Nonparametric Euler equation identification and estimation

Abstract

We consider nonparametric identi…cation and estimation of pricing kernels, or equivalently of marginal utility functions up to scale, in consumption based asset pricing Euler equations.Ours is the …rst paper to prove nonparametric identi…cation of Euler equations under low level conditions (without imposing functional restrictions or just assuming completeness). We also propose a novel nonparametric estimator based on our identi…cation analysis, which combines standard kernel estimation with the computation of a matrix eigenvector problem. Our estimator avoids the ill-posed inverse issues associated with existing nonparametric instrumental variables based Euler equation estimators. We derive limiting distributions for our estimator and for relevant associated functionals. We provide a Monte Carlo analysis and an empirical application to US household-level consumption data.

Pricing Kernel Estimation: A Local Estimating Equation Approach

“…Our paper is related to the work of Ludvigson (2009), Escanciano andHoderlein (2010), Lewbel, Linton, and Srisuma (2011), Fang, Ren, and Yuan (2011), and Chen, Favilukis, and Ludvigson (2012, among others. However, ours differs in the following aspects.…”

Local Identification of Nonparametric and Semiparametric Models

“…Escanciano and Hoderlein (2010) and Lewbel, Linton, and Srisuma (2012) have previously shown how homogeneous integral equations of the second kind arise in CCAPM models, though their models and identification results are different than those given here, as further discussed below. The nonparametric rank condition (Assumption 1 for g) will be uniqueness, up to scale, of the solution g 0 of E A t g(c t+1 )|W t = g(c t )e 3) is a homogeneous integral equation of the second kind.…”

Nonparametric stochastic discount factor decomposition

“…First, other quantities of interest, such as a habit formation component in a semiparametric C-CAPM (Chen et al, 2014) and marginal utility in nonparametric Euler equations (Lewbel, Linton, and Srisuma, 2011;Escanciano and Hoderlein, 2012), may be written as positive eigenfunctions of nonselfadjoint operators. Our estimators provide a computationally simple means of estimating these other models in a representative agent setting.…”

“…Our estimators provide a computationally simple means of estimating these other models in a representative agent setting. In contrast, implementation of the kernel-based estimator of Lewbel et al (2011) requires nonparametrically estimating conditional densities, a numerical integration step, and then solving a high-dimensional eigenfunction problem. The estimators and large-sample theory presented herein may be extended to study sieve estimation of these other models in a heterogeneous agent setting using mirco-level data.…”