Bayesian Analysis of Linear Inverse Problems with Applications in Economics and Finance

In my PhD thesis I propose a Bayesian nonparametric estimation method for structural econometric models where the functional parameter of interest describes the economic agent's behavior. The structural parameter is characterized as the solution of a functional equation, or by using more technical words, as the solution of an inverse problem that can be either ill-posed or well-posed. From a Bayesian point of view, the parameter of interest is a random function and the solution to the inference problem is the posterior distribution of this parameter. A regular version of the posterior distribution in functional spaces is characterized. However, the infinite dimension of the considered spaces causes a problem of non continuity of the solution and then a problem of inconsistency, from a frequentist point of view, of the posterior distribution (i.e. problem of ill-posedness). The contribution of this essay is to propose new methods to deal with this problem of ill-posedness. The first one consists in adopting a Tikhonov regularization scheme in the construction of the posterior distribution so that I end up with a new object that I call regularized posterior distribution and that I guess it is solution of the inverse problem. The second approach consists in specifying a prior distribution on the parameter of interest of the g-prior type. Then, I detect a class of models for which the prior distribution is able to correct for the ill-posedness also in infinite dimensional problems. I study asymptotic properties of these proposed solutions and I prove that, under some regularity condition satisfied by the true value of the parameter of interest, they are consistent in a "frequentist" sense. Once I have set the general theory, I apply my bayesian nonparametric methodology to different estimation problems. First, I apply this estimator to deconvolution and to hazard rate, density and regression estimation. Then, I consider the estimation of an Instrumental Regression that is useful in micro-econometrics when we have to deal with problems of endogeneity. Finally, I develop an application in finance: I get the bayesian estimator for the equilibrium asset pricing functional by using the Euler equation defined in the Lucas'(1978) tree-type models.

Welfare provision in Sweden and the dominant position of the Sap

There have been almost fifty years since Harry Eckstein' s classic monograph, A Theory of Stable Democracy (Princeton, 1961), where he sketched out the basic tenets of the “congruence theory”, which was to become one of the most important and innovative contributions to understanding democratic rule. His next work, Division and Cohesion in Democracy, (Princeton University Press: 1966) is designed to serve as a plausibility probe for this 'theory' (ftn.) and is a case study of a Northern democratic system, Norway. What is more, this line of his work best exemplifies the contribution Eckstein brought to the methodology of comparative politics through his seminal article, “ “Case Study and Theory in Political Science” ” (in Greenstein and Polsby, eds., Handbook of Political Science, 1975), on the importance of the case study as an approach to empirical theory. This article demonstrates the special utility of “crucial case studies” in testing theory, thereby undermining the accepted wisdom in comparative research that the larger the number of cases the better. Although not along the same lines, but shifting the case study unit of research, I intend to take up here the challenge and build upon an equally unique political system, the Swedish one. Bearing in mind the peculiarities of the Swedish political system, my unit of analysis is going to be further restricted to the Swedish Social Democratic Party, the Svenska Arbetare Partiet. However, my research stays within the methodological framework of the case study theory inasmuch as it focuses on a single political system and party. The Swedish SAP endurance in government office and its electoral success throughout half a century (ftn. As of the 1991 election, there were about 56 years - more than half century - of interrupted social democratic "reign" in Sweden.) are undeniably a performance no other Social Democrat party has yet achieved in democratic conditions. Therefore, it is legitimate to inquire about the exceptionality of this unique political power combination. Which were the different components of this dominance power position, which made possible for SAP's governmental office stamina? I will argue here that it was the end-product of a combination of multifarious factors such as a key position in the party system, strong party leadership and organization, a carefully designed strategy regarding class politics and welfare policy. My research is divided into three main parts, the historical incursion, the 'welfare' part and the 'environment' part. The first part is a historical account of the main political events and issues, which are relevant for my case study. Chapter 2 is devoted to the historical events unfolding in the 1920-1960 period: the Saltsjoebaden Agreement, the series of workers' strikes in the 1920s and SAP's inception. It exposes SAP's ascent to power in the mid 1930s and the party's ensuing strategies for winning and keeping political office, that is its economic program and key economic goals. The following chapter - chapter 3 - explores the next period, i.e. the period from 1960s to 1990s and covers the party's troubled political times, its peak and the beginnings of the decline. The 1960s are relevant for SAP's planning of a long term economic strategy - the Rehn Meidner model, a new way of macroeconomic steering, based on the Keynesian model, but adapted to the new economic realities of welfare capitalist societies. The second and third parts of this study develop several hypotheses related to SAP's 'dominant position' (endurance in politics and in office) and test them afterwards. Mainly, the twin issues of economics and environment are raised and their political relevance for the party analyzed. On one hand, globalization and its spillover effects over the Swedish welfare system are important causal factors in explaining the transformative social-economic challenges the party had to put up with. On the other hand, Europeanization and environmental change influenced to a great deal SAP's foreign policy choices and its domestic electoral strategies. The implications of globalization on the Swedish welfare system will make the subject of two chapters - chapters four and five, respectively, whereupon the Europeanization consequences will be treated at length in the third part of this work - chapters six and seven, respectively. Apparently, at first sight, the link between foreign policy and electoral strategy is difficult to prove and uncanny, in the least. However, in the SAP's case there is a bulk of literature and public opinion statistical data able to show that governmental domestic policy and party politics are in a tight dependence to foreign policy decisions and sovereignty issues. Again, these country characteristics and peculiar causal relationships are outlined in the first chapters and explained in the second and third parts. The sixth chapter explores the presupposed relationship between Europeanization and environmental policy, on one hand, and SAP's environmental policy formulation and simultaneous agenda-setting at the international level, on the other hand. This chapter describes Swedish leadership in environmental policy formulation on two simultaneous fronts and across two different time spans. The last chapter, chapter eight - while trying to develop a conclusion, explores the alternative theories plausible in explaining the outlined hypotheses and points out the reasons why these theories do not fit as valid alternative explanation to my systemic corporatism thesis as the main causal factor determining SAP's 'dominant position'. Among the alternative theories, I would consider Traedgaardh L. and Bo Rothstein's historical exceptionalism thesis and the public opinion thesis, which alone are not able to explain the half century social democratic endurance in government in the Swedish case.

Enhanced Mixed Integer Programming Techniques and Routing Problems

Mixed integer programming is up today one of the most widely used techniques for dealing with hard optimization problems. On the one side, many practical optimization problems arising from real-world applications (such as, e.g., scheduling, project planning, transportation, telecommunications, economics and finance, timetabling, etc) can be easily and effectively formulated as Mixed Integer linear Programs (MIPs). On the other hand, 50 and more years of intensive research has dramatically improved on the capability of the current generation of MIP solvers to tackle hard problems in practice. However, many questions are still open and not fully understood, and the mixed integer programming community is still more than active in trying to answer some of these questions. As a consequence, a huge number of papers are continuously developed and new intriguing questions arise every year. When dealing with MIPs, we have to distinguish between two different scenarios. The first one happens when we are asked to handle a general MIP and we cannot assume any special structure for the given problem. In this case, a Linear Programming (LP) relaxation and some integrality requirements are all we have for tackling the problem, and we are ``forced" to use some general purpose techniques. The second one happens when mixed integer programming is used to address a somehow structured problem. In this context, polyhedral analysis and other theoretical and practical considerations are typically exploited to devise some special purpose techniques. This thesis tries to give some insights in both the above mentioned situations. The first part of the work is focused on general purpose cutting planes, which are probably the key ingredient behind the success of the current generation of MIP solvers. Chapter 1 presents a quick overview of the main ingredients of a branch-and-cut algorithm, while Chapter 2 recalls some results from the literature in the context of disjunctive cuts and their connections with Gomory mixed integer cuts. Chapter 3 presents a theoretical and computational investigation of disjunctive cuts. In particular, we analyze the connections between different normalization conditions (i.e., conditions to truncate the cone associated with disjunctive cutting planes) and other crucial aspects as cut rank, cut density and cut strength. We give a theoretical characterization of weak rays of the disjunctive cone that lead to dominated cuts, and propose a practical method to possibly strengthen those cuts arising from such weak extremal solution. Further, we point out how redundant constraints can affect the quality of the generated disjunctive cuts, and discuss possible ways to cope with them. Finally, Chapter 4 presents some preliminary ideas in the context of multiple-row cuts. Very recently, a series of papers have brought the attention to the possibility of generating cuts using more than one row of the simplex tableau at a time. Several interesting theoretical results have been presented in this direction, often revisiting and recalling other important results discovered more than 40 years ago. However, is not clear at all how these results can be exploited in practice. As stated, the chapter is a still work-in-progress and simply presents a possible way for generating two-row cuts from the simplex tableau arising from lattice-free triangles and some preliminary computational results. The second part of the thesis is instead focused on the heuristic and exact exploitation of integer programming techniques for hard combinatorial optimization problems in the context of routing applications. Chapters 5 and 6 present an integer linear programming local search algorithm for Vehicle Routing Problems (VRPs). The overall procedure follows a general destroy-and-repair paradigm (i.e., the current solution is first randomly destroyed and then repaired in the attempt of finding a new improved solution) where a class of exponential neighborhoods are iteratively explored by heuristically solving an integer programming formulation through a general purpose MIP solver. Chapters 7 and 8 deal with exact branch-and-cut methods. Chapter 7 presents an extended formulation for the Traveling Salesman Problem with Time Windows (TSPTW), a generalization of the well known TSP where each node must be visited within a given time window. The polyhedral approaches proposed for this problem in the literature typically follow the one which has been proven to be extremely effective in the classical TSP context. Here we present an overall (quite) general idea which is based on a relaxed discretization of time windows. Such an idea leads to a stronger formulation and to stronger valid inequalities which are then separated within the classical branch-and-cut framework. Finally, Chapter 8 addresses the branch-and-cut in the context of Generalized Minimum Spanning Tree Problems (GMSTPs) (i.e., a class of NP-hard generalizations of the classical minimum spanning tree problem). In this chapter, we show how some basic ideas (and, in particular, the usage of general purpose cutting planes) can be useful to improve on branch-and-cut methods proposed in the literature.

La globalizzazione della bioetica: Analisi della bioetica latinoamericana

La tesi esplora la riflessione bioetica latino-americana e la sua evoluzione, valutandone i legami, intenzionali e non, con le posizioni bioetiche più consolidate e tendenzialmente dominanti del panorama internazionale. La trattazione indaga lo sviluppo della bioetica nel sub-continente latinoamericano, ponendo in evidenza lo sviluppo delle teorie morali che definiscono l'orizzonte interpretativo del dibattito contemporaneo, come pure le peculiarità della produzione sudamericana in materia di bioetica e la casistica tipica di questi territori. Per una comprensione delle caratteristiche di un pensiero bioetico, tipico di un territorio in via di sviluppo, la tesi presenta la trattazione di due precisi case studies: A- Il progetto peruviano: Propuesta de incorporación del enfoque intercultural y de representantes indígenas en los comités de ética en países multiculturales; B- La biomedicina e gli xenotrapianti in Messico. L'analisi dei casi studio è funzionale alla messa in luce delle caratteristiche costitutive del pensiero latinoamericano e della casistica tipica del territorio. La bioetica Latinoamericana, infatti, sviluppatasi circa con vent'anni di ritardo rispetto ai luoghi di nascita di questa disciplina (Gran Bretagna e USA), rivendica l'esigenza di un dibattito e di una prassi bioetica autoctone, capaci quindi di riassumere in sé stesse concetti e principi declinabili all'interno delle esperienze e delle concrete esigenze che prendono forma nella realtà culturale e socio-economica. Per questo motivo si discosta dalle cosiddette teorie bioetiche classiche rivendicando una bioetica di contestazione che si vincola costitutivamente al linguaggio dei diritti umani. La tesi propone inoltre l'utilizzo dei dati emersi dai casi studio per sviluppare una riflessione sulle modalità e su alcuni esiti della globalizzazione della bioetica. L’analisi si avvale di strumenti e categorie proprie della sociologia, dell’economia e della politica al fine di mettere in evidenza le diverse componenti costitutive e le criticità della bioetica globalizzata.