Dynamic self-control preferences and the behavior of the saving rate

We characterize the dynamics of the saving rate in an exogenous growth model where consumers exhibit present-biased preferences. Based on empirical evidence, we assume that consumers are subject to temptation and exhibit a preference for costly self-control. Moreover, we propose the intensity of these phenomena to depend on aggregate wealth. We show that in economies where consumers are present-biased, the saving rate follows a hump-shaped pattern after an exogenous destruction of the capital stock. The present-bias effect on the intertemporal consumption choice counteracts the standard effect from decreasing returns to capital. After a large destruction of capital, the temptation effect can dominate in the first periods of the adjustment process. By calibrating the model, we obtain a very good fit between our simulations and data concerning the saving rate, the growth rate, and the speed of convergence from the European recovery after World War II.