Fuzzy Parametric of Sample Selection Model Using Heckman Two-Step Estimation Models

Models with sample-selection biases are widely used in various fields of economics such as labour economics (see Maddala, Amemiya, and Mroz). The models are usually estimated by Heckman's two-step estimator. However, Heckman's two-step estimator often performs poorly (see Wales and Woodland, Nelson, Paarsch, and Nawata). The data used in this study originated from the survey was conducted by the National Population and Family Development Board of Malaysia under the Ministry of Women, Family and Community Development of Malaysia, called the Malaysian Population and Family Survey 1994 (MPFS, 1994). The survey was conducted through a questionnaire, were randomly and specifically for married women. The data set focus on married women which provides information on wages, educational attainment, household composition and other socioeconomic characteristic. The Original sample data based on Mroz (1987), there are 4444 records married women. It is necessary to use the maximum likelihood method to estimate the models in such cases. For solving uncertainty data of a parametric sample selection model, in this paper needs to consider the models estimation using fuzzy modeling approach, called Fuzzy Parametric Sample Selection Model (FPSSM). Fuzzy Parametric sample selection model (FPSSM) is builds as a hybrid to the conventional parametric sample selection model. Finally, the result showed, FPSSM by Maximum Likelihood Estimator (MLE) estimates of the mean, Standard Deviation (SD). Keywords: Econometrics, Fuzzy Number, Heckman Two-Step Estimator, Married Women, MLE, Non-participation, Sample Selection Model.

Marginal analysis evaluates changes in an objective function associated with a unit change in a relevant variable. The primary statistic of marginal analysis is the marginal effect (ME). The ME facilitates the examination of outcomes for defined patient profiles while measuring the change in original units (e.g., costs, probabilities). The ME has a long history in economics; however, it is not widely used in health services research despite its flexibility and ability to provide unique insights. This paper, the first in a two-part series, introduces and illustrates the calculation of the ME for a variety of regression models often used in health services research. Part One includes a review of prior studies discussing MEs, followed by derivation of ME formulas for various regression models including linear, logistic, multinomial logit model (MLM), generalized linear model (GLM) for continuous data, GLM for count data, two-part model, sample selection (two-stage) model, and parametric survival model. Prior theoretical papers in health services research reported the derivation and interpretation of ME primarily for the linear and logistic models, with less emphasis on count models, survival models, MLM, two-part models, and sample selection models. These additional models are relevant for health services research studies examining costs and utilization. Part Two of the series will focus on the methods for estimating and interpreting the ME in applied research. The illustration, discussion, and application of ME in this two-part series support the conduct of future studies applying the marginal concept.

Summary In sample selection models, a treatment can influence the observed outcome in two ways: by affecting the binary selection or participation decision and by affecting the latent outcome. The former is called the ‘extensive margin effect’, and the latter is called the ‘intensive margin effect’. Despite the popularity of these effects, however, the intensive margin effect does not have the traditional causal parameter interpretation because it is conditioned on the selecting or participating decision, which is a post-treatment variable possibly affected by the treatment. The paper presents a causal framework for sample selection models and introduces various subpopulation effects. It is difficult to separate such effects in general; however, in certain popular models (nearly parametric sample selection models, semiparametric ‘independence models’, semiparametric zero-censored models and ‘polynomial approximation’ models) with linear latent equations, they are separately identified and easily estimable with probit and least squares estimators. An empirical analysis is provided to illustrate these causal effects in sample selection models.

Over a few decades, regression model has received considerable attention and has been shown to be successful when applied together with other models. One of the most successful models is the sample selection model or the selectivity model. However, uncertainties and ambiguities do exist in the models, particularly the relationship between the endogenous and exogenous variables. Therefore, it will disrupt the ability and effectiveness of the model proceeded to give the estimated value that can explain the actual situation of a phenomenon. These are the questions and problems that are yet to be explored and the main aim of this study. A new framework for estimation of the sample selection model using the concept of fuzzy modelling is introduced. In this approach, a flexible fuzzy concept hybrid with the parametric sample selection model is known as fuzzy parametric sample selection model (FPSSM). The elements of vagueness and uncertainty in the models are represented in the model construction, as a way of increasing the available information to produce a more accurate model. This led to the development of the convergence theorem presented in the form of triangular fuzzy numbers to be used in the model. Consistency is an indicator of effectiveness of the developed models and justified using Monte Carlo simulation. Consistency and efficiency of the proposed model are considered in this study. In order to achieve that condition, a Monte Carlo simulation is used. Hence, the error terms of FPSSM are assumed to follow the normal and the chi-square distributions. Simulation results show that FPSSM is consistent and efficient when its distributions are normal. Instead, the FPSSM by chi-square distribution is found to be inconsistent.

The sample selection model is a combination of the regression and probit models. The models are usually estimated by Heckman’s two-step estimator. However, Heckman’s two-step estimator often performs poorly. In the context of the parametric method, Monte Carlo simulations are studied. The goal is to simulate and test as early as possible so that we can anticipate the problem of the accuracy of a model. The best approach is to take advantage of the tools provided by the theory of fuzzy sets. It appears very suitable for modeling vague concepts. It is difficult to determine some of the criteria and arrive at a quantitative value. Fuzzy sets theory and its properties through the concept of fuzzy number. The fuzzy function used for solving uncertain of a parametric sample selection model. Estimates from the fuzzy are used to calculate some of equation of the sample selection model. Finally, estimates of the Mean, Root Mean Square Error (RMSE) and the other estimators can be obtained by Heckman two-step estimator through iteration from some parameters and some of values.

This article is devoted to the comparative analysis of parametric and semiparametric sample selection models with two selection equations. Comparison has been conducted on simulated data under different random errors distributional assumptions: student, beta and mixture of normal. The results suggest that for student and beta distributions parametric models’ estimates are more or equally accurate as semiparametric. However, former methods provide more accurate estimates under mixture distribution case. Therefore, parametric sample selection model estimators seem to be robust to violations of normality assumption in terms of tails thickness and asymmetry but fail to account for bimodality as good as their semiparametric counterparts

A Comparison of Self-Selectivity Corrections in Economic Evaluations and Outcomes Research

The problem of non-random sample selectivity often occurs in practice in many different fields. In presence of sample selection, the data appears in the sample according to some selection rule. In these cases, the standard tools designed for complete samples, e.g. ordinary least squares, produce biased results, and hence, methods correcting this bias are needed. In his seminal work, Heckman proposed two estimators to solve this problem. These estimators became the backbone of the standard statistical analysis of sample selection models. However, these estimators are based on the assumption of normality and are very sensitive to small deviations from the distributional assumptions which are often not satisfied in practice. In this thesis we develop a general framework to study the robustness properties of estimators and tests in sample selection models. We use an infinitesimal approach, which allows us to explore the robustness issues and to construct robust estimators and tests.

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.

EBT2 films from the lot investigated in this study show response inhomogeneities, which lead to uncertainties in dose determination exceeding the commonly accepted tolerance levels. It is important to test further EBT2 lots regarding homogeneity before using the film in clinical routine.

Factors affecting economic output in developed countries: A copula approach to sample selection with panel data

The sample selection model has been studied in the context of semi-parametric methods. With the deficiencies of the parametric model, such as inconsistent estimators, semi-parametric estimation methods provide better alternatives. This article focuses on the context of fuzzy concepts as a hybrid to the semiparametric sample selection model. The better approach when confronted with uncertainty and ambiguity is to use the tools provided by the theory of fuzzy sets, which are appropriate for modeling vague concepts. A fuzzy membership function for solving uncertainty data of a semi-parametric sample selection model is introduced as a solution to the problem.

The aim of this paper is to describe the implementation and to provide a tutorial for the R package ssmrob, which is developed for robust estimation and inference in sample selection and endogenous treatment models. The sample selectivity issue occurs in practice in various fields, when a non-random sample of a population is observed, i.e., when observations are present according to some selection rule. It is well known that the classical estimators introduced by Heckman (1979) are very sensitive to small deviations from the distributional assumptions (typically the normality assumption on the error terms). Zhelonkin, Genton, and Ronchetti (2016) investigated the robustness properties of these estimators and proposed robust alternatives to the estimator and the corresponding test. We briefly discuss the robust approach and demonstrate its performance in practice by providing several empirical examples. The package can be used both to produce a complete robust statistical analysis of these models which complements the classical one and as a set of useful tools for exploratory data analysis. Specifically, robust estimators and standard errors of the coefficients of both the selection and the regression equations are provided together with a robust test of selectivity. The package therefore provides additional useful information to practitioners in different fields of applications by enhancing their statistical analysis of these models.

The Copula Approach to Sample Selection Modelling: An Application to the Recreational Value of Forests

A Flexible Sample Selection Model: A Gtl-Copula Approach