scholarly journals NONPARAMETRIC EULER EQUATION IDENTIFICATION AND ESTIMATION

2020 ◽  
pp. 1-41
Author(s):  
Juan Carlos Escanciano ◽  
Stefan Hoderlein ◽  
Arthur Lewbel ◽  
Oliver Linton ◽  
Sorawoot Srisuma
Keyword(s):  
Euler Equations ◽  
Instrumental Variables ◽  
Marginal Utility ◽  
Kernel Estimation ◽  
Monte Carlo Experiment ◽  
Nonparametric Identification ◽  
Nonparametric Estimator ◽  
Finite Sample ◽  
Ill Posed ◽  
Identification Analysis

Abstract We consider nonparametric identification and estimation of pricing kernels, or equivalently of marginal utility functions up to scale, in consumption-based asset pricing Euler equations. Ours is the first paper to prove nonparametric identification 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 identification analysis, which combines standard kernel estimation with the computation of a matrix eigenvector problem. Our estimator avoids the ill-posed inverse issues associated with nonparametric instrumental variables estimators. We derive limiting distributions for our estimator and for relevant associated functionals. A Monte Carlo experiment shows a satisfactory finite sample performance for our estimators.

scholarly journals DEMAND ANALYSIS AS AN ILL-POSED INVERSE PROBLEM WITH SEMIPARAMETRIC SPECIFICATION

2010 ◽  
Vol 27 (3) ◽  
pp. 609-638 ◽  
Author(s):  
Stefan Hoderlein ◽  
Hajo Holzmann
Keyword(s):  
Inverse Problem ◽  
Nonparametric Regression ◽  
Regression Models ◽  
Unobserved Heterogeneity ◽  
Monte Carlo Experiment ◽  
Finite Sample ◽  
Problematic Relationship ◽  
Endogenous Regressors ◽  
Semiparametric Estimator ◽  
Ill Posed

In this paper we are concerned with analyzing the behavior of a semiparametric estimator that corrects for endogeneity in a nonparametric regression by assuming mean independence of residuals from instruments only. Because it is common in many applications, we focus on the case where endogenous regressors and additional instruments are jointly normal, conditional on exogenous regressors. This leads to a severely ill-posed inverse problem. In this setup, we show first how to test for conditional normality. More importantly, we then establish how to exploit this knowledge when constructing an estimator, and we derive the large sample behavior of such an estimator. In addition, in a Monte Carlo experiment we analyze its finite sample behavior. Our application comes from consumer demand. We obtain new and interesting findings that highlight both the advantages and the difficulties of an approach that leads to ill-posed inverse problems. Finally, we discuss the somewhat problematic relationship between endogenous nonparametric regression models and the recently emphasized issue of unobserved heterogeneity in structural models.

ADMISSIBLE, SIMILAR TESTS: A CHARACTERIZATION

2019 ◽  
Vol 36 (2) ◽  
pp. 347-366 ◽  
Author(s):  
José Luis Montiel Olea
Keyword(s):  
Weight Function ◽  
Instrumental Variables ◽  
Structural Parameters ◽  
Average Power ◽  
Nuisance Parameter ◽  
Weighted Average ◽  
Necessary Condition ◽  
Ratio Test ◽  
Finite Sample ◽  
Characterization Result

This article studies a classical problem in statistical decision theory: a hypothesis test of a sharp null in the presence of a nuisance parameter. The main contribution of this article is a characterization of two finite-sample properties often deemed reasonable in this environment: admissibility and similarity. Admissibility means that a test cannot be improved uniformly over the parameter space. Similarity requires the null rejection probability to be unaffected by the nuisance parameter.The characterization result has two parts. The first part—established by Chernozhukov, Hansen, and Jansson (2009, Econometric Theory 25, 806–818)—states that maximizing weighted average power (WAP) subject to a similarity constraint suffices to generate admissible, similar tests. The second part—hereby established—states that constrained WAP maximization is (essentially) a necessary condition for a test to be admissible and similar. The characterization result shows that choosing an admissible, similar test is tantamount to selecting a particular weight function to report weighted average power. This result applies to full vector inference with a nuisance parameter, not to subvector inference.The article also revisits the theory of testing in the instrumental variables model. Specifically—and in light of the relevance of the weighted average power criterion in the main theoretical result—the article suggests a weight function for the structural parameters of the homoskedastic instrumental variables model, based on the priors proposed by Chamberlain (2007). The corresponding test is, by construction, admissible and similar. In addition, the test is shown to have finite- and large-sample properties comparable to those of the conditional likelihood ratio test.

scholarly journals Nonparametric Instrumental-Variable Estimation

2018 ◽  
Vol 18 (4) ◽  
pp. 937-950 ◽  
Author(s):  
Denis Chetverikov ◽  
Dongwoo Kim ◽  
Daniel Wilhelm
Keyword(s):  
Instrumental Variable ◽  
Estimation Methods ◽  
Monte Carlo Experiment ◽  
Finite Sample ◽  
Gasoline Demand ◽  
Tuning Parameters ◽  
Demand Functions ◽  
Instrumental Variable Estimation ◽  
Finite Sample Properties ◽  
Shape Restriction

In this article, we introduce the commands npiv and npivcv, which implement nonparametric instrumental-variable (NPIV) estimation methods without and with a cross-validated choice of tuning parameters, respectively. Both commands can impose the constraint that the resulting estimated function is monotone. Using such a shape restriction may significantly improve the performance of the NPIV estimator (Chetverikov and Wilhelm, 2017, Econometrica 85: 1303–1320) because the ill-posedness of the NPIV estimation problem leads to unconstrained estimators that suffer from particularly poor statistical properties such as high variance. However, the constrained estimator that imposes the monotonicity significantly reduces variance by removing nonmonotone oscillations of the estimator. We provide a small Monte Carlo experiment to study the estimators’ finite-sample properties and an application to the estimation of gasoline demand functions.

scholarly journals TRUNCATED SUM OF SQUARES ESTIMATION OF FRACTIONAL TIME SERIES MODELS WITH DETERMINISTIC TRENDS

2019 ◽  
Vol 36 (4) ◽  
pp. 751-772 ◽  
Author(s):  
Javier Hualde ◽  
Morten Ørregaard Nielsen
Keyword(s):  
Time Series ◽  
Asymptotic Normality ◽  
Relative Strength ◽  
Sum Of Squares ◽  
Monte Carlo Experiment ◽  
Time Series Models ◽  
Finite Sample ◽  
Generalized Polynomial ◽  
Finite Sample Properties ◽  
Deterministic Components

We consider truncated (or conditional) sum of squares estimation of a parametric model composed of a fractional time series and an additive generalized polynomial trend. Both the memory parameter, which characterizes the behavior of the stochastic component of the model, and the exponent parameter, which drives the shape of the deterministic component, are considered not only unknown real numbers but also lying in arbitrarily large (but finite) intervals. Thus, our model captures different forms of nonstationarity and noninvertibility. As in related settings, the proof of consistency (which is a prerequisite for proving asymptotic normality) is challenging due to nonuniform convergence of the objective function over a large admissible parameter space, but, in addition, our framework is substantially more involved due to the competition between stochastic and deterministic components. We establish consistency and asymptotic normality under quite general circumstances, finding that results differ crucially depending on the relative strength of the deterministic and stochastic components. Finite-sample properties are illustrated by means of a Monte Carlo experiment.

An Introduction to the Augmented Inverse Propensity Weighted Estimator

2010 ◽  
Vol 18 (1) ◽  
pp. 36-56 ◽  
Author(s):  
Adam N. Glynn ◽  
Kevin M. Quinn
Keyword(s):  
Monte Carlo ◽  
Propensity Score ◽  
Regression Model ◽  
Interesting Property ◽  
Outcome Variable ◽  
Monte Carlo Experiment ◽  
Finite Sample ◽  
Propensity Score Model ◽  
Matching Estimator ◽  
Score Model

In this paper, we discuss an estimator for average treatment effects (ATEs) known as the augmented inverse propensity weighted (AIPW) estimator. This estimator has attractive theoretical properties and only requires practitioners to do two things they are already comfortable with: (1) specify a binary regression model for the propensity score, and (2) specify a regression model for the outcome variable. Perhaps the most interesting property of this estimator is its so-called “double robustness.” Put simply, the estimator remains consistent for the ATE if either the propensity score model or the outcome regression is misspecified but the other is properly specified. After explaining the AIPW estimator, we conduct a Monte Carlo experiment that compares the finite sample performance of the AIPW estimator to three common competitors: a regression estimator, an inverse propensity weighted (IPW) estimator, and a propensity score matching estimator. The Monte Carlo results show that the AIPW estimator has comparable or lower mean square error than the competing estimators when the propensity score and outcome models are both properly specified and, when one of the models is misspecified, the AIPW estimator is superior.

scholarly journals Additive Nonparametric Instrumental Regressions: A Guide to Implementation

2017 ◽  
Vol 6 (1) ◽  
Author(s):  
Samuele Centorrino ◽  
Frederique Feve ◽  
Jean-Pierre Florens
Keyword(s):  
Instrumental Variables ◽  
Regularization Method ◽  
Regression Models ◽  
Regression Function ◽  
Data Driven ◽  
Finite Sample ◽  
Partially Linear ◽  
Regularization Parameters ◽  
Finite Sample Properties ◽  
Additive Nonparametric Regression

AbstractWe present a review on the implementation of regularization methods for the estimation of additive nonparametric regression models with instrumental variables. We consider various versions of Tikhonov, Landweber-Fridman and Sieve (Petrov-Galerkin) regularization. We review data-driven techniques for the sequential choice of the smoothing and the regularization parameters. Through Monte Carlo simulations, we discuss the finite sample properties of each regularization method for different smoothness properties of the regression function. Finally, we present an application to the estimation of the Engel curve for food in a sample of rural households in Pakistan, where a partially linear specification is described that allows one to embed other exogenous covariates.

SEMIPARAMETRIC ESTIMATION OF MULTIPLE EQUATION MODELS

2000 ◽  
Vol 16 (4) ◽  
pp. 551-575 ◽  
Author(s):  
Gabriel A. Picone ◽  
J.S. Butler
Keyword(s):  
Monte Carlo ◽  
Choice Model ◽  
Average Distance ◽  
Sample Selection ◽  
Semiparametric Estimation ◽  
Monte Carlo Experiment ◽  
Finite Sample ◽  
Semiparametric Estimator ◽  
Multinomial Choice ◽  
Multiple Equation Models

This paper proposes a semiparametric estimator for multiple equations multiple index (MEMI) models. Examples of MEMI models include several sample selection models and the multinomial choice model. The proposed estimator minimizes the average distance between the dependent variable unconditional and conditional on an index. The estimator is √N-consistent and asymptotically normally distributed. The paper also provides a Monte Carlo experiment to evaluate the finite-sample performance of the estimator.

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