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.

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.