Solving Euler Equations via Two-Stage Nonparametric Penalized Splines

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

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Original languageEnglish
Journal / PublicationJournal of Econometrics
Online published21 Sep 2020
Publication statusOnline published - 21 Sep 2020


This study proposes a novel estimation-based approach to solving asset pricing models for both stationary and time-varying observations. Our method is robust to misspecification errors while inheriting a closed-form solution. By representing the Euler equation into a well-posed integral equation of the second kind, we propose a penalized two-stage nonparametric estimation method and establish its optimal convergence under mild conditions. With the merit of penalized splines, our estimate is less sensitive to the spline setting and we also design a fast data-driven algorithm to effectively tune the key smoother, i.e. the penalty amount. Our approach exhibits excellent finite sample performance. Using the US data from 1947 to 2017, we reinvestigate the return predictability and find that the estimated implied dividend yield significantly predicts lower future cash flows and higher interest rates at short horizons.

Research Area(s)

  • Euler equation, Nonparametric penalized splines, Two-stage regression, Return predictability, mplied price-dividend ratios