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In the second chapter, I introduce an alternative group of estimators to the Generalized Empirical Likelihood (GEL) family. The new group is constructed by employing demeaned moment functions in the objective function while using the original moment functions in the constraints. This designation modifies the higher-order properties of estimators. I refer to these new estimators as Demeaned Generalized Empirical Likelihood (DGEL) estimators. Although Newey and Smith (2004) show that the EL estimator in the GEL family has fewer sources of bias and is higher-order efficient after bias-correction, the demeaned exponential tilting (DET) estimator in the DGEL group has those superior properties. In addition, if data are symmetrically distributed, every estimator in the DGEL family shares the same higher-order properties as the best member.
In the first chapter of this dissertation, we approach the estimation of dynamic stochastic general equilibrium models through a moments-based estimator, the empirical likelihood. We try to show that this inference process can be a valid alternative to maximum likelihood. The empirical likelihood estimator only requires knowledge about the moments of the data generating process of the model. In this context, we exploit the fact that these economies can be formulated as a set of moment conditions to infer on their parameters through this technique. For illustrational purposes, we consider the standard real business cycle model with a constant relative risk adverse utility function and indivisible labour, driven by a normal technology shock. In the second chapter, we explore further aspects of the estimation of dynamic stochastic general equilibrium models using the empirical likelihood family of estimators. In particular, we propose possible ways of tackling the main problems identified in the first chapter. These problems resume to: (i) the possible existence of dependence between the random variables; (ii) the definition of moment conditions in the dynamic stochastic general equilibrium models setup; (iii) the alternatives to the data generation process used in the first chapter. In the third chapter, we investigate the short run effects of macroeconomic and scal volatility on the decision of the policy maker on how much to consume and how much to invest. To that end, we analyse a panel of 10 EU countries during 1991-2007. Our results suggest that increases in the volatility of regularly collected and cyclical revenues such as the VAT and income taxes tend to tilt the expenditure composition in favour of public investment. In contrast, increases in the volatility of ad hoc-type of taxes such as capital taxes tend to favour public consumption spending, albeit only a little.
This paper analyzes near exogeneity and weak identification in Generalized Empirical Likelihood Estimators. Near exogeneity and weak identification are related to the exogeneity and relevance of the instruments, respectively. These two issues are important from an applied perspective, such as empirical growth theory and labor economics. In the case of empirical growth and institutional economics literature a small number of moments/instruments are used in studies. First, we analyze the limit behavior of estimators and tests under fixed number of weak moments and near exogeneity. We show that Anderson-Rubin (1949) and Kleibergen (2002) type of tests' limits change when there is small correlation between the instruments and the structural equation error. The new limits are obtained under the null hypothesis at the true vale of the parameter. The test statistics are no longer asymptotically pivotal in the joint case of near exogeneity and weak instruments compared to the weak identification case. We also show that when used with the x2 critical values, which are not valid in the case of near exogeneity and weak instruments, the tests show very large size distortions. This is an important warning to applied researchers who may use these tests without taking into account the near exogeneity problem. We try subsampling and delete-d jackknife methods to recover asymptotic limits. Both of these methods are inconsistent. However, we show that the asymptotic limit of delete-d jackknife is arbitrarily close to true limit and only slightly liberal. In simulations, exponential tilting based tests with delete-d jackknife method have good size compared to the others. Then we develop the limits of estimators and tests under many weak moments with near exogeneity. The results are different from the fixed moments case. Estimators are consistent, and test limits are simple, noncentral x2.
In this dissertation, we develop likelihood based inferences for dependent functional data analysis. This is done by utilizing the empirical likelihood framework, which provides likelihood based inferences without stringent parametric model assumptions. We first consider an adjusted block-wise empirical likelihood (ABEL) method that is designed to work with weakly dependent multivariate data. This method removes the upper limit on the coverage probability of the empirical likelihood confidence region, and the adjustment tuning parameter in ABEL is shown to be related to the Bartlett correction factor. Indeed, by selecting the tuning parameter accordingly, we can achieve the Bartlett corrected coverage error rate. In the setting of a functional AR(1) model, we then propose a maximum empirical likelihood estimator for the kernel operator. Furthermore, we discuss a framework for applying the empirical likelihood method to more general models for dependent functional data. Our method combines basis expansions with a penalization approach, and it allows the number of basis functions used in the expansion to grow as sample size increases. This allows us to obtain a maximum empirical likelihood estimator that converges to the fully functional true parameter of interest. Similar to ABEL, our method breaks free from the convex hull constraint; therefore, it provides an empirical likelihood confidence region with improved coverage accuracy. Automatic tuning parameter selection is also discussed.
This thesis intends to exploit the roots of empirical likelihood and its related methods in mathematical programming and computation. The roots will be connected and the connections will induce new solutions for the problems of estimation, computation, and generalization of empirical likelihood.
This thesis provides a preliminary investigation of empirical likelihood approach estimation of structural equation models. An auxiliary variable approach built on general estimating equation methods in the EL settings is followed. An auxiliary variable is proposed and estimation/inference based upon it is developed. Testing of model covariance structure for over-identified model is suggested. Asymptotic efficiency connection with Un-weighted Least Squares estimator and multi-normal MLE is established. Estimation example of non-elliptical distribution data is provided.