On the long-run fluctuations of inheritance in two-sector OLG models

Florian Pelgrin (1) , Alain Venditti (2, 1)

1 EDHEC - EDHEC Business School
2 AMSE - Aix-Marseille Sciences Economiques

This paper provides a long-run cycle perspective to explain the behavior of the annual flow of inheritance. Based on the low- and medium frequency properties of long time bequests series in Sweden, France, UK, and Germany, we explore the extent to which a two-sector Barro-type OLG model is consistent with such empirical regularities. As long as agents are sufficiently impatient and preferences are non-separable, we show that endogenous fluctuations are likely to occur through two mechanisms, which can generate independently or together either period-2 cycles or Hopf bifurcations. The first mechanism relies on the elasticity of intertemporal substitution or equivalently the sign of the cross-derivative of the utility function whereas the second rests on sectoral technologies through the sign of the capital intensity difference across two sectors. Furthermore, building on the quasi-palindromic nature of the degree-4 characteristic equation, we derive some meaningful sufficient conditions associated to the occurrence of complex roots and a Hopf bifurcation in a two-sector OLG model.

Mots clés: Two-sector overlapping generations model; Altruism; Bequest; Endogenous fluctuations; Quasi-palindromic polynomial; Periodic and quasi-periodic cycles

Domaines: Economies et finances; Mathématiques [math]

Florian Pelgrin, Alain Venditti. On the long-run fluctuations of inheritance in two-sector OLG models. Journal of Mathematical Economics, 2022, 101, pp.102670. ⟨10.1016/j.jmateco.2022.102670⟩. ⟨hal-03869121⟩