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.

Rigorous results in Spin Glasses and Monomer-Dimer systems

In this work I reported recent results in the field of Statistical Mechanics of Equilibrium, and in particular in Spin Glass models and Monomer Dimer models . We start giving the mathematical background and the general formalism for Spin (Disordered) Models with some of their applications to physical and mathematical problems. Next we move on general aspects of the theory of spin glasses, in particular to the Sherrington-Kirkpatrick model which is of fundamental interest for the work. In Chapter 3, we introduce the Multi-species Sherrington-Kirkpatrick model (MSK), we prove the existence of the thermodynamical limit and the Guerra's Bound for the quenched pressure together with a detailed analysis of the annealed and the replica symmetric regime. The result is a multidimensional generalization of the Parisi's theory. Finally we brie y illustrate the strategy of the Panchenko's proof of the lower bound. In Chapter 4 we discuss the Aizenmann-Contucci and the Ghirlanda-Guerra identities for a wide class of Spin Glass models. As an example of application, we discuss the role of these identities in the proof of the lower bound. In Chapter 5 we introduce the basic mathematical formalism of Monomer Dimer models. We introduce a Gaussian representation of the partition function that will be fundamental in the rest of the work. In Chapter 6, we introduce an interacting Monomer-Dimer model. Its exact solution is derived and a detailed study of its analytical properties and related physical quantities is performed. In Chapter 7, we introduce a quenched randomness in the Monomer Dimer model and show that, under suitable conditions the pressure is a self averaging quantity. The main result is that, if we consider randomness only in the monomer activity, the model is exactly solvable.

Essays in Applied Health Economics: Evidence on Health and Health Care in Italy and UK

This thesis is the result of my experience as a PhD student taking part in the Joint Doctoral Programme at the University of York and the University of Bologna. In my thesis I deal with topics that are of particular interest in Italy and in Great Britain. Chapter 2 focuses on the empirical test of the existence of the relationship between technological profiles and market structure claimed by Sutton’s theory (1991, 1998) in the specific economic framework of hospital care services provided by the Italian National Health Service (NHS). In order to test the empirical predictions by Sutton, we identify the relevant markets for hospital care services in Italy in terms of both product and geographic dimensions. In particular, the Elzinga and Hogarty (1978) approach has been applied to data on patients’ flows across Italian Provinces in order to derive the geographic dimension of each market. Our results provide evidence in favour of the empirical predictions of Sutton. Chapter 3 deals with the patient mobility in the Italian NHS. To analyse the determinants of patient mobility across Local Health Authorities, we estimate gravity equations in multiplicative form using a Poisson pseudo maximum likelihood method, as proposed by Santos-Silva and Tenreyro (2006). In particular, we focus on the scale effect played by the size of the pool of enrolees. In most of the cases our results are consistent with the predictions of the gravity model. Chapter 4 considers the effects of contractual and working conditions on selfassessed health and psychological well-being (derived from the General Health Questionnaire) using the British Household Panel Survey (BHPS). We consider two branches of the literature. One suggests that “atypical” contractual conditions have a significant impact on health while the other suggests that health is damaged by adverse working conditions. The main objective of our paper is to combine the two branches of the literature to assess the distinct effects of contractual and working conditions on health. The results suggest that both sets of conditions have some influence on health and psychological well-being of employees.

The Effectiveness of the Clean Development Mechanism – A law and economics analysis

Climate change has been acknowledged as a threat to humanity. Most scholars agree that to avert dangerous climate change and to transform economies into low-carbon societies, deep global emission reductions are required by the year 2050. Under the framework of the Kyoto Protocol, the Clean Development Mechanism (CDM) is the only market-based instrument that encourages industrialised countries to pursue emission reductions in developing countries. The CDM aims to pay the incremental finance necessary to operationalize emission reduction projects which are otherwise not financially viable. According to the objectives of the Kyoto Protocol, the CDM should finance projects that are additional to those which would have happened anyway, contribute to sustainable development in the countries hosting the projects, and be cost-effective. To enable the identification of such projects, an institutional framework has been established by the Kyoto Protocol which lays out responsibilities for public and private actors. This thesis examines whether the CDM has achieved these objectives in practice and can thus be considered an effective tool to reduce emissions. To complete this investigation, the book applies economic theory and analyses the CDM from two perspectives. The first perspective is the supply-dimension which answers the question of how, in practice, the CDM system identified additional, cost-effective, sustainable projects and, generated emission reductions. The main contribution of this book is the second perspective, the compliance-dimension, which answers the question of whether industrialised countries effectively used the CDM for compliance with their Kyoto targets. The application of the CDM in the European Union Emissions Trading Scheme (EU ETS) is used as a case-study. Where the analysis identifies inefficiencies within the supply or the compliance dimension, potential improvements of the legal framework are proposed and discussed.

Quantifying the Economics of Medical Malpractice - A View from a Civil Law Perspective

Life is full of uncertainties. Legal rules should have a clear intention, motivation and purpose in order to diminish daily uncertainties. However, practice shows that their consequences are complex and hard to predict. For instance, tort law has the general objectives of deterring future negligent behavior and compensating the victims of someone else's negligence. Achieving these goals are particularly difficult in medical malpractice cases. To start with, when patients search for medical care they are typically sick in the first place. In case harm materializes during the treatment, it might be very hard to assess if it was due to substandard medical care or to the patient's poor health conditions. Moreover, the practice of medicine has a positive externality on the society, meaning that the design of legal rules is crucial: for instance, it should not result in physicians avoiding practicing their activity just because they are afraid of being sued even when they acted according to the standard level of care. The empirical literature on medical malpractice has been developing substantially in the past two decades, with the American case being the most studied one. Evidence from civil law tradition countries is more difficult to find. The aim of this thesis is to contribute to the empirical literature on medical malpractice, using two civil law countries as a case-study: Spain and Italy. The goal of this thesis is to investigate, in the first place, some of the consequences of having two separate sub-systems (administrative and civil) coexisting within the same legal system, which is common in civil law tradition countries with a public national health system (such as Spain, France and Portugal). When this holds, different procedures might apply depending on the type of hospital where the injury took place (essentially whether it is a public hospital or a private hospital). Therefore, a patient injured in a public hospital should file a claim in administrative courts while a patient suffering an identical medical accident should file a claim in civil courts. A natural question that the reader might pose is why should both administrative and civil courts decide medical malpractice cases? Moreover, can this specialization of courts influence how judges decide medical malpractice cases? In the past few years, there was a general concern with patient safety, which is currently on the agenda of several national governments. Some initiatives have been taken at the international level, with the aim of preventing harm to patients during treatment and care. A negligently injured patient might present a claim against the health care provider with the aim of being compensated for the economic loss and for pain and suffering. In several European countries, health care is mainly provided by a public national health system, which means that if a patient harmed in a public hospital succeeds in a claim against the hospital, public expenditures increase because the State takes part in the litigation process. This poses a problem in a context of increasing national health expenditures and public debt. In Italy, with the aim of increasing patient safety, some regions implemented a monitoring system on medical malpractice claims. However, if properly implemented, this reform shall also allow for a reduction in medical malpractice insurance costs. This thesis is organized as follows. Chapter 1 provides a review of the empirical literature on medical malpractice, where studies on outcomes and merit of claims, costs and defensive medicine are presented. Chapter 2 presents an empirical analysis of medical malpractice claims arriving to the Spanish Supreme Court. The focus is on reversal rates for civil and administrative decisions. Administrative decisions appealed by the plaintiff have the highest reversal rates. The results show a bias in lower administrative courts, which tend to focus on the State side. We provide a detailed explanation for these results, which can rely on the organization of administrative judges career. Chapter 3 assesses predictors of compensation in medical malpractice cases appealed to the Spanish Supreme Court and investigates the amount of damages attributed to patients. The results show horizontal equity between administrative and civil decisions (controlling for observable case characteristics) and vertical inequity (patients suffering more severe injuries tend to receive higher payouts). In order to execute these analyses, a database of medical malpractice decisions appealed to the Administrative and Civil Chambers of the Spanish Supreme Court from 2006 until 2009 (designated by the Spanish Supreme Court Medical Malpractice Dataset (SSCMMD)) has been created. A description of how the SSCMMD was built and of the Spanish legal system is presented as well. Chapter 4 includes an empirical investigation of the effect of a monitoring system for medical malpractice claims on insurance premiums. In Italy, some regions adopted this policy in different years, while others did not. The study uses data on insurance premiums from Italian public hospitals for the years 2001-2008. This is a significant difference as most of the studies use the insurance company as unit of analysis. Although insurance premiums have risen from 2001 to 2008, the increase was lower for regions adopting a monitoring system for medical claims. Possible implications of this system are also provided. Finally, Chapter 5 discusses the main findings, describes possible future research and concludes.

Three Essays in Economics of Gender

During recent decades, economists' interest in gender-related issues has risen. Researchers aim to show how economic theory can be applied to gender related topics such as peer effect, labor market outcomes, and education. This dissertation aims to contribute to our understandings of the interaction, inequality and sources of differences across genders, and it consists of three empirical papers in the research area of gender economics. The aim of the first paper ("Separating gender composition effect from peer effects in education") is to demonstrate the importance of considering endogenous peer effects in order to identify gender composition effect. This fact is analytically illustrated by employing Manski's (1993) linear-in-means model. The paper derives an innovative solution to the simultaneous identification of endogenous and exogenous peer effects: gender composition effect of interest is estimated from auxiliary reduced-form estimates after identifying the endogenous peer effect by using Graham (2008) variance restriction method. The paper applies this methodology to two different data sets from American and Italian schools. The motivation of the second paper ("Gender differences in vulnerability to an economic crisis") is to analyze the different effect of recent economic crisis on the labor market outcome of men and women. Using triple differences method (before-after crisis, harder-milder hit sectors, men-women) the paper used British data at the occupation level and shows that men suffer more than women in terms of probability of losing their job. Several explanations for the findings are proposed. The third paper ("Gender gap in educational outcome") is concerned with a controversial academic debate on the existence, degree and origin of the gender gap in test scores. The existence of a gap both in mean scores and the variability around the mean is documented and analyzed. The origins of the gap are investigated by looking at wide range of possible explanations.

A Law and Economics Analysis of Lobbying Regulation Towards an optimal structure through the Cost Indicator Index

This research primarily represents a contribution to the lobbying regulation research arena. It introduces an index which for the first time attempts to measure the direct compliance costs of lobbying regulation. The Cost Indicator Index (CII) offers a brand new platform for qualitative and quantitative assessment of adopted lobbying laws and proposals of those laws, both in the comparative and the sui generis dimension. The CII is not just the only new tool introduced in the last decade, but it is the only tool available for comparative assessments of the costs of lobbying regulations. Beside the qualitative contribution, the research introduces an additional theoretical framework for complementary qualitative analysis of the lobbying laws. The Ninefold theory allows a more structured assessment and classification of lobbying regulations, both by indication of benefits and costs. Lastly, this research introduces the Cost-Benefit Labels (CBL). These labels might improve an ex-ante lobbying regulation impact assessment procedure, primarily in the sui generis perspective. In its final part, the research focuses on four South East European countries (Slovenia, Serbia, Montenegro and Macedonia), and for the first time brings them into the discussion and calculates their CPI and CII scores. The special focus of the application was on Serbia, whose proposal on the Law on Lobbying has been extensively analysed in qualitative and quantitative terms, taking into consideration specific political and economic circumstances of the country. Although the obtained results are of an indicative nature, the CII will probably find its place within the academic and policymaking arena, and will hopefully contribute to a better understanding of lobbying regulations worldwide.

Fighting corruption with pyramids: A Law and Economics approach to combating corruption in post-socialist countries

Corruption is, in the last two decades, considered as one of the biggest problems within the international community, which harms not only a particular state or society but the whole world. The discussion on corruption in law and economics approach is mainly run under the veil of Public choice theory and principal-agent model. Based on this approach the strong international initiatives taken by the UN, the OECD and the Council of Europe, provided various measures and tools in order to support and guide countries in their combat against corruption. These anti-corruption policies created a repression -prevention-transparency model for corruption combat. Applying this model, countries around the world adopted anti-corruption strategies as part of their legal rules. Nevertheless, the recent researches on the effects of this move show non impressive results. Critics argue that “one size does not fit all” because the institutional setting of countries around the world varies. Among the countries which experience problems of corruption, even though they follow the dominant anti-corruption trends, are transitional, post-socialist countries. To this group belong the countries which are emerging from centrally planned to an open market economy. The socialist past left traces on institutional setting, mentality of the individuals and their interrelation, particularly in the domain of public administration. If the idiosyncrasy of these countries is taken into account the suggestion in this thesis is that in public administration in post-socialist countries, instead of dominant anti-corruption scheme repression-prevention-transparency, corruption combat should be improved through the implementation of a new one, structure-conduct-performance. The implementation of this model is based on three regulatory pyramids: anti-corruption, disciplinary anti-corruption and criminal anti-corruption pyramid. This approach asks public administration itself to engage in corruption combat, leaving criminal justice system as the ultimate weapon, used only for the very harmful misdeeds.

Essays in behavioral economics

In this work we conduct an experimental analysis on different behavioral models of economic choice. In particular, we analyze the role of overconfidence in shaping the beliefs of economics agents about the future path of their consumption or investment. We discuss the relevance of this bias in expectation formation both from a static and from a dynamic point of view and we analyze the effect of possible interventions aimed to achieve some policy goals. The methodology we follow is both theoretical and empirical. In particular, we make large use of controlled economic field experiments in order to test the predictions of the theoretical models we propose. In the second part of the thesis we discuss the role of cognition and personality in affecting economic preferences and choices. In this way we make a bridge between established psychological research and novel findings in economics. Finally, we conduct a field study on the role of incentives on education. We design different incentive schemes and we test, on randomized groups of students, their effectiveness in improving academic performance.

Three Essays in Spatial Economics

This work contributes to the field of spatial economics by embracing three distinct modelling approaches, belonging to different strands of the theoretical literature. In the first chapter I present a theoretical model in which the changes in urban system’s degree of functional specialisation are linked to (i) firms’ organisational choices and firms’ location decisions. The interplay between firms’ internal communication/managing costs (between headquarters and production plants) and the cost of communicating with distant business services providers leads the transition process from an “integrated” urban system where each city hosts every different functions to a “functionally specialised” urban system where each city is either a primary business center (hosting advanced business services providers, a secondary business center or a pure manufacturing city and all this city-types coexist in equilibrium.The second chapter investigates the impact of free trade on welfare in a two-country world modelled as an international Hotelling duopoly with quadratic transport costs and asymmetric countries, where a negative environmental externality is associated with the consumption of the good produced in the smaller country. Countries’ relative sizes as well as the intensity of negative environmental externality affect potential welfare gains of trade liberalisation. The third chapter focuses on the paradox, by which, contrary to theoretical predictions, empirical evidence shows that a decrease in international transport costs causes an increase in foreign direct investments (FDIs). Here we propose an explanation to this apparent puzzle by exploiting an approach which delivers a continuum of Bertrand- Nash equilibria ranging above marginal cost pricing. In our setting, two Bertrand firms, supplying a homogeneous good with a convex cost function, enter the market of a foreign country. We show that allowing for a softer price competition may indeed more than offset the standard effect generated by a decrease in trade costs, thereby restoring FDI incentives.

Essays in Household and Demographic Economics

This dissertation consists of three empirical studies that are believed to provide new contributions to the literature exploring the determinants of children/adolescents achievement test scores (Chapter 2), adolescent health risk behaviors (Chapter 3), and children time use patterns (Chapter 4). The second and third studies look at the separate roles of fathers and of mothers in influencing outcomes, wherein parental time is the resource input of interest quantitatively measured and directly derived from time diaries. The last chapter looks at the time allocation of children and how it varies according to child and household characteristics.

Essays in Behavioral Personnel Economics

The thesis contemplates 4 papers and its main goal is to provide evidence on the prominent impact that behavioral analysis can play into the personnel economics domain.The research tool prevalently used in the thesis is the experimental analysis.The first paper provide laboratory evidence on how the standard screening model–based on the assumption that the pecuniary dimension represents the main workers’choice variable–fails when intrinsic motivation is introduced into the analysis.The second paper explores workers’ behavioral reactions when dealing with supervisors that may incur in errors in the assessment of their job performance.In particular,deserving agents that have exerted high effort may not be rewarded(Type-I errors)and undeserving agents that have exerted low effort may be rewarded(Type-II errors).Although a standard neoclassical model predicts both errors to be equally detrimental for effort provision,this prediction fails when tested through a laboratory experiment.Findings from this study suggest how failing to reward deserving agents is significantly more detrimental than rewarding undeserving agents.The third paper investigates the performance of two antithetic non-monetary incentive schemes on schooling achievement.The study is conducted through a field experiment.Students randomized to the main treatments have been incentivized to cooperate or to compete in order to earn additional exam points.Consistently with the theoretical model proposed in the paper,the level of effort in the competitive scheme proved to be higher than in the cooperative setting.Interestingly however,this result is characterized by a strong gender effect.The fourth paper exploits a natural experiment setting generated by the credit crunch occurred in the UK in the2007.The economic turmoil has negatively influenced the private sector,while public sector employees have not been directly hit by the crisis.This shock–through the rise of the unemployment rate and the increasing labor market uncertainty–has generated an exogenous variation in the opportunity cost of maternity leave in private sector labor force.This paper identifies the different responses.