Thanks for taking to the time to check my post.

Since this is a longish post, here is my question in a nutshell (read on for context and greater detail):

“Would applying a weighted average formula twice, to two subsets of a group (so, once for each subset) (method A), instead of once to the whole group, (method B) inherently mean the value outcome of A would be lower than B? Specifically since the elements that go into the formula are in part simple averages?”

The situation:

My mother has retired after 44 years. Of these, 41 are relevant to her pention. Her career remuneration follows an ascendant curve, reflecting her career progression and yearly wage “updates”.

Pension is normally calculated using a weighted average formula:

P (Pension) = (P1*C1)+(P2*C2)/C

Where:

P1 is the result of R1 (simple average of the best 10 of the last 15 years) multiplied by 2% and then by N (number of relevant years to a max. of 40)

C1 is the number of year until end of 2006

P2 is the result of R2 (simple average of the best 40 years) multiplied by between 2.3% and 2% (R2 is broken down into tiers in relation to a constant (K) where the first tier is multiplied by 2.3%, the second by 2.25% and so on) and then by N (as above)

C2 is the number of years from 2007

C is C1 + C2

When I apply this formula, I get a pension of 866, or one and half times the minimum wage, about 80% of her final salary and roughly in line with what you would expect given her career earnings.

The issue is that this is not how it was calculated. Of the relevant 41 years, 26 were spent in the private sector and 15 in public service. This means she contributed to two systems (a public system for private sector workers and a public system for public sector workers... go figure) and that she then gets what is term a “unified pension”. Under the law this should mean that the contributive periods are totalized and one pension is assigned. In fact what they do is calculate two pensions and totalize the amounts.

So, they use the exact sane formula twice, once for the 26 year period and once for the 15 year one. The result, a whopping 600, or just over the minimum wage and about half of her last wage. Now this, even though it might not seem huge, is reason for some distress given our family situation.

I have checked their calculations and they seem correct. I have also double checked my own. I can see, in terms of the calculation, why and when this difference manifests. (Not wanting to bloat this post further I will refrain for elaborating here but am happy to discuss this and supply data if needed).

What I am trying to understand is if this difference is a result of the properties of this formula or its composing elements, (or, to put it differently, if this is structural and will therefore apply in a greater or lesser extent to any case treated similarly) or if this simply circumstantial and somehow related to the specifics of the case.

If it proves to be the first, then this might prove relevant for thousands of people, so without meaning to sugar coat it, this might be your good deed of the week and then some!

If it proves to be the second, then it wont hurt because I feel we still have enough to go on as it is – it is hard to describe how arbitrary and unfair this comes across, given that someone with the exact same history but contributing to only one system would get the first value I mentioned. Especially because both systems are under one roof and they have been integrating them for 20 years... - and regardless of the outcome you have our thanks.

On the subject, if you've made it this far, thanks for that!

My own background is in History and Anthropology so I have to admit to a small amount of (foolish) pride in managing to get this far, but I am not sure if I can answer that question in time and we are on a budget as well as a deadline to contest her pension.

Again, our thanks for your time and advice.

Good weekend all,

J

Ps Please drop me a line if there is a more appropriate place to post this.