Solving Euler Equations via Two-Stage Nonparametric Penalized Splines

Abstract

This study proposes a novel nonparametric estimation approach to solving asset-pricing models. Our method is robust to misspecification errors and it inherits a closed-form solution that facilitates ease of implementation. By transforming the Euler equation, our estimate is fully identified, and we establish large sample properties of the proposed estimate for a broad class of stationary Markov state variables. Using the merit of penalized splines, we design a fast data-based algorithm to e↵ectively tune the smoothing parameter. Our approach exhibits superior performance even with a small sample size. For application, using US data from 1947 to 2017, we reinvestigate the return predictability and find that high implied dividend yield, obtained from our misspecification-free approach, significantly predicts lower future cash flows and higher interest rates at short horizons.

Keywords: Euler equation, implied price-dividend ratio, nonparametric, penalized splines, two-stage regression, return predictability.

JEL Classification: C1, C3, C4, C5, E1, G12