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vii Abstract People are by nature social beings. Most of us have a complex social network that connects us with other people in numerous aspects of our lives: neighbours, co-workers or peers in schools, and friends. Moreover, it is widely believed that people's behaviour is to some extent affected by others in their social networks, which is known as peer effects. Therefore, a precise understanding of the behaviour of an individual necessarily includes understanding her interactions with others within her social network. The first part of this thesis, literature review, summarizes contemporary research on peer effects, shows which aspects of human behaviour may be affected by social interactions, and highlights the importance of peer effects research. In the second part, the estimation of the linear- in-means peer effects model, we provide a detailed description of the model, derivations of its alternative formulations, and show the identification conditions. The main contribution of the second part is that we provide a step-by-step analysis of the linear-in-means peer effects model and detailed proofs of theorems in one place. The third part provides an empirical analysis of peer effects in education in the Czech Republic. In particular, we examine how the test scores of pupils are affected by their...

Kriging techniques are regression methods used for evaluation of continuous spatial processes. If the covariance structure of process is unknown, then it's necessary to estimate it from the data. The first part of this Master's thesis is devoted to description the kriging method and to estimate of a variogram fuction, which describes the covariance structure of considered process. The second part includes the implementation of kriging method in MATLAB for simulated and real data.

Title: Stochastic Models in Financial Mathematics Author: Bc. Oliver Waczulík Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Jan Hurt, CSc., Department of Probability and Mathe- matical Statistics Abstract: This thesis looks into the problems of ordinary stochastic models used in financial mathematics, which are often influenced by unrealistic assumptions of Brownian motion. The thesis deals with and suggests more sophisticated alternatives to Brownian motion models. By applying the fractional Brownian motion we derive a modification of the Black-Scholes pricing formula for a mixed fractional Bro- wnian motion. We use Lévy processes to introduce subordinated stable process of Ornstein-Uhlenbeck type serving for modeling interest rates. We present the calibration procedures for these models along with a simulation study for estima- tion of Hurst parameter. To illustrate the practical use of the models introduced in the paper we have used real financial data and custom procedures program- med in the system Wolfram Mathematica. We have achieved almost 90% decline in the value of Kolmogorov-Smirnov statistics by the application of subordinated stable process of Ornstein-Uhlenbeck type for the historical values of the monthly PRIBOR (Prague Interbank Offered Rate) rates in...

Diese Doktorarbeit untersucht drei Fragestellungen. Erstens, wie die Wirkung von plötzlichen Änderungen exogener Faktoren auf endogene Variablen empirisch im Allgemeinen zu bestimmen ist. Zweitens, welche Effekte eine Erhöhung der Staatsausgaben im Speziellen hat. Drittens, wie optimale Geldpolitik bestimmt werden kann, wenn der Entscheider keine eindeutigen Modelle für die ökonomischen Rahmenbedingungen hat. Im ersten Kapitel entwickele ich eine Methode, mithilfe derer die Effekte von plötzlichen Änderungen exogener Faktoren auf endogene Variablen geschätzt werden können. Dazu wird die gemeinsame Verteilung von Parametern einer Vektor Autoregression (VAR) und eines stochastischen allgemeinen Gleichgewichtsmodelles (DSGE) bestimmt. Auf diese Weise können zentrale Probleme gelöst werden: das Identifikationsproblem der VAR und eine mögliche Misspezifikation des DSGE Modells. Im zweitem Kapitel wende ich die Methode aus dem ersten Kapitel an, um den Effekt einer angekündigten Erhöhung der Staatsausgaben auf den privaten Konsum und die Reallöhne zu untersuchen. Die Identifikation beruht auf der Einsicht, dass endogene Variablen, oft qualitative Unterschiede in der Periode der Ankündigung und nach der Realisation zeigen. Die Ergebnisse zeigen, dass der private Konsum negativ im Zeitraum der Ankündigung reagiert und positiv nach der Realisation. Reallöhne steigen zum Zeitpunkt der Ankündigung und sind positiv für zwei Perioden nach der Realisation. Im abschließendem Kapitel untersuche ich gemeinsam mit Christian Stoltenberg, wie Geldpolitik gesteuert werden sollte, wenn die Modellierung der Ökonomie unsicher ist. Wenn ein Modell um einen Parameter erweitert wird, kann das Modell dadurch so verändert werden, dass sich die Politikempfehlungen zwischen dem ursprünglichen und dem neuen Modell unterscheiden. Oft wird aber lediglich das erweiterte Modell betrachtet. Wir schlagen eine Methode vor, die beiden Modellen Rechnung trägt und somit zu einer besseren Politik führt. / This thesis is concerned with three questions: first, how can the effects macroeconomic policy has on the economy in general be estimated? Second, what are the effects of a pre-announced increase in government expenditures? Third, how should monetary policy be conducted, if the policymaker faces uncertainty about the economic environment. In the first chapter I suggest to estimate the effects of an exogenous disturbance on the economy by considering the parameter distributions of a Vector Autoregression (VAR) model and a Dynamic Stochastic General Equilibrium (DSGE) model jointly. This allows to resolve the major issue a researcher has to deal with when working with a VAR model and a DSGE model: the identification of the VAR model and the potential misspecification of the DSGE model. The second chapter applies the methodology presented in the preceding chapter to investigate the effects of a pre-announced change in government expenditure on private consumption and real wages. The shock is identified by exploiting its pre-announced nature, i.e. different signs of the responses in endogenous variables during the announcement and after the realization of the shock. Private consumption is found to respond negatively during the announcement period and positively after the realization. The reaction of real wages is positive on impact and positive for two quarters after the realization. In the last chapter ''Optimal Policy Under Model Uncertainty: A Structural-Bayesian Estimation Approach'' I investigate jointly with Christian Stoltenberg how policy should optimally be conducted when the policymaker is faced with uncertainty about the economic environment. The standard procedure is to specify a prior over the parameter space ignoring the status of some sub-models. We propose a procedure that ensures that the specified set of sub-models is not discarded too easily. We find that optimal policy based on our procedure leads to welfare gains compared to the standard practice.

Regional integration gained popularity and is prioritised globally, especially in developing economies, including those on the African continent. This is based on its potential to accelerate trade, stimulate economic growth, and increase access to basic necessities and to induce a sustainable increase in economic output and improved standards of living. Regional integration in the context of developing economies is entirely implicit. Modern literature observes it as a policy option for dealing with a wide variety of issues related to politics, economic factors, and societal welfare. The SACU, existing since 1910, made several trade agreements globally. The union aims at reducing inequalities, ensuring continuous improvement in the general welfare of the population, and sustainable economic growth. Research, though, indicates that the region persistently reflects poor socio-economic conditions. This is accompanied by limited development in infrastructure, lowly skilled and experienced workforce. Primary sector activities dominate their economies, such as mining and agriculture, high levels of inequalities and poverty. Regional integration was implemented differently in several countries globally, and Africa in particular. The research noted that literature on regional integration and its implications on socio-economic development lacks, especially in the context of SACU. A deficiency was also emphasised the universal measurement of regional integration, which is not standardised. Some research employed single variables as a proxy, whilst some composite indices were also compiled and implemented, suiting the diverse setups and environments. The development measurements, therefore, cannot universally be applied attributable to context-specific concerns, prevalent in regions or countries. This study developed the SACU Regional Integration Index (SRII) because the existing indices on regional integration are limited concerning applicability. Most of the indices established in the literature were developed for specific countries and regions with diverse characteristics from those of the SACU region. In addition to a detailed literature review and closing methodological divergencies, this study evaluated the effects of regional integration on socio-economic development in the SACU countries. The objectives of the study were first, to produce the SACU Regional Integration Index. Second, the study aimed at evaluating the effect of regional integration on various socio-economic development factors listed as economic growth, investments, and the Human Development Index (HDI), inequalities and poverty. Third, the study provided policy recommendations to the socio-economic problems encountered by the SACU countries; and lastly, to implement the proposed SRII as a way of providing policymakers with the actual impacts. The study employed the principal component analysis (PCA) to construct the SRII. The Ordinary Least Squares (LSDV), fixed effects and random effects were employed to ascertain the effect of regional integration on socio-economic development in the SACU countries. The constructed SACU index comprises four dimensions. These are trade integration; productive integration; infrastructure integration; and financial and macroeconomic policies integration. The index revealed that SACU countries are dominated by trade and productive integration. Further analysis of the results indicated that collaboration on the financial and macroeconomic policies is lacking and the infrastructure dimension is lagging in the SACU region. Based on the second objective, the results indicate that regional integration is critical in improving trade openness and HDI, especially in Lesotho, Botswana, and Namibia. The effect of regional integration on real Gross Domestic Product (GDP) growth, inequalities, and poverty reduction was realised in the long run through the interaction of all variables under study. This supported the dynamic effects posited by the dynamic theory of regional integration. It was established that growth, though, in infrastructure is insignificant compared to other dimensions of regional integration. This explains why regional integration was unsupportive concerning stimulating investments in all the economies forming the SACU region. The third objective was to proffer policy recommendations. Several practical policy recommendations emerged from this study, based on the literature findings and review. These recommendations include implementing inclusive development programmes, promotion private sector participation in economic activities, and policies, to boost production capacity in the countries in this region. Based on the fourth objective, this study further recommends SACU as a region, to integrate into the global economy. This can be conducted by participating in global production networks for manufacturing and taking advantage of emerging economies. This would diversify their export markets and their sources of finance development. SACU countries should make regional integration and trade a part of their national and sectoral development plans, ensuring coherent trade and industrial policies. They should also improve their labour, education, social protection, and safety nets. With data availability, this research can be extended to incorporate quarterly data or more years of study. Time-series methods can be applied, such as the Autoregressive Distributive Lag (ARDL) method. This will increase the sample size and the number of observations, which can improve the outcome from the statistical and econometric analysis. Future studies may also evaluate the applicability of the index constructed in this study. / Economics / D. Phil. (Economics)