Precautionary savings over the life cycle: e cient two-stage nonparametric instrumental variables estimation

This paper considers the problem of estimating a structural model of optimal life-cycle savings, controlling both for uncertainty about health-care expenditures and household risk aversion. To avoid misleading inference, we propose a new estimation technique that compared to those already proposed in the literature enables us to deal simultaneously with the presence of (i) unobserved cross-sectional heterogeneity, (ii) flexible unknown form in the Euler equation and (iii) endogenous covariates. We propose one-step backfitting estimators based on first di↵erencing techniques that are combined through a minimum distance estimation approach. The resulting estimators are shown to be oracle e cient and they exhibit the optimal rate of convergence for this smoothness problem. To illustrate the feasibility and possible gains of this method, we present an application about household’s precautionary savings over the life-cycle. From this empirical application, we obtain (i) households accumulate wealth at least in two periods in life. In younger stages, in order to guard against uncertainty about potential income downturns, and when they become older due to other reasons such as retirement and bequests. (ii) Public health programs have a negative impact on precautionary savings. The paper concludes with a Monte Carlo simulation where the small sample properties of the estimators. [1] JEL codes: C01, C14, C33