Research Database

Under a narrow set of assumptions, Chamley (1986) established that the optimal tax rate on capital income is eventually zero. This study examines and extends that result by relaxing Chamley’s assumptions, one by one, to see if the result still holds. It does. This study unifies the work of other researchers, who have confirmed the result independently using different types of models and approaches. This study uses just one type of model (discrete time) and just one approach (primal). Chamley’s result holds when agents are heterogeneous rather than identical, the economy’s growth rate is endogenous rather than exogenous, the economy is open rather than closed, and agents live in overlapping generations rather than forever. (With this last assumption, the result holds under stricter conditions than with the others.)

This paper develops a Limited-Dependent Rational Expectations (LD-RE) model where the bounds can be fixed for an extended period, but are subject to occasional jumps. In this case, the behavior of the endogenous variable is affected by the agent's expectations about both the occurrence and the size of the jump. The RE solution for the one-sided and two-sided band are derived and shown to encompass the cases of perfectly predictable and stochastically varying bounds examined by earlier literature. We demonstrate that the solution for the one-sided band exists and is unique when the coefficient of the expectational variable is less than one. In the case of a two-sided band, the RE solution exists for all the parameter values and is unique if the coefficient of the expectational variable is less than or equal to one. These results hold even when the jump probability is stochastically varying and the error terms are conditionally heteroscedastic. As an illustration, we estimate a model of exchange rate determination in a target zone using data for the Franc/Mark exchange rate. Empirical results provide support for the non-linear model with time-varying realignment probability and indicate that the agents correctly anticipated most of the observed changes in the central parity.