Roberto Fantaccione

The Leslie model and population stability: an application

Angrisani Massimo, Di Palo Cinzia, Fantaccione Roberto and Palazzo Anna Maria

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Review of Applied Socio-Economic Research, 2013, vol. 6, issue 2, pages 4-14

Abstract: In many countries with high socio-economic development, demographic trends highlight meaningful changes in the population structure and size especially due to the joined effects of declining fertility rates and increasing life expectancies, particularly at older ages. This phenomenon leads mainly to a drastic increase in the ratio of the elderly to the young active population and undermines the welfare systems. Specifically, it puts hard pressure on pension systems where the current expenditure is paid by the current contributions in the light of a pay-as-you-go financing because it occurs that the former is increasing and the latter is decreasing due to the afore-said phenomenon. In this paper, first we analyse the population forecast of five high-income countries on the basis of the current values of fertility rates and survival probabilities. We apply the Leslie model in a form elaborated by one of the authors in a previous article written in collaboration. Our findings confirm that the considered populations numerically decrease according to the value of the Leslie dominant eigenvalue lower than one, while the percentage distribution by age stabilises itself proportionally to the Leslie dominant eigenvector. The structure of this distribution indicates the afore-said ‘reversal’ of the ratio of the elderly to the young population. Therefore, also consistently with the criterion of Brauer-Solow, we estimate the adjustment rate of the fertility rates at all ages in the female Leslie matrix so that the dominant eigenvalue is equal to one and thus the population tends to stabilise in its size in addition to its percentage distribution by age. As it is clear, this adjustment also involves a change in the Leslie dominant eigenvector and a realignment of the ratio of the elderly to the young population on lower values.

Keywords: population stability; demographic changes; Leslie matrix model. (search for similar items in EconPapers)
JEL-codes: C02 J10 J11 (search for similar items in EconPapers)
Date: 2013
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The inefficiency of the immigration-based demographic equilibrium

Anna Maria Palazzo (palazzo@unicas.it) and Roberto Fantaccione
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Review of Applied Socio-Economic Research, 2017, vol. 13, issue 1, 52-58

Abstract: This study investigates the impact that a possible increase in fertility rates and the control of immigration have on population stationarity following the approach used in Angrisani and Di Palo (2016). Our paper shows that using immigration for population stationarity leads to a gross inefficiency in terms of size and age distribution of the stationary population. Indeed, we show that immigration-based population stationarity is inefficient as the stationary population results in having a larger size than that obtained bringing the fertility rates to the whole natural level of equilibrium. Furthermore, the immigration-based stationary population results in being unbalanced in terms of ratios between old and young age groups pro the former ones. In order to perform population evolution, the Leslie model has been used in a two sex form already applied in a previous work, and in order to introduce the effect of possible changes in fertility or immigration in the model the modified approach of Angrisani and Di Palo (2016), has been used in a slightly simplified version. Numerical illustration is obtained on data by gender for the Italian population.

Keywords: population stationarity; Leslie population model; immigration. (search for similar items in EconPapers)
JEL-codes: C02 J10 J11 (search for similar items in EconPapers)
Date: 2017
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