Endogenous time preference, fertility, and optimal growth

• Main Author: Stern, Michael L
• Format: Dissertation
• Language: English
• Published: ProQuest Dissertations & Theses 01.01.2003
• Subjects: Adults; Altruism; Capital stock; Consumption; Copyright; Correspondence; Cost control; Economic growth; Economic theory; Fertility; Growth models; Investments; Production functions; Studies; Time
• ISBN: 0496594680; 9780496594689

This dissertation concerns itself with two major issues in growth theory. I begin by examining the issue of time preference, often referred to as the rate of discount or the degree of consumer impatience. Despite the fact that attitudes toward immediacy play a major role in determining the savings behavior of households, economists have long trivialized this issue and merely assumed that the degree of household impatience is an exogenously specified constant. I explore the implications of relaxing this restrictive assumption by adapting the classic optimal growth model to include an endogenous rate of time preference along the lines of Becker and Mulligan (1997). The resulting model provides a general theory as to the simultaneous evolution of time preference, consumption, and capital. The optimal growth model with endogenous discounting is both time-consistent and analytically tractable. Capital sequences are shown to be monotone under very general circumstances using modern lattice programming techniques. A turnpike theorem concerning the global long-run stability of optimal paths is established and the model is analyzed under Cobb-Douglas and linear production. I provide cases of explicit solutions, unique steady states, multiple steady states, and conditionally sustained growth. Hence, the endogenous discounting model does not necessarily exhibit global convergence to a unique steady state or balanced growth path. I also argue that the model is more sensitive than the classic model to technology shocks since they can alter key behavioral parameters related to consumer impatience. The second major growth issue examined in this dissertation is fertility. I rigorously establish sufficient conditions for monotone dynamics in a growth model with endogenous fertility. The framework covers important variants of the Barro-Becker model and the early model of Razin and Ben-Zion (1975). I utilize lattice programming methods that do not require the uniqueness of the optimal path or the differentiability of the value function due to the lack of concave structure present in the Barro-Becker framework. The Razin and Ben-Zion variant of the model has a much greater degree of concave structure present and hence I provide conditions for uniqueness, differentiability of the value function, and the local normality of capital.