In many economic settings, the variable of interest is often a fraction or a proportion, being defined only on the unit interval. The bounded nature of such variables and, in some cases, the possibility of nontrivial probability mass accumulating at one or both boundaries raise some interesting estimation and inference issues. In this paper we (i) provide a comprehensive survey of the main alternative models and estimation methods suitable to deal with fractional response variables, (ii) propose a full testing methodology to assess the validity of the assumptions required by each alternative estimator and (iii) examine the finite-sample properties of most of the estimators and tests discussed through an extensive Monte Carlo study. An application concerning corporate capital structure choices is also provided.

Data envelopment analysis (DEA) is commonly used to measure the relative efficiency of decision-making units. Often, in a second stage, a regression model is estimated to relate DEA efficiency scores to exogenous factors. In this paper, we argue that the traditional linear or tobit approaches to second-stage DEA analysis do not constitute a reasonable data-generating process for DEA scores. Under the assumption that DEA scores can be treated as descriptive measures of the relative performance of units in the sample, we show that using fractional regression models are the most natural way of modeling bounded, proportional response variables such as DEA scores. We also propose generalizations of these models and, given that DEA scores take frequently the value of unity, examine the use of two-part models in this framework. Several tests suitable for assessing the specification of each alternative model are also discussed.

In this paper we examine the following two hypotheses which traditional theories of capital structure are relatively silent about: (i) the determinants of financial leverage decisions are different for micro, small, medium and large firms; and (ii) the factors that determine whether or not a firm issues debt are different from those that determine how much debt it issues. Using a binary choice model to explain the probability of a firm raising debt and a fractional regression model to explain the relative amount of debt issued, we find strong support for both hypotheses. Confirming recent empirical evidence, we find also that, although larger firms are more likely to use debt, conditional on having some debt firm size is negatively related to the proportion of debt used by firms.

This study investigates why and where self-employment is related to higher levels of eudaimonic well-being. We focus on meaningfulness as an important eudaimonic process and subjective vitality as a eudaimonic well-being outcome that is central to entrepreneurs' proactivity. Building on self-determination theory, we posit that self-employment, relative to wage-employment, is a more self-determined and volitional career choice, which enhances the experience of meaningfulness at work and perceptions of work autonomy. In a multi-level study of 22,002 individuals and 16 European countries, meaningfulness at work mediates the relationship between self-employment and subjective vitality and explains this relationship better than work autonomy. We identify moderating effects of context: the societal legitimacy of entrepreneurship in a country affects the choice set of alternative career options that individuals can consider and thus shapes the experience of meaningfulness at work and work autonomy, and thereby indirectly subjective vitality. These findings expand our understanding of eudaimonic well-being, entrepreneurs' work, and the role of context in entrepreneurship and well-being research. They complement existing research on hedonic well-being of entrepreneurs and extend the scarce literature on their eudaimonic well-being.

The present article discusses alternative regression models and estimation methods for dealing with multivariate fractional response variables. Both conditional mean models, estimable by nonlinear least squares and quasi-maximum likelihood, and fully parametric models (Dirichlet and Dirichlet-multinomial), estimable by maximum likelihood, are considered.In contrast to previous papers but similarly to the univariate case, a new parameterization is proposed here for the parametric models, which allows the same specification of the conditional mean of interest to be used in all models, irrespective of the specific functional form adopted for it. The text also discusses at some length the specification analysis of fractional regression models, proposing several tests that can be performed through artificial regressions. Finally, an extensive Monte Carlo study evaluates the finite sample properties of most of the estimators and tests considered.JEL classification code: C35.

In this article, we investigate the influence of family ownership on firm leverage across different subgroups of family and non-family firms. In addition, we examine the influence of firm size, geographical location and the 2008 global financial crisis on the capital structure of family firms. In both cases, we study the probability of firms using debt and, conditional on its use, the proportion of debt issued. We find that family ownership affects both decisions positively, namely, when the firm is large or located in a metropolitan area. For small firms located outside metropolitan areas, there is no clear family ownership effect. We also find the 2008 crisis had a substantial, but diversified, impact on family firm leverage. On the one hand, all family firms were more prone to use debt after 2008; on the other, the proportion of debt held by levered family firms decreased for micro and small firms, but increased for large firms. Overall, the crisis effects on family firm leverage seem to be the result of both supply-and demand-side factors, with the former particularly affecting the availability of debt to micro and small firms.

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