Risks linked to an imbalanced pension scheme with a changing population

Risks linked to an imbalanced pension scheme

with a changing population

Abstract: Since the end of the Second World War, it has been compulsory for every French worker to pay pension contributions. The various fluctuations that are occurring in a demographic point of view in the country have led to a deficit of the pension scheme. Indeed, many reforms have already been applied, the most noteworthy being in 2003, because of this demographic imbalance. The aim of the study is to analyze the demographic evolution of the French population and to build a cartography of the risks in order to identify the potential failures of the current pension scheme chosen by the State that are likely to occur. A model will then be built so as to prove that the current pension scheme chosen by France is unstable, which means that it requires a continuous adjustment by the government in order to make it sustainable. Finally, we will provide the reader with lines of thought concerning some solutions to improve the situation.

Keywords: Pension scheme, pension reform, ageing population, life expectancy

1. INTRODUCTION

The pension scheme used in France is based on the principle of repartition (“payg” or “pay-as-you-go” systems). This means that at the year n, the contributions paid by the labor force directly supply the retired people with their pension. This system is opposed to the one managed through capitalization (used in the USA for example). In this type of pension scheme, starting from a first fixed age (the retirement age), every member of the labor force that became pensioner starts to get the stock of capital he or she had accumulated during his or her previous years of subscription.

As A. Brun-Schammé describes it in her thesis [2], the main advantages of a system managed by repartition is that there is a sharing of risks between the different generations, and that it limits the irregularities of wages (for example thanks to minima of pension). In our paper, we stick to this repartition principle, because it is hard to consider changing the whole pension system. In fact, if we decide to do so, the last generation would not obtain pension allowances since the first one benefitted from it “gratis”, without having paid before their retirement. This situation would be catastrophic. Therefore, all the solutions that will be provided here stay in the context of a repartition managed pension system.

2. WHAT ARE THE RISKS?

We can build a fault tree to understand the risks of the scheme failure or imbalance (see below).

This fault tree is not exhaustive, but we tried to give an idea of the multitude of factors that can be taken into account.

Pension systems are exposed to three kinds of risks: economic, demographic and political.

According to A. Kruse ([3]), the economic risk is the risk of a low or even negative rate of return. In a funded system (based on the principle of capitalization) the rate of return is that of the capital market, whereas in a pure “pay-as-you-go system” (payg), like the French system, it is the growth rate in the economy, i.e. changes in productivity and demography. Thus, a funded system is exposed to capital market risks, a payg-system to growth risks. Both kinds of systems are exposed to political risks, that is, the risks of more or less abrupt changes in the design caused by political decisions.

3. MODELISATION

3.1. Basic equations and parameters introduction

As described in Kruse’s article [3], the basic equations for modeling a pension scheme are:

Total amount of contributions = Total amount of pensions (2.1)

Total amount of contributions = , (2.2)

where q is the contribution rate, w is the average wage and L is the labor force.

Total amount of pensions = , (2.3)

where b is the average benefit level and P is the number of pensioners.

Thus, two solutions are possible regarding the risk of changing life expectancy.

- We can either set the replacement ratio with the formula:

(2.4)

In this case, the risk is totally borne by the working generation since q will increase if P/L increases.

- Or set the contribution rate q with the formula:

(2.5)

In this case, the risk is totally borne by the pensioners since b will decrease if P/L increases.

3.2. Forecasting

In this part, we are going to see the evolution over time of the contribution rate q. In order to make a simple analysis we need to build a scheme which represents the evolution of the population year after year.

The model of the population is the following:

We have three categories of people: young people (people under 20, who are consider as non-taxpayers), laborers (the active part of population), pensioners (those one who benefit of pension).

We also have an input, represented by newborns – which we will consider like a constant input – and a box which represents the deaths: a mortality rate is associated with each state and with the input. In other words we could say that the real input is (1-α)*input, with α representing the mortality rate of the first year.

Each year, a part of each category grows to another (represented by the people on the border age, such nineteen-years-olds and fifty-nine-years-olds), a minor part will not survive and the majority will remain in the same category.

We need now to model this dynamic system and to quantify the transitions between the classes, thus we define the transition matrix M as follows:

where N = newborns, Y = young (< 20 years old), L = laborers, P = pensioners, D =

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