This paper develops a model selection technique based on the penalized empirical likelihood procedure and provides the guideline for extending it to the more general setting of the GEL. By using this procedure which, in the linear and GMM settings, has been called "least absolute shrinkage and selection operator'' (LASSO), we are able to combine the selection and estimation steps together and improve the post-selection properties of the resulting estimators. On top of these, this technique is easier to implement and consumes less computation resources so that renders the model selection feasible, even in a model with a large number of parameters. As a further contribution, I use the existing framework of the penalized maximum likelihood to investigate the penalized empirical likelihood with a fairly general penalty function. I introduce a new penalty function which helps us to construct a PEL estimator which has a implied probability measure with better entropy properties than the implied probability measure of EL estimator. We also conduct a simulation study to compare the properties of the model selection method proposed here with some of the already available ones. The simulation results show the better performance of the method developed in this paper compared to the classical methods like AIC, BIC, and DT.

  In this paper we introduce the modulation method in the framework of empirical likelihood estimator. This method is an example of what are generally known as shrinkage methods. Shrinkage methods are frequently used to improve an existing estimator, and they provide powerful tools to correct ill-posed inference problems due to small samples, unknown heteroskedasticity, etc. Here we show how modulation method work in theory, and how we can implement it in special, yet important estimation problems. Although devising algorithms to implement all of the methods and procedures introduced in this paper is currently a work in progress, I will conduct Monte Carlo simulations using two important examples, which show the advantages of using the shrinkage procedures introduced in this paper over their regular counterparts, specially when the sample size is very small. Also, very recently, I have realized that it is possible to use this method to design moment selection procedures in the framework of EL and GEL estimators.

  Imitation is one of those personal behaviors which have profound social and economical implications. It has been suggested that this phenomenon is the leading cause of wide spread modes and fashions.  Even financial markets with rational, and to some extent, experienced and serious participants are not immune from imitative behaviors. The term animal spirit was adopted by Keynes mostly in reference to these kind of behaviors. Although, this Keynesian view has been somewhat overshadowed by the considerable successes of rational expectation argument, new research in herd behavior, informational cascades, and behavioral economics  has shown that not all herd behaviors necessarily caused by irrationality, nor can learning, and training, completely prevent irrational behaviors. In this paper, we study a model of imitation in which not all participating agents carry the same weight when it comes to affecting other people's behavior. We show, how having a star or celebrity player impacts the entire herd formation. Embedding this model in a simple market with a single asset to be traded, we show how this celebrity effect can inflate prices and be a very important cause of bubble formation in the financial market.

 The standard approach to testing statistical hypothesis, and reporting empirical results in econometrics is to provide point estimates and standard errors. Unfortunately, this method fails under the assumption of weak identification. For instance in the linear instrumental variables (IVs) regression, when IVs are weak, two-stage least squares (2SLS) has significant bias and is poorly approximated by a normal distribution. The problem of testing and constructing confidence intervals persist when we deal with non-linear models like GMM and GEL. Anderson-Rubin (AR) statistic is the oldest solution to the testing and constructing confidence intervals for linear models with weak identification. In recent years, other robust test statistics have been proposed to improve AR. Some of the alternatives to the AR test are Lagrange multiplier test (LM), and conditional likelihood ratio (CLR) tests. Several authors have constructed AR, LM, and CLR tests for the GMM case. Analytical results from linear case and simulation results from GMM, shows that CLR test has better power compare to the other weak IVs robust tests. While AR and LM tests are available for the GEL model, currently there is no CLR test available  for this model. Since CLR preforms better in the linear and GMM case, one might assume that such a test has a superior performance in the GEL model as well. In this paper we construct a CLR test for the GEL model and preform simulations to compare its power properties with, the previously available, LM, and AR tests.

  Estimating, and forecasting the return volatility is a fundamental task for both practitioners and  those how are interested in studying the financial markets. A natural measure of ex-post return variability is the integrated volatility (IV) measure. Although, theoretically the IV measure provides a complete picture of the volatility function associated with the diffusion process representing the price, in practice IV is not directly observable. The closet measure to IV is the so called realized volatility (RV), which is the summation of high-frequency squared return from the price diffusion. Basic theorems of stochastic analysis guarantee that RV approaches IV, when the sampling frequency increases, or the time between to samples goes to zero. In practice, when the frequency is too high, the market microstructure noise becomes a major factor blurring the whole process. In this paper, using the continuous times stochastic filtering theory, we try to model the market microstructure noise and derive a more reliable corrected RV which is robust to this kind of noise