How Does Consumption Respond to a Transitory Income Shock? Departing From a Random Walk Consumption to Reconcile Semi-Structural Estimates With Natural Experiment Results

I show that a generalized version of the semi-structural estimation method developed by Blundell, Pistaferri, and Preston (2008), which relaxes their assumption that log-consumption is a random walk, estimates the elasticity of consumption to a transitory income shock to be large. With the same PSID dataset, the average yearly elasticity of nondurable consumption rises to 0.59, a magnitude consistent with findings from natural experiments. I explain that the seminal random walk expression of consumption initially developed by Hall (1978) is not an approximation of the standard life-cycle model but erroneously obtained by linearizing an identity. Contrary to this, in general, the standard life-cycle model generates a consumption process that departs from a random walk because of precautionary behavior. Numerical simulations show that, when calibrated with the persistence of the transitory income process and of the variance of the transitory and permanent shocks that I re-estimated, the standard life-cycle model generates an elasticity of 0.42.