Esmeralda A. Ramalho

ALTERNATIVE ESTIMATING AND TESTING EMPIRICAL STRATEGIES FOR FRACTIONAL REGRESSION MODELS

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.

Regression models for choice-based samples with misclassification in the response variable

Abstract In this paper, we provide a general framework to deal with the presence of misclassification in the response variable in choice-based samples. The contaminated data sampling distribution is written as a function of the error-free conditional distribution of the dependent variable given the covariates and the conditional misclassification probabilities of the observable variable of interest given its latent values. We propose an extension of Imbens’ (Econometrica 60 (1992) 1187) efficient generalized method of moments to estimate this model and outline a specification test to detect the presence of this sort of measurement error. The performance of both the estimators and the test is investigated in a Monte Carlo simulation study, which shows very encouraging results.

Alternative Versions of the RESET Test for Binary Response Index Models: A Comparative Study*

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.

A Generalized Goodness‐of‐Functional Form Test for Binary and Fractional Regression Models

This paper proposes a new conditional mean test to assess the validity of binary and fractional parametric regression models. The new test checks the joint significance of two simple functions of the fitted index and is based on a very flexible parametric generalization of the postulated model. A Monte Carlo study reveals a promising behaviour for the new test, which compares favourably with that of the well-known RESET test as well as with tests where the alternative model is nonparametric.

Is neglected heterogeneity really an issue in binary and fractional regression models? A simulation exercise for logit, probit and loglog models

Theoretical and simulation analysis is performed to examine whether unobserved heterogeneity independent of the included regressors is really an issue in logit, probit and loglog models with both binary and fractional data. It is found that unobserved heterogeneity has the following effects. First, it produces an attenuation bias in the estimation of regression coefficients. Second, although it is innocuous for logit estimation of average sample partial effects, it may generate biased estimation of those effects in the probit and loglog models. Third, it has much more deleterious effects on the estimation of population partial effects. Fourth, it is only for logit models that it does not substantially affect the prediction of outcomes. Fifth, it is innocuous for the size of Wald tests for the significance of observed regressors but, in small samples, it substantially reduces their power.

Moment-Based Estimation of Nonlinear Regression Models with Boundary Outcomes and Endogeneity, with Applications to Nonnegative and Fractional Responses

ABSTRACT In this article, we suggest simple moment-based estimators to deal with unobserved heterogeneity in a special class of nonlinear regression models that includes as main particular cases exponential models for nonnegative responses and logit and complementary loglog models for fractional responses. The proposed estimators: (i) treat observed and omitted covariates in a similar manner; (ii) can deal with boundary outcomes; (iii) accommodate endogenous explanatory variables without requiring knowledge on the reduced form model, although such information may be easily incorporated in the estimation process; (iv) do not require distributional assumptions on the unobservables, a conditional mean assumption being enough for consistent estimation of the structural parameters; and (v) under the additional assumption that the dependence between observables and unobservables is restricted to the conditional mean, produce consistent estimators of partial effects conditional only on observables.

Bias-Corrected Moment-Based Estimators for Parametric Models Under Endogenous Stratified Sampling

This paper provides an integrated approach for estimating parametric models from endogenous stratified samples. We discuss several alternative ways of removing the bias of the moment indicators usually employed under random sampling for estimating the parameters of the structural model and the proportion of the strata in the population. Those alternatives give rise to a number of moment-based estimators that are appropriate for both cases where the marginal strata probabilities are known and unknown. The derivation of our estimators is very simple and intuitive and incorporates as particular cases most of the likelihood-based estimators previously suggested by other authors.

Exponential Regression of Fractional-Response Fixed-Effects Models with an Application to Firm Capital Structure

Abstract 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.

On the weighted maximum likelihood estimator for endogenous stratified samples when the population strata probabilities are unknown

The popular weighted maximum likelihood estimator for endogenous stratified samples requires knowledge on the population proportions of each stratum. In this paper we extend their estimator for cases where such information is not available.

Two-Step Empirical Likelihood Estimation under Stratified Sampling when Aggregate Information is Available

Empirical likelihood is appropriate to estimate moment condition models when a random sample from the target population is available. However, many economic surveys are subject to some form of stratification, in which case direct application of empirical likelihood will produce inconsistent estimators. In this paper we propose a two-step empirical likelihood estimator to deal with stratified samples in models defined by unconditional moment restrictions in the presence of some aggregate information such as the mean and the variance of the variable of interest. A Monte Carlo simulation study reveals promising results for many versions of the two-step empirical likelihood estimator.