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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

Performance of stock markets is determined by three classes of variables: macroeconomic indicators, industry & firm heterogeneity and third country effects. When assessing performance of a stock market index, impact of industry & firm heterogeneity is marginal as it is already embedded in the index through its constituent companies. This paper will therefore focus on the other two. Chinese stock market was selected as an application as their performance compared to other domestic indicators (mainly GDP growth) is considered inferior by many researchers. Using econometric framework for panel data and a Bayesian extension, the paper estimates multiple models of Chinese stock market performance examining individual determinants of it. Subsequently, it predicts development of theoretical prices of two main Chinese stock indices on two time samples until 2013. The paper then demonstrates underperformance of Chinese stock market by comparing the modeled prices to actual prices realized on the market. JEL Classification C23, C51, C53, G15, G17 Keywords underperformance, panel data, fixed effects model, Bayesian Model Averaging Author's e-mail roman_kovac@ymail.com Supervisor's e-mail karel.bata@seznam.cz

MASTER THESIS Determinants of Economic Growth: A Bayesian Model Averaging Author: Bc. Nikoloz Kudashvili Abstract The paper estimates the economic growth determinants across 72 countries using a Bayesian Model Averaging. Unlike the other studies we include debt to GDP ratio as an explanatory variable among 29 growth determinants. For given values of the other variables debt to GDP ratio up to the threshold level is positively related with the growth rate. The coefficient on the ratio has nearly 0.8 posterior inclusion probability suggesting that debt to GDP ratio is an important long term growth determinant. We find that the initial level of GDP, life expectancy and equipment investments have a strong effect on the GDP per capita growth rate together with the debt to GDP ratio.

In this paper we investigate the economic, political, institutional, and societal factors that encourage entrepreneurial activity. We do so by applying Bayesian Model Averaging, which controls for model uncertainty, to a panel data set for 33 countries. Our results indicate that the general state of macroeconomic activity, the availability of financing, the level of human capital, fiscal policies implemented and the type of economic system are the main determinants of the level of entrepreneurship. We also document a non-linear, U-shaped relation between distortionary taxation and entrepreneurial activity. Keywords: Entrepreneurship, Entrepreneurial Activity, Total Early-Stage Activity (TEA), Global Entrepreneurial Monitor (GEM), Bayesian Model Averaging (BMA), Panel Estimation. JEL Classification: B30, B53, C11, C23, J20, M13, O10, O40

Ecological data is often fraught with many problems such as Missing Data and Spatial Correlation. In this dissertation we use a data set collected by the Ohio EPA as motivation for studying techniques to address these problems. The data set is concerned with the benthic health of Ohio's waterways. A new method for incorporating covariate structure and missing data mechanisms into missing data analysis is considered. This method allows us to detect relationships other popular methods do not allow. We then further extend this method into model selection. In the special case where the unobserved covariates are assumed normally distributed we use the Bayesian Model Averaging method to average the models, select the highest probability model and do variable assessment. Accuracy in calculating the posterior model probabilities using the Laplace approximation and an approximation based on the Bayesian Information Criterion (BIC) are explored. It is shown that the Laplace approximation is superior to the BIC based approximation using simulation. Finally, Hierarchical Spatial Linear Models are considered for the data and we show how to combine analysis which have spatial correlation within and between clusters. / Ph. D.

Bayesian Model Averaging (BMA) is a new area in modern applied statistics that provides data analysts with an efficient tool for discovering promising models and obtaining esti-mates of their posterior probabilities via Markov chain Monte Carlo (MCMC). These probabilities can be further used as weights for model averaged predictions and estimates of the parameters of interest. As a result, variance components due to model selection are estimated and accounted for, contrary to the practice of conventional data analysis (such as, for example, stepwise model selection). In addition, variable activation probabilities can be obtained for each variable of interest. This dissertation is aimed at connecting BMA and various ramifications of the multivari-ate technique called Reduced-Rank Regression (RRR). In particular, we are concerned with Canonical Correspondence Analysis (CCA) in ecological applications where the data are represented by a site by species abundance matrix with site-specific covariates. Our goal is to incorporate the multivariate techniques, such as Redundancy Analysis and Ca-nonical Correspondence Analysis into the general machinery of BMA, taking into account such complicating phenomena as outliers and clustering of observations within a single data-analysis strategy. Traditional implementations of model averaging are concerned with selection of variables. We extend the methodology of BMA to selection of subgroups of observations and im-plement several approaches to cluster and outlier analysis in the context of the multivari-ate regression model. The proposed algorithm of cluster analysis can accommodate re-strictions on the resulting partition of observations when some of them form sub-clusters that have to be preserved when larger clusters are formed. / Ph. D.

L’objectif de cette thèse est la mise en place d’un Système d’Alerte Précoce comme instrument de prévision de la survenance des crises bancaires et des crises de la dette souveraine dans 48 pays de 1977 à 2010. Il s’agit à la fois d’identifier les facteurs capables de prédire ces événements et ceux annonçant leurs interactions éventuelles. La présente étude propose une approche à la fois originale et robuste qui tient compte de l’incertitude des modèles et des paramètres par la méthode de combinaison bayésienne des modèles de régression ou Bayesian Model Averaging (BMA). Nos résultats montrent que les avoirs étrangers nets en pourcentage du total des actifs, la dette à court terme en pourcentage des réserves totales et enfin la dette publique en pourcentage du PIB ont un pouvoir prédictif élevé pour expliquer les crises de la dette souveraine pour plusieurs pays. De plus, la croissance de l’activité et du crédit bancaire, le degré de libéralisation financière et le poids de la dette extérieure sont des signaux décisifs des crises bancaires. Notre approche offre le meilleur compromis entre les épisodes manqués et les fausses alertes. Enfin, nous étudions le lien entre les crises bancaires et les crises de la dette souveraine pour 62 pays de 1970 à 2011, en développant une approche basée sur un modèle Vecteur Auto-Régressif (VAR). Nos estimations montrent une relation significative et bidirectionnelle entre les deux types d’évènements. / The main purpose of this thesis is the development of an Early Warning System to predict banking and sovereign debt crises in 48 countries from 1977 to 2010. We are interested in identifying both factors that predict these events and those announcing their possible interactions. In particular, our empirical works provide an original and robust approach accounting for model and parameter uncertainty by means of the Bayesian Model Averaging method. Our results show that: Net foreign assets to total assets, short term debt to total reserves, and public debt to GDP have a high predictive power to signal sovereign debt crises in many countries. Furthermore, the growth rates of economic activity and credit, financial liberalization, and the external indebtedness are decisive signals of banking crises. Our approach offers the best compromise between missed episodes and false alarms. Finally, we study the link between banking and sovereign debt crises for 62 countries from 1970 to 2011 by developing an approach based on a Vector Autoregressive model (VAR). Our estimates show a significant two-way relationship between the two types of events.

Sequential experimentation is often employed in process optimization wherein a series of small experiments are run successively in order to determine which experimental factor levels are likely to yield a desirable response. Although there currently exists a framework for identifying optimal follow-up designs after an initial experiment has been run, the accepted methods frequently point to multiple designs leaving the practitioner to choose one arbitrarily. In this thesis, we apply preposterior analysis and Bayesian model-averaging to develop a methodology for further discriminating between optimal follow-up designs while controlling for both parameter and model uncertainty.

The expected equity premium is an important parameter in many financial models, especially within portfolio optimization. A good forecast of the future equity premium is therefore of great interest. In this thesis we seek to forecast the equity premium, use it in portfolio optimization and then give evidence on how sensitive the results are to estimation errors and how the impact of these can be minimized. Linear prediction models are commonly used by practitioners to forecast the expected equity premium, this with mixed results. To only choose the model that performs the best in-sample for forecasting, does not take model uncertainty into account. Our approach is to still use linear prediction models, but also taking model uncertainty into consideration by applying Bayesian model averaging. The predictions are used in the optimization of a portfolio with risky assets to investigate how sensitive portfolio optimization is to estimation errors in the mean vector and covariance matrix. This is performed by using a Monte Carlo based heuristic called portfolio resampling. The results show that the predictive ability of linear models is not substantially improved by taking model uncertainty into consideration. This could mean that the main problem with linear models is not model uncertainty, but rather too low predictive ability. However, we find that our approach gives better forecasts than just using the historical average as an estimate. Furthermore, we find some predictive ability in the the GDP, the short term spread and the volatility for the five years to come. Portfolio resampling proves to be useful when the input parameters in a portfolio optimization problem is suffering from vast uncertainty.