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This dissertation adds to the literature on least squares model averaging by studying and extending current least squares model averaging techniques. The first chapter reviews existing literature and discusses the contributions of this dissertation. The second chapter proposes a new estimator for least squares model averaging. A model average estimator is a weighted average of common estimates obtained from a set of models. I propose computing weights by minimizing a model average prediction criterion (MAPC). I prove that the MAPC estimator is asymptotically optimal in the sense of achieving the lowest possible mean squared error. For statistical inference, I derive asymptotic tests on the average coefficients for the "core" regressors. These regressors are of primary interest to researchers and are included in every approximation model. In Chapter Three, two empirical applications for the MAPC method are conducted. I revisit the economic growth models in Barro (1991) in the first application. My results provide significant evidence to support Barro's (1991) findings. In the second application, I revisit the work by Durlauf, Kourtellos and Tan (2008) (hereafter DKT). Many of my results are consistent with DKT's findings and some of my results provide an alternative explanation to those outlined by DKT. In the fourth chapter, I propose using the model averaging method to construct optimal instruments for IV estimation when there are many potential instrument sets. The empirical weights are computed by minimizing the model averaging IV (MAIV) criterion through convex optimization. I propose a new loss function to evaluate the performance of the estimator. I prove that the instrument set obtained by the MAIV estimator is asymptotically optimal in the sense of achieving the lowest possible value of the loss function. The fifth chapter develops a new forecast combination method based on MAPC. The empirical weights are obtained through a convex optimization of MAPC. I prove that with stationary observations, the MAPC estimator is asymptotically optimal for forecast combination in that it achieves the lowest possible one-step-ahead second-order mean squared forecast error (MSFE). I also show that MAPC is asymptotically equivalent to the in-sample mean squared error (MSE) and MSFE. / Thesis (Ph.D, Economics) -- Queen's University, 2013-07-17 15:46:54.442

For the empirical macroeconomist, accounting for nonlinearities in data series by using regime switching techniques has a long history. Over the past 25 years, there have been tremendous advances in both the estimation of regime switching and the incorporation of regime switching into macroeconomic models. In this dissertation, I apply techniques from this literature to study two topics that are of particular relevance to the conduct of monetary policy: asset bubbles and the Federal Reserve’s policy reaction function. My first chapter utilizes a recently developed Markov-Switching model in order to test for asset bubbles in simulated data. I find that this flexible model is able to detect asset bubbles in about 75% of simulations. In my second and third chapters, I focus on the Federal Reserve’s policy reaction function. My second chapter advances the literature in two important directions. First, it uses meeting- based timing to more properly account for the target Federal Funds rate; second, it allows for the inclusion of up to 14 economic variables. I find that the long-run inflation response coefficient is larger than had been found in previous studies, and that increasing the number of economic variables that can enter the model improves both in-sample fit and out-of-sample forecasting ability. In my third chapter, I introduce a new econometric model that allows for Markov-Switching, but can also remove variables from the model, or enforce a restriction that there is no regime switching. My findings indicate that the majority of coefficients in the Federal Reserve’s policy reaction function have not changed over time.

The Gaussian mixture model has been used for model-based clustering analysis for decades. Most model-based clustering analyses are based on the Gaussian mixture model. Model averaging approaches for Gaussian mixture models are proposed by Wei and McNicholas, based on a family of 14 Gaussian parsimonious clustering models. In this thesis, we use non-Gaussian mixture models, namely the tEigen family, for our averaging approaches. This paper studies fitting in an averaged model from a set of multivariate t-mixture models instead of fitting a best model. / Thesis / Master of Science (MSc)

This thesis studies the problem of frequentist model averaging over a set of multiple $\epsilon$-support vector regression (SVR) models, where the support vector machine (SVM) algorithm was extended to function estimation involving continuous targets, instead of categorical ones. By assigning weights to a set of candidate models instead of selecting the least misspecified one, model averaging presents a strong alternative to model selection for tackling model uncertainty. Not only do we describe the construction of smoothed BIC/AIC model averaging weights, but we also propose a Mallows model averaging procedure which selects model weights by minimizing Mallows' criterion. We conduct two studies where the set of candidate models can either include or not include the true model by making use of simulated random samples obtained from different data-generating processes of analytic form. In terms of mean squared error, we demonstrate that our proposed method outperforms other model averaging and model selection methods that were tested, and the gain is more substantial for smaller sample sizes with larger signal-to-noise ratios. / Thesis / Master of Science (MSc)

The primary aim of this research is to shed more light on the issue of model uncertainty in applied econometrics in general and cross-country growth as well as happiness and well-being regressions in particular. Model uncertainty consists of three main types: theory uncertainty, focusing on which principal determinants of economic growth or happiness should be included in a model; heterogeneity uncertainty, relating to whether or not the parameters that describe growth or happiness are identical across countries; and functional form uncertainty, relating to which growth and well-being regressors enter the model linearly and which ones enter nonlinearly. Model averaging methods including Bayesian model averaging and Frequentist model averaging are the main statistical tools that incorporate theory uncertainty into the estimation process. To address functional form uncertainty, a variety of techniques have been proposed in the literature. One suggestion, for example, involves adding regressors that are nonlinear functions of the initial set of theory-based regressors or adding regressors whose values are zero below some threshold and non-zero above that threshold. In recent years, however, there has been a rising interest in using nonparametric framework to address nonlinearities in growth and happiness regressions. The goal of this research is twofold. First, while Bayesian approaches are dominant methods used in economic empirics to average over the model space, I take a fresh look into Frequentist model averaging techniques and propose statistical routines that computationally ease the implementation of these methods. I provide empirical examples showing that Frequentist estimators can compete with their Bayesian peers. The second objective is to use recently-developed nonparametric techniques to overcome the issue of functional form uncertainty while analyzing the variance of distribution of per capita income. Nonparametric paradigm allows for addressing nonlinearities in growth and well-being regressions by relaxing both the functional form assumptions and traditional assumptions on the structure of error terms. / Ph. D.

nÃo hà / O presente trabalho busca investigar eventual relaÃÃo entre o desenvolvimento financeiro e desigualdade de renda. Para tal, foram utilizados os dados dos 184 municÃpios cearenses, para o ano de 2010, firmando-se como medida de desigualdade o Ãndice de Gini e, como variÃveis explicativas, as razÃes estabelecidas entre crÃdito e PIB, entre operaÃÃes de crÃdito e PIB; entre operaÃÃes de crÃdito e populaÃÃo; entre financiamentos e PIB e, por fim, entre financiamentos e populaÃÃo, como proxies para o desenvolvimento financeiro. Foi utilizado o mÃtodo denominado Jackknife Model Averaging, que se caracteriza por ser um procedimento de estimaÃÃo que leva em consideraÃÃo todas as possÃveis especificaÃÃes de modelo com base em um conjunto de variÃveis. Empregou-se, ainda, a abordagem FMA, sugerida em Hansen e Racine (2012). Os resultados obtidos indicam que o desenvolvimento financeiro nÃo à estatisticamente relevante para interferir na reduÃÃo da desigualdade de renda. / This work seeks to investigate an eventual relationship between financial development and income inequality. For this, was used data from 184 cities from CearÃ, at the year of 2010, Using as a measure of inequality, the Gini index and, as explanatory variables, the reasons established between credit and GDP, between credit and GDP operations; between credit and population operations; between financing and GDP and, finally, between funding and population, as proxies for financial development. Was used the method called Jackknife Model Averaging, which is characterized by being a procedure of estimation that takes into account all possible model specifications based on a set of variables. We used also the FMA approach suggested in Hansen and Racine (2012). The results indicate that financial development is not statistically relevant to interfere in reducing income inequality.

Cluster analysis is commonly described as the classification of unlabeled observations into groups such that they are more similar to one another than to observations in other groups. Model-based clustering assumes that the data arise from a statistical (mixture) model and typically a group of many models are fit to the data, from which the `best' model is selected by a model selection criterion (often the BIC in mixture model applications). This chosen model is then the only model that is used for making inferences on the data. Although this is common practice, proceeding in this way ignores a large component of model selection uncertainty, especially for situations where the difference between the model selection criterion for two competing models is relatively insignificant. For this reason, recent interest has been placed on selecting a subset of models that are close to the selected best model and using a weighted averaging approach to incorporate information from multiple models in this set. Model averaging is not a novel approach, yet its presence in a clustering framework is minimal. Here, we use Occam's window to select a subset of models eligible for two types of averaging techniques: averaging a posteriori probabilities, and direct averaging of model parameters. The efficacy of these model-based averaging approaches is demonstrated for a family of generalized hyperbolic mixture models using real and simulated data. / Thesis / Master of Science (MSc)

We propose a method to deal simultaneously with model uncertainty and correlated regressors in linear regression models by combining elastic net specifications with a spike and slab prior. The estimation method nests ridge regression and the LASSO estimator and thus allows for a more flexible modelling framework than existing model averaging procedures. In particular, the proposed technique has clear advantages when dealing with datasets of (potentially highly) correlated regressors, a pervasive characteristic of the model averaging datasets used hitherto in the econometric literature. We apply our method to the dataset of economic growth determinants by Sala-i-Martin et al. (Sala-i-Martin, X., Doppelhofer, G., and Miller, R. I. (2004). Determinants of Long-Term Growth: A Bayesian Averaging of Classical Estimates (BACE) Approach. American Economic Review, 94: 813-835) and show that our procedure has superior out-of-sample predictive abilities as compared to the standard Bayesian model averaging methods currently used in the literature. (authors' abstract) / Series: Research Report Series / Department of Statistics and Mathematics

The exchange rate forecasting has been an interesting topic for a long time. Beating the random walk model has been the goal of many researchers, who applied various techniques and used various datasets. We tried to beat it using bayesian model averaging technique, which pools a large amount of models and the final forecast is the average of forecasts of these models. We used quarterly data from 1980 to 2013 and attempted to predict the value of exchange rate return of five currency pairs. The novelty was the fact that none of these currency pairs included U.S. Dollar. The forecasting horizon was one, two, four and eight quarters. In addition to random walk, we also compared our results to historical average return model using several benchmarks, such as root mean squared error, mean absolute error or direction of change statistic. We found out that bayesian model averaging can not generally outperform random walk or historical average return, but in specific setting it can produce forecasts with low error and with high percentage of correctly predicted signs of change.