2. The demographic model

The demographic model is constructed to represent the transmission of the relevant part of the estate from its owner to one of his/her heirs. Various details of its construction are mentioned in Appendix 1.

We use directly the most recent data available from Insee, the French National Institute of Statistics and Economic Studies, corresponding to the year 2019 [23]. Note in this regard that the data for the years 2020 and 2021 may have been affected by the COVID-19 pandemic.

These data represent average values for the French population, and it is clear that for a particular investor, his/her own values concerning the age of children or life expectancy may differ significantly. Our results will therefore be average values, and may therefore differ from the result of a valuation that would be made for a particular case.

#### 2.1 Generation gap

Data from Insee [23] allow us to calculate the probability distribution of the age gap between two generations. We represent below (Figure 1) the number of children born alive according to the age of the mother, which has the same shape as this distribution. The average age of the mother is 31 years, with a standard deviation of 5.27 years.

#### Figure 1.

Number of children born alive by age of mother. x-axis: age of mother in years; y-axis: number of children. Data for France (excluding Mayotte), 2019 (source: [23]).

#### Figure 2.

Life expectancy by age (men and women). x-axis: age; y-axis: life expectancy, in years. Data for France, 2017–2019 (source: [23]).

#### 2.2 Life expectancy as a function of age

According to the same source, we know the life expectancy as a function of age, for men and women taken together. In Figure 2, we represent this expectation, which has a convex shape, especially after the age of 80, meaning that at each birthday, the estimated date of death is pushed forward.

For instance, if at the age of 70, life expectancy for a woman (resp. man) is 19.20 years (resp. 15.91 years), ten years later, for a woman who has reached the age of 80, it is not 9.20 years (resp. 5.91 years), but 11.28 years (resp. 9.20 years). Note that the COVID-19 pandemic has recently reduced life expectancy in most countries by a few months.

#### 2.3 Mortality quotient

We represent below (Figure 3) the mortality quotient per 100,000 survivors at age x, i.e., assuming a representative population of 100,000 persons of the same age x, the number of persons dying in year n.

#### 2.4 Evolution of the age of the owner of a plot of forested land

Let us now suppose that we examine the evolution of the age of the owner of a wellidentified plot of forested land, or a forest as a whole but which will not be divided in the future by inheritance. For example, let us assume that the owner has at the beginning (t = 1) an age a(1) = 38 years. The following year, at t = 2, the probability of death being very low at this age, the owner will have, with a high probability, the age a(2) = 39. And so on, finally leading him/her to pass on the plot, following his/her death, whose probabilities have been evaluated according to his/her increasing age (see Figure 3).

This transmission benefits a direct descendant (a child, whose age probability distribution is calculated from the data presented in Figure 1), or an indirect descendant (grandchild), if the direct descendant is already deceased (the probability is known); and so on if the indirect descendant is himself/herself deceased (see more details in Appendix 1).

Assessment of the Impacts of an Inheritance Taxation Relief on the Profitability… DOI: http://dx.doi.org/10.5772/intechopen.101380

#### Figure 3.

Number of deaths in a year based on a population of 100,000 people of the relevant age (men and women). x-axis: age; y-axis: number of deaths. Data for France, 2017–2019 (source: [23]).

Figure 4 allows us to visualize that the probability distribution of this age converges to a stable distribution, which is, in fact, independent of the starting age a(1) of the woodlot owner.

#### 2.5 Comparison of model results and forest owner ages

We present in Figure 5 the year-by-year probability distribution of the age of the owner of the woodlot or forest under consideration, after a sufficiently long time for this distribution to stabilize.

We can now compare these probabilities with data from the general population in France and from the Agreste survey of forest owners [24] in Aquitaine. As there are

#### Figure 4.

Evolution of very low at this age, the owner will have, with a high probability, the age a(2) = 39. For better visibility, the graph is truncated at a probability of 0.1. As time goes by, this graph converges, whatever the age of departure, toward a distribution of this age which is stable with respect to time.

#### Figure 5.

Age limit distribution of the owner of the forest or woodlot under consideration. x-axis: age of owner; y-axis: probability year by year. Result of the model presented above and in Annex 1.

#### Figure 6.

Comparison of model results (left bars), then Agreste survey data [24] on forest owners, then [23] on the general population, and finally the same Insee data [23] for the population over 30 years old. x-axis: age group; y-axis: percentage (see text).

very few forest owners under 30 years old, we also show the distribution of the French population (see [23]) for only those over 30 years old (Figure 6).

Overall, we see that the results of the model are very close to the results of the Agreste survey and quite different from those of the general population. This can be explained by and corroborates the fact that "family transmission appears to be the essential factor in the acquisition process. Nearly three out of four owners received their first "forestry property" by inheritance or donation. The purchase, with a view to building up a forest estate, concerns 27% of owners (30% of surfaces) and the creation by planting of wooded territories less than 1%" [24].
