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.