Empirical likelihood inference with applications to some econometric models

In this paper we analyse the higher order asymptotic properties of the empirical likelihood ratio test, by means of the dual likelihood theory. It is shown that when the econometric model is just identified, these tests are accurate to an order o(1/n), and this accuracy can always be improved to an order O(1/n^2) by means of a scale correction, as in standard parametric theory. To show this, we first develop a valid Edgeworth expansion for the empirical likelihood ratio under a local alternative in terms of an "induced" local alternative. As a by-product of the expansion, we find an explicit expression for the Bartlett correction in terms of cumulants of dual likelihood derivatives which is slightly different from the standard adjustment reported in the literature on Bartlett corrections of the empirical likelihood ratio. We then highlight the connection between the empirical likelihood method and the bootstrap by obtaining a valid Edgeworth expansion for a bootstrap based empirical likelihood ratio test. The theory is then applied to some standard econometric models and illustrated by means of some Monte Carlo simulations.

Bartlett-type Adjustments for Empirical Discrepancy Test Statistics

This paper derives two Bartlett-type adjustments that can be used to obtain higher-order improvements to the distribution of the class of empirical discrepancy test statistics recently introduced by Corcoran (1998) as a generalisation of Owen's (1988)empirical likelihood. The corrections are illustrated in the context of the so-called Cressie-Read goodness-of-fit statistic Baggerly, and their effectiveness in finite samples is evaluated using simulations.asymptotic expansions; Bartlett and Bartlett-type corrections; empirical likelihood; nonparametric likelihood inference

On the density of generalised quadratic forms with applications to asymptotic expansions for test statistics

In this note we derive a general formula useful to express the density of generalised noncentral quadratic forms (i.e. of a scalar random variable obtained by contracting non zero mean multivariate normal vectors over multidimensional arrays) in terms of linear combinations of noncentral chi square random variables. The formula can be used to obtain explicit expressions for the terms appearing in the asymptotic expansions for test statistics under a local alternative.Edgeworth expansions; Generalised noncentral quadratic forms; Local alternatives.

Robust nonlinear regression estimation in null recurrent time series

Under embargo until: 2022-12-04In this article, we study parametric robust estimation in nonlinear regression models with regressors generated by a class of non-stationary and null recurrent Markov processes. The nonlinear regression functions can be either integrable or asymptotically homogeneous, covering many commonly-used functional forms in parametric nonlinear regression. Under regularity conditions, we derive both the consistency and limit distribution results for the developed general robust estimators (including the nonlinear least squares, least absolute deviation and Huber’s M-estimators). The convergence rates of the estimation depend on not only the functional form of the nonlinear regression, but also on the recurrence rate of the Markov process. Some Monte-Carlo simulation studies are conducted to examine the numerical performance of the proposed estimators and verify the established asymptotic properties in finite samples. Finally two empirical applications illustrate the usefulness of the proposed robust estimation method.acceptedVersio

A Simple Test for Identification in GMM under Conditional Moment Restrictions

This paper proposes a simple, fairly general, test for global identification of unconditional moment restrictions implied from point-identified conditional moment restrictions. The test is based on the Hausdorff distance between an estimator that is consistent even under global identification failure of the unconditional moment restrictions, and an estimator of the identified set of the unconditional moment restrictions. The proposed test has a chi-squared limiting distribution and is also able to detect weak identification alternatives. Some Monte Carlo experiments show that the proposed test has competitive finite sample properties already for moderate sample sizes

Pillars of Trust: An Experimental Study on Reputation and Its Effects

This paper presents the results of laboratory experiments on the relevance of reputation for trust and cooperation in social interaction. We have extended a repeated investment game by adding new treatments where reputation is taken more explicitly into account than before. We then compared treatments where the investor and the trustee rate each other and treatments where the investor and the trustee were rated by a third party. The results showed that: (i) third party reputation positively affects cooperation by encapsulating trust; (ii) certain differences in the reputation mechanism can generate different cooperation outcomes. These results have interesting implications for the recent sociological debate on the normative pillars of markets