Decreasing marginal impatience and capital accumulation in a two-country world economy
Ken-Ichi Hirose and Shinsuke Ikeda,
Decreasing Marginal Impatience and Capital Accumulation in a Two-country World Economy
Backgrounds:
Although many theoretical studies on macroeconomic dynamics have been conducted using endogenous time preferences (see, e.g., Epstein, 1987a, b; Lucas and Stokey, 1984; Obstfeld, 1990; Ikeda, 2006), it has been usually assumed that the degree of impatience, measured by the pure rate of time preference, is marginally increasing in wealth so as to ensure stability: When the degree of impatience is marginally decreasing in wealth, the wealthier are more patient and, ceteris paribus, become even wealthier over time. However, many of the existing empirical studies often support the validity of decreasing marginal impatience (hereafter DMI) (e.g., Lawrance, 1991; Samwick, 1998; Harrison et al., 2002; Ikeda et al., 2006). To develop realistic macroeconomic models, it is necessary to examine dynamic implications of DMI in general equilibrium settings.
Objectives:
Using a two-country capital-accumulation model, the purpose of this paper is to derive theoretical implications of DMI for dynamical stability, open-macro economical adjustments, and policy effects. This is the first attempts to characterize two-country general equilibrium solutions under DMI.
Results:
Supposing that one country has a DMI preference, for the steady-state equilibrium to be saddle-point stable, it is necessary that the other country displays increasing marginal impatience (hereafter IMI). Although the same property is valid in the case of an endowment economy, saddle-point stability condition is more restrictive in our capital-accumulation economy than in the endowment economy.
For investigating the implications of DMI, we thus consider the case in which one country exhibits DMI while the other country exhibits IMI, with retaining the saddle-point stability of the equilibrium dynamics. Then, an upward shift of the subjective discount rate schedule in IMI country lowers the steady-state interest rate, and hence increases the steady-state capital stock and output in both counties. This paradoxical result cannot be obtained in the case where both counties display IMI as in Devereux and Shi (1991).
Considering the saddle-path dynamics after international transfers in our capital-accumulation economy, the interest rate and the capital stock initially and sluggishly deviate from their constant steady-state values and then return to them again. Besides, although the convergence path of IMI country's consumption is monotonic, that of DMI country's consumption is non-monotonic. Such non-monotonic consumption adjustment after international transfers never emerges if both counties have IMI preference.
As the effects of improvements in productivity, we obtain the following results. First, the interest rate falls in the long run, although it rises in the short run. Second, the steady-state capital stock and output increase in both countries. Third, the steady-state consumption increases in the DMI country while it decreases in the IMI country. Fourth, an improvement in the DMI country's productivity typically increases its steady-state net foreign assets, whereas an improvement in the IMI country's productivity typically decreases its steady-state net foreign assets. These results also quite differ from those in the case of Devereux and Shi (1991).