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.

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 Environmental Economics

This dissertation comprises four essays on the topic of environmental economics and industrial organization. In the first essay, we develop a two-country world differential game model with a polluting firm in each country to investigate the equilibrium of the game between firms when they decide to trade or not and to see under which conditions social welfare coincides with the market equilibrium. In the second essay, we built a model where firms strategically choose whether to participate in an auction/lottery to attain pollution permits, or instead invest in green R&D, to show that, somewhat counterintuitively, a desirable side effect of the auction is in fact that of fostering environmental R&D in an admissible range of the model parameters. The third essay investigates a second-best trade agreement between two countries when pollution spillovers are asymmetric to examine the strategic behavior of governments in using pollution taxes and tariffs under trade liberalization. The fouth essay studies the profitability of exogenous output constraint in a differential game model with price dynamics under the feedback strategies.

Essays in Health Economics

In the first chapter we develop a theoretical model investigating food consumption and body weight with a novel assumption regarding human caloric expenditure (i.e. metabolism), in order to investigate why individuals can be rationally trapped in an excessive weight equilibrium and why they struggle to lose weight even when offered incentives for weight-loss. This assumption allows the theoretical model to have multiple equilibria and to provide an explanation for why losing weight is so difficult even in the presence of incentives, without relying on rational addiction, time-inconsistency preferences or bounded rationality. In addition to this result we are able to characterize under which circumstances a temporary incentive can create a persistent weight loss. In the second chapter we investigate the possible contributions that social norms and peer effects had on the spread of obesity. In recent literature peer effects and social norms have been characterized as important pathways for the biological and behavioral spread of body weight, along with decreased food prices and physical activity. We add to this literature by proposing a novel concept of social norm related to what we define as social distortion in weight perception. The theoretical model shows that, in equilibrium, the effect of an increase in peers' weight on i's weight is unrelated to health concerns while it is mainly associated with social concerns. Using regional data from England we prove that such social component is significant in influencing individual weight. In the last chapter we investigate the relationship between body weight and employment probability. Using a semi-parametric regression we show that men and women employment probability do not follow a linear relationship with body mass index (BMI) but rather an inverted U-shaped one, peaking at a BMI way over the clinical threshold for overweight.