Do local financial and legal systems affect SMEs capital structure?

This note investigates the role of institutional differences at the local level as determinants of firms' capital structure. Specifically, its aim is to empirically assess whether and to what extent SMEs' financial decisions are affected by local financial development – evaluating this influence both ceteris paribus, and by allowing it to be conditional on different levels of legal enforcement inefficiency. Controlling for debt inertia, firms' heterogeneity and endogeneity problems, we find that local financial development may be an important determinant of SMEs' capital structure, and that firms appear to have better access to financial debt in areas characterized by a higher quality of the legal system. Thus, despite the international process of capital markets integration, local financial institutions do not seem to become irrelevant for SMEs, which are in need of well developed institutions at local level to gain easier access to external financial resources.firms' capital structure; bank debt; local financial development; local enforcement system, SMEs.

Moment Priors for Bayesian Model Choice with Applications to Directed Acyclic Graphs

We propose a new method for the objective comparison of two nested models based on non-local priors. More specifically, starting with a default prior under each of the two models, we construct a moment prior under the larger model, and then use the fractional Bayes factor for a comparison. Non-local priors have been recently introduced to obtain a better separation between nested models, thus accelerating the learning behaviour, relative to currently used local priors, when the smaller model holds. Although the argument showing the superior performance of non-local priors is asymptotic, the improvement they produce is already apparent for small to moderate samples sizes, which makes them a useful and practical tool. As a by-product, it turns out that routinely used objective methods, such as ordinary fractional Bayes factors, are alarmingly slow in learning that the smaller model holds. On the downside, when the larger model holds, non-local priors exhibit a weaker discriminatory power against sampling distributions close to the smaller model. However, this drawback becomes rapidly negligible as the sample size grows, because the learning rate of the Bayes factor under the larger model is exponentially fast, whether one uses local or non-local priors. We apply our methodology to directed acyclic graph models having a Gaussian distribution. Because of the recursive nature of the joint density, and the assumption of global parameter independence embodied in our prior, calculations need only be performed for individual vertices admitting a distinct parent structure under the two graphs; additionally we obtain closed-form expressions as in the ordinary conjugate case. We provide illustrations of our method for a simple three-variable case, as well as for a more elaborate seven-variable situation. Although we concentrate on pairwise comparisons of nested models, our procedure can be implemented to carry-out a search over the space of all models.Fractional Bayes factor; Gaussian graphical model; Non-local prior; Objective Bayes network; Stochastic search; Structural learning.

Objective Bayes Factors for Gaussian Directed Acyclic Graphical Models

We propose an objective Bayesian method for the comparison of all Gaussian directed acyclic graphical models defined on a given set of variables. The method, which is based on the notion of fractional Bayes factor, requires a single default (typically improper) prior on the space of unconstrained covariance matrices, together with a prior sample size hyper-parameter, which can be set to its minimal value. We show that our approach produces genuine Bayes factors. The implied prior on the concentration matrix of any complete graph is a data-dependent Wishart distribution, and this in turn guarantees that Markov equivalent graphs are scored with the same marginal likelihood. We specialize our results to the smaller class of Gaussian decomposable undirected graphical models, and show that in this case they coincide with those recently obtained using limiting versions of hyper-inverse Wishart distributions as priors on the graph-constrained covariance matrices.Bayes factor; Bayesian model selection; Directed acyclic graph; Exponential family; Fractional Bayes factor; Gaussian graphical model; Objective Bayes;Standard conjugate prior; Structural learning. network; Stochastic search; Structural learning.

A survey on C 1,1 fuctions: theory, numerical methods and applications

In this paper we survey some notions of generalized derivative for C 1,1 functions. Furthermore some optimality conditions and numerical methods for nonlinear minimization problems involving C1,1 data are studied.