Francesco Bravo

Empirical Likelihood Based Inference with Applications to Some Econometric Models

This paper uses the concept of dual likelihood to develop some higher order asymptotic theory for the empirical likelihood ratio test for parameters defined implicitly by a set of estimating equations. The resulting theory is likelihood based in the sense that it relies on methods developed for ordinary parametric likelihood models to obtain valid Edgeworth expansions for the maximum dual likelihood estimator and for the dual/empirical likelihood ratio statistic. In particular, the theory relies on certain Bartlett-type identities that can be used to produce a simple proof of the existence of a Bartlett correction for the dual/empirical likelihood ratio. The paper also shows that a bootstrap version of the dual/empirical likelihood ratio achieves the same higher order accuracy as the Bartlett-corrected dual/empirical likelihood ratio.This paper is based on Chapter 2 of my Ph.D. dissertation at the University of Southampton. Partial financial support under E.S.R.C. grant R00429634019 is gratefully acknowledged. I thank my supervisor, Grant Hillier, for many stimulating conversations and Peter Phillips, Andrew Chesher, and Jan Podivisnky for some useful suggestions. In addition, I am very grateful to the co-editor Donald Andrews and two referees for many valuable comments that have improved noticeably the original draft. All remaining errors are my own responsibility.

Blockwise Generalized Empirical Likelihood Inference for Non-Linear Dynamic Moment Conditions Models

This paper shows how the blockwise generalized empirical likelihood method can be used to obtain valid asymptotic inference in non-linear dynamic moment conditions models for possibly non-stationary weakly dependent stochastic processes. The results of this paper can be used to construct test statistics for overidentifying moment restrictions, for additional moments, and for parametric restrictions expressed in mixed implicit and constraint form. Monte Carlo simulations seem to suggest that some of the proposed test statistics have competitive finite sample properties. Copyright

Empirical Likelihood for Efficient Semiparametric Average Treatment Effects

This article considers empirical likelihood in the context of efficient semiparametric estimators of average treatment effects. It shows that the empirical likelihood ratio converges to a nonstandard distribution, and proposes a corrected test statistic that is asymptotically chi-squared. A small Monte Carlo experiment suggests that the corrected empirical likelihood ratio statistic has competitive finite sample properties. The results of the article are applied to estimate the environmental effect of the World Trade Organisation.

Blockwise empirical Cressie–Read test statistics for α-mixing processes

In this paper we use the empirical Cressie-Read discrepancy function to obtain a class of nonparametric likelihood statistics for smooth functions of means of [alpha]-mixing processes both in the finite- and infinite-dimensional case.

Semiparametric estimation with missing covariates

This paper considers estimation in semiparametric models when some of the covariates are missing at random. The paper proposes an iterative estimator based on inverse probability weighting and local linear estimation of the nonparametric component. The resulting estimator is very general and can be used in the context of semiparametric maximum likelihood, quasi likelihood and robust estimation. The paper establishes the asymptotic normality of the estimator using both nonparametric and parametric estimation of the unknown probability weights. Two general examples illustrate the theory and Monte Carlo simulations show that the proposed estimator has good finite sample properties.

Two-step generalised empirical likelihood inference for semiparametric models

This paper shows how the generalised empirical likelihood method can be used to obtain valid asymptotic inference for the finite dimensional component of semiparametric models defined by a set of moment conditions. The results of the paper are illustrated using three well-known semiparametric regression models: partially linear single index, linear transformation with random censoring, and quantile regression with random censoring. Monte Carlo simulations suggest that some of the proposed test statistics have competitive finite sample properties. The results of the paper are applied to test for functional misspecification in a hedonic price model of a housing market.

Testing linear restrictions in linear models with empirical likelihood

In this paper we analyse the higher order asymptotic behaviour of a profiled empirical likelihood ratio which can be used to test a set of linear restrictions in linear regression models. We show that the resulting profiled empirical likelihood ratio admits a Bartlett correction which can be used to improve to third order the accuracy of commonly used tests in applied research without any distributional assumptions about the error process.

Bootstrap HAC Tests for Ordinary Least Squares Regression

There is a need for tests that are derived from the ordinary least squares (OLS) estimators of regression coefficients and are useful in the presence of unspecified forms of heteroskedasticity and autocorrelation. A method that uses the moving block bootstrap and quasi-estimators in order to derive a consistent estimator of the asymptotic covariance matrix for the OLS estimators and robust significance tests is proposed. The method is shown to be asymptotically valid and Monte Carlo evidence indicates that it is capable of providing good control of significance levels in finite samples and good power compared with two other bootstrap tests.

Generalized Empirical Likelihood Testing in Semiparametric Conditional Moment Restrictions Models

This paper shows how generalized empirical likelihood can be used to obtain specification tests in semiparametric conditional moment restrictions models. The resulting test statistics are similar in spirit to classical Kolmogorov–Smirnov and Cramer von Mises goodness‐of‐fit statistics and are based on an integrated version of the original moment restrictions. The results are applied to test the correct specification of an instrumental variable smooth varying coefficient model and of a censored non‐linear quantile regression model. Monte Carlo results suggest that the proposed tests have competitive finite sample properties.

Semiparametric estimation of moment condition models with weakly dependent data

ABSTRACT This paper develops the asymptotic theory for the estimation of smooth semiparametric generalized estimating equations models with weakly dependent data. The paper proposes new estimation methods based on smoothed two-step versions of the generalised method of moments and generalised empirical likelihood methods. An important aspect of the paper is that it allows the first-step estimation to have an effect on the asymptotic variances of the second-step estimators and explicitly characterises this effect for the empirically relevant case of the so-called generated regressors. The results of the paper are illustrated with a partially linear model that has not been previously considered in the literature. The proofs of the results utilise a new uniform strong law of large numbers and a new central limit theorem for U-statistics with varying kernels that are of independent interest.