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.

Essays in Media and Finance

This Ph.D. thesis consists in three research papers focused on the relationship between media industry and the financial sector. The importance of a correct understanding what is the effect of media on financial markets is becoming increasingly important as long as fully informed markets hypothesis has been challenged. Therefore, if financial markets do not have access to complete information, the importance of information professionals, the media, follows. On the other side, another challenge for economic and finance scholar is to understand how financial features are able to influence media and to condition information disclosure. The main aim of this Ph.D. dissertation is to contribute to a better comprehension for both the phenomena. The first paper analyzes the effects of owning equity shares in a newspaper- publishing firm. The main findings show how for a firm being part of the ownership structure of a media firm ends to receive more and better coverage. This confirms the view in which owning a media outlet is a source of conflicts of interest. The second paper focuses on the effect of media-delivered information on financial markets. In the framework of IPO in the U.S. market, we found empirical evidence of a significant effect of the media role in the IPO pricing. Specifically, increasing the quantity and the quality of the coverage increases the first-day returns (i.e. the underpricing). Finally the third paper tries to summarize what has been done in studying the relationship between media and financial industries, putting together contributes from economic, business, and financial scholars. The main finding of this dissertation is therefore to have underlined the importance and the effectiveness of the relationship between media industry and the financial sector, contributing to the stream of research that investigates about the media role and media effectiveness in the financial and business sectors.