The Time Path of the Saving Rate: Hyperbolic Discounting and Short-Term Planning
The standard neoclassical growth model with Cobb-Douglas production predicts a monotonically declining saving rate, when reasonably calibrated. Ample empirical evidence, however, shows that the transition paths of most countries’ saving rates exhibit a statistically significant hump-shaped pattern. Prior literature shows that CES production may imply a hump-shaped pattern of the saving rate (Goméz, 2008). However, the implied magnitude of the hump falls short of what is seen in empirical data. We introduce two non-standard features of preferences into a neoclassical growth model with CES production: hyperbolic discounting and short planning horizons. We show that, in contrast to the commonly accepted argument, in general (except for the special case of logarithmic utility) a model with hyperbolic discounting is not observationally equivalent to one with exponential discounting. We also show that our framework implies a hump-shaped saving rate dynamics that is consistent with empirical evidence. Hyperbolic discounting turns out to be a major factor explaining the magnitude of the hump of the saving rate path. Numerical simulations employing a generalized class of hyperbolic discount functions, which we term regular discount functions, support the results.
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