We study how the extent of commitment ability influences equilibrium allocations in one-sector growth models in which households have non-geometric discounting functions. Our analysis covers the standard model, in which the economy approaches a stationary equilibrium, and the AKAK model, which allows for perpetual growth of per-capita output. We demonstrate that higher commitment ability implies a higher level (in the standard model) and a higher growth rate (in the AKAK model) of long-run per-capita output. Unlike similar studies, we assume that the commitment technology is stochastic and that the non-geometric nature of time-preference is caused by idiosyncratic shocks to households.
A commonly made assumption in intertemporal economic models is that decision makers have constant time-preference rates. Formally, this means that an agent deciding at time t discounts utility that is derived at time s≥ts≥t by the factor d(s;t)=e−ρ(s−t)d(s;t)=e−ρ(s−t), where ρρ is a positive real number (the time-preference rate). This model of time-preference is called geometric (or exponential) discounting. Experimental studies of time-preference, however, suggest that the time-preference rate is a decreasing function of s−ts−t; see, for example, Ainslie (1992), Loewenstein and Prelec (1992), Loewenstein and Thaler (1989), and Thaler (1981). These experiments, together with the theoretical results derived by Strotz (1956), imply that there exists a problem of dynamic inconsistency. In other words, if decision makers use discounting functions that differ from the geometric one and if they are not able to precommit their decisions fully at time t, then they will not stick to these decisions but re-optimize their plans if given the opportunity. This shows that the availability of commitment technologies may have important implications for the behavior of individual agents and for the development of the economy in general, a fact that has already been pointed out by several economists including Strotz (1956), Laibson (1997), and Barro (1999). Following this line of reasoning, the present paper studies how the extent of commitment ability influences equilibrium allocations in one-sector growth models in which households have non-geometric discounting functions.
Our study is closely related to the work of Barro, but differs from the latter in the specific models of time-preference and commitment ability that are used to describe household behavior. Whereas Barro considers a representative consumer with deterministic preferences and access to a deterministic commitment technology, our approach is an extension of the stochastic model proposed by Harris and Laibson (2000). In our model, households are subject to idiosyncratic time-preference shocks such that, at any given point in time, some households behave patiently while others are more impatient. Furthermore, we do not restrict ourselves to the standard model of Ramsey (1928), Cass (1965), and Koopmans (1965) but consider the AKAK model as well, which allows for perpetual growth of per-capita output. Our approach allows for a simple characterization of the long-run effects of time-preference
