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 as identified by Piketty [51] for France and Atkinson [3] for the UK. Using a two-sector Barro-type [9] OLG model with non-separable preferences and bequests, we show that endogenous fluctuations are likely to occur through period-2 cycles or Hopf bifurcations. Two key mechanisms, which can generate independently or together quasi-periodic cycles, can be identified as long as agents are sufficiently impatient. 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 in a two-sector OLG model. Finally, we show that our theoretical results are consistent with some empirical evidence for medium- and long-run swings in the inheritance flows as a fraction of national income in France over the period 1896-2008.

Mots clés: altruism; bequest; two-sector overlapping generations model; optimal growth; endogenous fluctuations; quasi-palindromic polynomial; periodic and quasi-periodic cycles

Domaines: Economies et finances

Florian Pelgrin, Alain Venditti. On the long-run fluctuations of inheritance in two-sector OLG models. 2020. ⟨halshs-03080407⟩