On the finite-sample properties of conditional empirical likelihood estimators

We provide Monte Carlo evidence on the finite sample behavior of the conditional empirical likelihood (CEL) estimator of Kitamura, Tripathi, and Ahn (2004) and the conditional Euclidean empirical likelihood (CEEL) estimator of Antoine, Bonnal, and Renault (2007) in the context of a heteroskedastic linear model with an endogenous regressor. We compare these estimators with three heteroskedasticity-consistent instrument-based estimators in terms of various performance measures. Our results suggest that the CEL and CEEL with fixed bandwidths may suffer from the no-moment problem, similarly to the unconditional generalized empirical likelihood estimators studied by Guggenberger (2008). We also study the CEL and CEEL estimators with automatic bandwidths selected through cross-validation. We do not find evidence that these suffer from the no-moment problem. When the instruments are weak, we find CEL and CEEL to have finite sample properties --in terms of mean squared error and coverage probability of confidence intervals-- poorer than the heteroskedasticity-consistent Fuller (HFUL) estimator. In the strong instruments case the CEL and CEEL estimators with automatic bandwidths tend to outperform HFUL in terms of mean squared error, while the reverse holds in terms of the coverage probability, although the differences in numerical performance are rather small.Conditional empirical likelihood; conditional Euclidean likelihood; heteroskedasticity; weak instruments; cross-validation

On the Finite Sample Properties of Conditional Empirical Likelihood Estimators

We provide Monte Carlo evidence on the finite-sample behavior of the conditional empirical likelihood (CEL) estimator of Kitamura, Tripathi, and Ahn and the conditional Euclidean empirical likelihood (CEEL) estimator of Antoine, Bonnal, and Renault in the context of a heteroscedastic linear model with an endogenous regressor. We compare these estimators with three heteroscedasticity-consistent instrument-based estimators and the Donald, Imbens, and Newey estimator in terms of various performance measures. Our results suggest that the CEL and CEEL with fixed bandwidths may suffer from the no-moment problem, similarly to the unconditional generalized empirical likelihood estimators studied by Guggenberger. We also study the CEL and CEEL estimators with automatic bandwidths selected through cross-validation. We do not find evidence that these suffer from the no-moment problem. When the instruments are weak, we find CEL and CEEL to have finite-sample properties—in terms of mean squared error and coverage probability of confidence intervals—poorer than the heteroscedasticity-consistent Fuller (HFUL) estimator. In the strong instruments case, the CEL and CEEL estimators with automatic bandwidths tend to outperform HFUL in terms of mean squared error, while the reverse holds in terms of the coverage probability, although the differences in numerical performance are rather small

On the finite-sample properties of conditional empirical likelihood estimators

We provide Monte Carlo evidence on the finite sample behavior of the conditional empirical likelihood (CEL) estimator of Kitamura, Tripathi, and Ahn (2004) and the conditional Euclidean empirical likelihood (CEEL) estimator of Antoine, Bonnal, and Renault (2007) in the context of a heteroskedastic linear model with an endogenous regressor. We compare these estimators with three heteroskedasticity-consistent instrument-based estimators in terms of various performance measures. Our results suggest that the CEL and CEEL with fixed bandwidths may suffer from the no-moment problem, similarly to the unconditional generalized empirical likelihood estimators studied by Guggenberger (2008). We also study the CEL and CEEL estimators with automatic bandwidths selected through cross-validation. We do not find evidence that these suffer from the no-moment problem. When the instruments are weak, we find CEL and CEEL to have finite sample properties --in terms of mean squared error and coverage probability of confidence intervals-- poorer than the heteroskedasticity-consistent Fuller (HFUL) estimator. In the strong instruments case the CEL and CEEL estimators with automatic bandwidths tend to outperform HFUL in terms of mean squared error, while the reverse holds in terms of the coverage probability, although the differences in numerical performance are rather small

On the finite-sample properties of conditional empirical likelihood estimators

We provide Monte Carlo evidence on the finite sample behavior of the conditional empirical likelihood (CEL) estimator of Kitamura, Tripathi, and Ahn (2004) and the conditional Euclidean empirical likelihood (CEEL) estimator of Antoine, Bonnal, and Renault (2007) in the context of a heteroskedastic linear model with an endogenous regressor. We compare these estimators with three heteroskedasticity-consistent instrument-based estimators in terms of various performance measures. Our results suggest that the CEL and CEEL with fixed bandwidths may suffer from the no-moment problem, similarly to the unconditional generalized empirical likelihood estimators studied by Guggenberger (2008). We also study the CEL and CEEL estimators with automatic bandwidths selected through cross-validation. We do not find evidence that these suffer from the no-moment problem. When the instruments are weak, we find CEL and CEEL to have finite sample properties --in terms of mean squared error and coverage probability of confidence intervals-- poorer than the heteroskedasticity-consistent Fuller (HFUL) estimator. In the strong instruments case the CEL and CEEL estimators with automatic bandwidths tend to outperform HFUL in terms of mean squared error, while the reverse holds in terms of the coverage probability, although the differences in numerical performance are rather small

A Conditional Empirical Likelihood Based Method for Model Parameter Estimation from Complex survey Datasets

We consider an empirical likelihood framework for inference for a statistical model based on an informative sampling design. Covariate information is incorporated both through the weights and the estimating equations. The estimator is based on conditional weights. We show that under usual conditions, with population size increasing unbounded, the estimates are strongly consistent, asymptotically unbiased and normally distributed. Our framework provides additional justification for inverse probability weighted score estimators in terms of conditional empirical likelihood. In doing so, it bridges the gap between design-based and model-based modes of inference in survey sampling settings. We illustrate these ideas with an application to an electoral survey

Empirical likelihood estimation of the spatial quantile regression

The spatial quantile regression model is a useful and flexible model for analysis of empirical problems with spatial dimension. This paper introduces an alternative estimator for this model. The properties of the proposed estimator are discussed in a comparative perspective with regard to the other available estimators. Simulation evidence on the small sample properties of the proposed estimator is provided. The proposed estimator is feasible and preferable when the model contains multiple spatial weighting matrices. Furthermore, a version of the proposed estimator based on the exponentially tilted empirical likelihood could be beneficial if model misspecification is suspect

Targeted Maximum Likelihood Estimation using Exponential Families

Targeted maximum likelihood estimation (TMLE) is a general method for estimating parameters in semiparametric and nonparametric models. Each iteration of TMLE involves fitting a parametric submodel that targets the parameter of interest. We investigate the use of exponential families to define the parametric submodel. This implementation of TMLE gives a general approach for estimating any smooth parameter in the nonparametric model. A computational advantage of this approach is that each iteration of TMLE involves estimation of a parameter in an exponential family, which is a convex optimization problem for which software implementing reliable and computationally efficient methods exists. We illustrate the method in three estimation problems, involving the mean of an outcome missing at random, the parameter of a median regression model, and the causal effect of a continuous exposure, respectively. We conduct a simulation study comparing different choices for the parametric submodel, focusing on the first of these problems. To the best of our knowledge, this is the first study investigating robustness of TMLE to different specifications of the parametric submodel. We find that the choice of submodel can have an important impact on the behavior of the estimator in finite samples

Moment Restriction-based Econometric Methods: An Overview

Moment restriction-based econometric modelling is a broad class which includes the parametric, semiparametric and nonparametric approaches. Moments and conditional moments themselves are nonparametric quantities. If a model is specified in part up to some finite dimensional parameters, this will provide semiparametric estimates or tests. If we use the score to construct moment restrictions to estimate finite dimensional parameters, this yields maximum likelihood (ML) estimates. Semiparametric or nonparametric settings based on moment restrictions have been the main concern in the literature, and comprise the most important and interesting topics. The purpose of this special issue on “Moment Restriction-based Econometric Methods†is to highlight some areas in which novel econometric methods have contributed significantly to the analysis of moment restrictions, specifically asymptotic theory for nonparametric regression with spatial data, a control variate method for stationary processes, method of moments estimation and identifiability of semiparametric nonlinear errors-in-variables models, properties of the CUE estimator and a modification with moments, finite sample properties of alternative estimators of coefficients in a structural equation with many instruments, instrumental variable estimation in the presence of many moment conditions, estimation of conditional moment restrictions without assuming parameter identifiability in the implied unconditional moments, moment-based estimation of smooth transition regression models with endogenous variables, a consistent nonparametric test for nonlinear causality, and linear programming-based estimators in simple linear regression.robustness;testing;estimation;model misspecification;moment restrictions;parametric;semiparametric and nonparametric methods