Generalized Empirical Likelihood Methods And Its Application

In an effort to improve the small sample properties of generalized methods of moments (GMM), generalized empirical likelihood (GEL) has been suggested. It can be shown that they have the same asymptotic distribution but the former has lower high order asymptotic bias than the latter. However, the advantage of high order asymptotic bias is not necessarily true in small samples. Meanwhile, applications usually need instruments and suffer the correlation magnitude of instruments and their proxies and the numbers of instruments used. So it is important to investigate the choice between these two classes of estimators. In general, applied econometrians are not too familiar with GEL. As a result, it is important to show how to use GEL. This paper focuses on GEL and its applications, and its main research contents and conclusions can be summarized as following:Firstly, this paper formulates thoroughly and systematically the estimator bias on single equation instruments model, the large sample properties of GMM, and the effects on estimators under weak instruments. If explanatory variables correlated with error then OLS is biased and instruments are used. If instruments are compliance and regular conditions met, GMM is consistent and asymptotically normality. However, week instruments and sample error would affect the bias correction. Monte Carlo simulation reveal that if the instruments is a poor one, then the results will tends to be biased and highly misleading. In this case the estimated coefficient is concentrated around a value that is related to the amount of feedback rather than to the true coefficient. And sample error coming from instruments and disturbance would lead the coefficients convergence to infinite.Secondly, this paper formulates thoroughly and systematically the core idea and whole framework of GEL, introducing the empirical likelihood exponential titling and continuous update estimator in detail, also the logic relations among the GMM and GEL. Population moments which coming from economics theory its expectation equal zero, that the observations have a discrete distribution called implied probabilities and the sample mean equals zero called orthogonal conditions. If model is specified correctly, then the distribution and moments are similar among sample and population. GMM assuming equal distributions compliance to orthogonal conditions and GEL assuming sample moments equal zero compliance to the implied probabilities approximate population probabilities. Based on this, comprehensive Monte Carlo evidence is provided that compares the small sample properties of GEL to GMM in linear single equation structure model. We focus on sample median, mean and the asymptotic error correction. The main results indicate that small sample behavior of all the estimators perform a process of bad to good then return bad. In a word GEL is better than GMM in weak instruments and many instruments. The bias correction decrease as the number of instruments increases but its effects constricted by the instruments'weak or strong magnitude.Based on the above, this paper's innovation and meaning lie in:firstly, from the data generation process has weak and many instruments this paper investigated the bias and validity of GMM and GEL estimators and reveal that GEL has better performance than GMM in small sample which is different from the existing literature. Secondly, this paper made up the shortage of current studies ignoring the application of GEL, propose a new technique to ranking funds and analysis the change after inflation expectation. And the results show how to manage funds and inflation expectation that has pointed applied values and practical significance.