break down.

Now, instead of asking the Belgians to return the table to me, I ask them to deliver it to someone in Germany. I have arranged the sale of the table to someone in Germany. Only now is there a change in ownership. So the finished table is recorded as the export from France of the finished table. (It is just as though the table was transiting in a lorry through Belgium).

If there is no transfer pricing then French GDP would only increase by the value added of managing the contracts with the Belgians and Germans.

But of course there may be some transfer pricing going on in Ireland. Also, the increase in firms re-domiciling themselves as Irish further muddies the waters.