Semiparametric and nonparametric estimation of sample selection models under symmetry

Estimation of Sample Selection Models with Spatial Dependence

Estimation of spatial sample selection models: A partial maximum likelihood approach

Summary Sample selection models are important for correcting the effects of non-random sampling. This paper is about semiparametric estimation using a series approximation to the correction term. Regression spline and power series approximations are considered. Asymptotic normality and consistency of an asymptotic variance estimator are shown.

This paper applies both parametric and semiparametric methods to the estimation of wage and participation equations for married women in Portugal. The semiparametric estimators considered are the two‐stage estimators proposed by Newey (1991) and Andrews and Schafgans (1998). The selection equation results are compared using the specification tests proposed by Horowitz (1993), Horowitz and Härdle (1994), and the wage equation results are compared using a Hausman test. Significant differences between the two approaches indicate the inappropriateness of the standard parametric methods to the estimation of the model and for the purpose of policy simulations. The greater departure seems to occur in the range of the low values of the index corresponding to a specific group of women. Copyright © 2001 John Wiley & Sons, Ltd.

SummaryWe consider estimating binary response models on an unbalanced panel, where the outcome of the dependent variable may be missing due to nonrandom selection, or there is self‐selection into a treatment. In the present paper, we first consider estimation of sample selection models and treatment effects using a fully parametric approach, where the error distribution is assumed to be normal in both primary and selection equations. Arbitrary time dependence in errors is permitted. Estimation of both coefficients and partial effects, as well as tests for selection bias, are discussed. Furthermore, we consider a semiparametric estimator of binary response panel data models with sample selection that is robust to a variety of error distributions. The estimator employs a control function approach to account for endogenous selection and permits consistent estimation of scaled coefficients and relative effects.

The econometric issue of sample selection concerns the possible biases that arise when a nonrandomly sampled set of observations from a population is used as if the sample were random to make inferences about that population. Current literature, with a few exceptions noted below, has focused on, and finely tuned, the known results relating to this issue in the framework of the linear regression model and analysis of a continuous dependent variable, such as hours worked or wages. This paper will examine an extension of the sample selection model to the Poisson regression model for discrete, count data, such as numbers of patents, of children, of visits to facilities such as shops or recreation sites, of convictions for crimes committed, and so on.

Estimation of the female labor supply models by Heckman’s two-step estimator and the maximum likelihood estimator

Summary The problem of non-random sample selectivity often occurs in practice in many fields. The classical estimators introduced by Heckman are the backbone of the standard statistical analysis of these models. However, these estimators are very sensitive to small deviations from the distributional assumptions which are often not satisfied in practice. We develop a general framework to study the robustness properties of estimators and tests in sample selection models. We derive the influence function and the change-of-variance function of Heckman's two-stage estimator, and we demonstrate the non-robustness of this estimator and its estimated variance to small deviations from the model assumed. We propose a procedure for robustifying the estimator, prove its asymptotic normality and give its asymptotic variance. Both cases with and without an exclusion restriction are covered. This allows us to construct a simple robust alternative to the sample selection bias test. We illustrate the use of our new methodology in an analysis of ambulatory expenditures and we compare the performance of the classical and robust methods in a Monte Carlo simulation study.

This article introduces semiparametric methods for the estimation of simultaneous-equation microeconometric models with index restrictions. The methods are motivated by a semiparametric minimum-distance procedure, which unifies the estimation of both regression-type and linear or nonlinear simultaneous-equation models without emphasis on the construction of instrumental variables. Single-equation and systematic estimation methods and optimal weighting procedures are considered. The estimators are √n-consistent and asymptotically normal. For the estimation of nonparametric regression and some sample selection models where the variances of disturbances are functions of the same indices, the optimal weighted estimator attains Chamberlain's efficient bound for models with conditional moment restrictions. The weighted estimator is shown to be optimal within a class of semiparametric instrumental variables estimators. JEL classification numbers: C14, C24, C34.

Stresses that control function estimators explicitly recognize that nonrandom selection into a program may give rise to an endogeneity problem—nonrandom selection could cause participation to correlate with unobserved factors that influence the outcome variable. When randomized controlled trials prove unusable to estimate program impacts, different types of estimators can work for nonexperimental data. An important issue when applying the various methods remains whether they assume that program participation could depend on unobserved factors. If this proves possible, one alternative remains instrumental variables (IV) methods and control function methods. Economists have used IV methods for many decades, but control function methods remain a relatively new approach. Control function methods remove bias caused by selection on unobservables by explicitly modeling the selection process and how it relates to the observed outcomes. The major challenge in applying these methods for estimating program impacts comes from the need to separately identify the intercept of the control function from the treatment effect.

Problem statement: It is well known that, the standard approach to estimating a sample selection models shows an inconsistent estimation results if the distributional assumption are incorrect. Approach: An important progress in the last decade to develop an alternative to overcome the deficiency is through the used of semi-parametric method. However, the usage of semi-parametric approach still does not cover the deficiency of the model. Results: We introduced a fuzzy membership function for solving uncertainty data of a sample selection model and employed method for sample selection models, that is, the two-step estimators to estimate a model of the so-called the self-selection decision. Fuzzy Parametric of Sample Selection Model (FPSSM) is builds as a hybrid to the conventional parametric sample selection model. Conclusion/Recommendations: The result showed that as a whole, the FPSSM give a better estimate and consistent when compared to the Parametric of Sample Selection Model (PSSM). This application demonstrate that the proposed fuzzy modeling approach was quite reasonable and provides an important and significant finding compared with conventional method especially in terms of estimation and consistency.

Bootstrap is a widely applicable computational statistical method. The focus of this paper lies in developing a bootstrap method for linear mixed models under homoscedasticity violation (heteroscedasticity) in variance of errors. We assume that the form of heteroscedasticity is unknown. To generate bootstrap response data as close as possible to the actual response data, we transform the marginal residuals to ensure that the variance of the modified marginal residuals in bootstrap samples is an unbiased estimator for the variance of the response variable in the linear mixed models. The consistency is proved, implying that the parameter estimators by the proposed method are asymptotically unbiased. The simulations are conducted with varying error terms and sample sizes to show improvement of the proposed method in parameter estimation. The simulation results are compared to demonstrate that the proposed method outperforms the other considered approaches including the wild method in the heteroscedastic linear mixed models under small samples and performs competitively with the parametric method and both methods outperform the other considered methods in homoscedastic linear mixed models. The proposed bootstrap method is applied to squid data for illustration of its effectiveness.

In this article, a general class of estimators for the linear regression model affected by outliers and collinearity is introduced and studied in some detail. This class of estimators combines the theory of light, maximum entropy, and robust regression techniques. Our theoretical findings are illustrated through a Monte Carlo simulation study.

Many estimation methods have been proposed for the parameters of the regression models with serially correlated errors. In this work, we develop an asymptotic theory for estimation in the short panel data models with bilinear error. We propose a comparative study by simulation between several estimators (adaptive, ordinary and weighted least squares) for the coefficients of panel data models when the errors are bilinear serially correlated. As a consequence of the uniform local asymptotic normality property, we obtain adaptive estimates of the parameters. Finally, we illustrate the performance of the proposed estimators via Monte Carlo simulation study. We show that the adaptive estimates are more efficient than the weighted and ordinary least squares estimates.

Functional relationship model is used to study the data that are subjected to errors. In this paper, we consider the linear functional relationship model with bivariate circular data where the pair of errors is with unequal concentration parameters. The parameter estimation of the model for circular data is different from linear data due to its wrapped around nature. We propose some improvements on the parameter estimation where some iterative procedures are considered. The concentration parameters are estimated based on the Bessel function. Also, we derive the corresponding covariance matrix of the model based on the Fisher Information matrix. Monte Carlo simulation studies were performed to study the suitability of the estimation method. It is found that the biasness of the estimates is small. Practical application of the method is illustrated by using real data set. Keywords: circular data; covariance matrix; Von Mises distribution; simulation study