Consequences of Modeling Habit Persistence

Abstract

In this paper, we study the stationary and non-stationary equilibria of a deterministic, pure exchange, two-period overlapping generations model with habit persistence. We show that preferences with multiplicative habits can lead to quite different equilibrium outcomes compared to subtractive ones. The two most commonly adopted habit specifications can differ in terms of homotheticity, gross substitutability, and uniqueness of equilibria. We illustrate these differences in terms of steady state equilibria, as well as local dynamics.JEL Classification: E52, E63.

Endogenous Growth, Habit Formation and Convergence Speed

“…Bunzel (2006) shows that the qualitative dynamic properties of SH and MH models are similar in a twoperiod pure exchange overlapping generations model. However, Bossi and Gomis-Porqueras (2009) argue that her results are driven by the specific choice of the utility function, and show that both models can differ in terms of concavity, homotheticity, uniqueness of equilibria and local dynamics. Wendner (2003) finds that SH and MH models may have different implications on household savings behaviour.…”

Internal vs. External Habit Formation in a Growing Economy with Overlapping Generations

“…5 In general, h t depends c t−1 alone and h t+1 is determined by c t and x t . Since we have assumed that young agents do not consume, the stock of consumption habits held by the adult agents does not involve their past consumption.…”

“…In contrast, c t in (5) means the internal habit 5 In the recent literature, Alonso-Carrera et al Lahiri and Puhakka (1998), Wendner (2002Wendner ( , 2003 employ the subtractive form of habit formation. 6 More generally, we may assume that h t+1 also depends on the average consumption in the economy at large when agents are young, that is, h t+1 = h (c t ,c t , x t ) , wherec t denotes the average consumption when young.…”

A Closed-form Solution of a Two-sector Endogenous Growth Model with Habit Formation

“…Several works have studied the implications for the economy dynamics, the introducing of habits into the utility function, e.g. Ryder and Heal (); Carroll et al (); Alvarez‐Cuadrado et al (); Alonso‐Carrera et al (); Gomez (, ); Doi and Mino (); Bossi and Gomis‐Porqueras () and Hiraguchi (). Among them, only Hiraguchi () considers a two‐sector endogenous growth model with physical and human capital of Lucas type.…”

“…Bossi and Gomis‐Porqueras () studied a two‐period overlapping generations model with habit persistence. They show that modelling preferences with multiplicative habit ( MH ) or with substractive habit ( SH ) yields theoretical predictions that are not necessarily equivalent, and thus, the resulting qualitative properties of the economy under SH and that under MH can be quite different.…”