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.

New fixed-effects estimators are proposed for logit and complementary loglog fractional regression models. The standard specifications of these models are transformed into a form of exponential regression with multiplicative individual effects and time-variant heterogeneity, from which four alternative estimators that do not require assumptions on the distribution of the unobservables are proposed. All new estimators are robust to both time-variant and time-invariant heterogeneity and can accomodate fractional responses with observations at the boundary value of zero. Additionally, some of these estimators can be applied to dynamic panel data models and can accommodate endogenous explanatory variables without requiring the specification of a reduced form model. A Monte Carlo study and an application to firm capital structure choices illustrate the usefulness of the suggested estimators.

Using a unique dataset containing information of around 256 thousand residential property sales, this paper discloses a clear sales premium for most energy efficient dwellings, which is more pronounced for apartments (13%) than for houses (5 to 6%). Crosscountry comparisons support the finding that energy efficiency price premiums are higher in the Portuguese residential market than in central and northern European markets. Results emphasize the relevance of data issues in hedonic regression models. They illustrate how the use of appraisal prices, explanatory variables with measurement errors, and the omission of variables associated with the quality of the properties, may seriously bias energy efficiency partial effect estimates. These findings provide valuable information not only to policy-makers, but also to researchers interested in this area.

Binary response index models may be affected by several forms of misspecification, which range from pure functional form problems (e.g. incorrect specification of the link function, neglected heterogeneity, heteroskedasticity) to various types of sampling issues (e.g. covariate measurement error, response misclassification, endogenous stratification, missing data). In this article we examine the ability of several versions of the RESET test to detect such misspecifications in an extensive Monte Carlo simulation study. We find that: (i) the best variants of the RESET test are clearly those based on one or two fitted powers of the response index; and (ii) the loss of power resulting from using the RESET instead of a test directed against a specific type of misspecification is very small in many cases.