Estimation of Sample Selection Models with Spatial Dependence

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

Semiparametric and nonparametric estimation of sample selection models under symmetry

When employing the spatial diagnostics examined in Chapter 4, social scientists will often find evidence of spatial autocorrelation (see, e.g., Eff 2004). As discussed in Chapter 1, this predisposition of social science data toward spatial autocorrelation often results from interdependence between the units studied by social scientists. In other cases, social science data exhibit spatial dependence not as a result of behavioral interdependence but as a consequence of spatial clustering in the sources of behaviors of interest to social scientists. The spatial dependence, in short, may be consistent with either a spatial lag model or a spatial error model. Substantive theory will often lead scholars to believe that a spatial lag specification or a spatial error specification is more appropriate for their particular substantive application. Scholars may, for example, expect that a spatial diffusion process is at work and thus believe that a spatial lag model is warranted. Although such a specification may seem appropriate, such a theoretical expectation should not go untested. It would be inappropriate to estimate a diffusion model with a spatially lagged dependent variable if the spatial dependence diagnosed via, for example, the univariate Moran's I , is instead produced by spatial clustering in the sources of otherwise independent behaviors. This model misspecification will lead the researcher to inappropriate substantive inferences about the nature of the spatial dependence in her data. Inappropriate spatial model specification is all the more problematic because of the close mathematical relationship between a spatial lag model and a spatial error model with spatial autoregressive error dependence. As this chapter will discuss, a spatial autoregressive error model can be rewritten as a spatial Durbin model with both spatially lagged dependent and independent variables if a set of nonlinear common factor constraints are valid. Because of this close relationship between spatial autoregressive dependence in a spatial lag model and spatial autoregressive dependence in a spatial error model, a significant spatial parameter in a spatial lag model may reflect spatial clustering in omitted sources of the behavior of interest rather than true spatial lag dependence consistent with a diffusion process.

If the ordinary least squares (OLS) diagnostics discussed in the previous chapter indicate the existence of spatial lag or spatial error dependence, the researcher will wish to model the type of dependence indicated by these diagnostics. If the OLS diagnostics indicate the presence of a diffusion process, the researcher will wish to estimate a spatial lag model via maximum likelihood (ML) estimation or an instrumental variables specification incorporating instruments for the spatially lagged dependent variable. Alternatively, if the OLS diagnostics indicate the existence of spatial error dependence, the researcher may choose to estimate a more fully specified OLS model to model the spatial dependence or may choose to employ a ML or generalized method of moments (GMM) approach incorporating the spatial dependence in the errors. The spatial dependence diagnosed via the diagnostics discussed in Chapter 5 may alternatively be produced by spatial heterogeneity in the effects of covariates. If this is the only source of spatial dependence, modeling this heterogeneity will be sufficient to capture the spatial dependence. As a consequence, any specification search should also consider the possibility of spatial heterogeneity, which is the focus of Chapter 7. This chapter will first, however, examine alternative approaches for modeling spatial dependence if spatial heterogeneity is not present. This chapter begins by examining ML estimation of spatial lag models that derives from Ord (1975). Next, I explore alternative instrumental variables and GMM estimators for spatial lag dependence. Next, I turn to approaches for estimating spatial error models. I conclude by considering areas of concern in the estimation of spatial models. These include estimators for large sample sizes and diagnostics for continued spatial dependence. MAXIMUM LIKELIHOOD SPATIAL LAG ESTIMATION The mixed regressive, spatial autoregressive model, or spatial lag model, extends the pure spatial autoregressive model considered in Section 3.2 to include also the set of covariates and associated parameters: y = ρ W y +Xβ+e where X is again an N by K matrix of observations on the covariates, β is a K by 1 vector of parameters, and the remaining notation is as discussed in Section 3.2.

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.

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.

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.

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.

Monte Carlo evidence on the choice between sample selection and two-part models

The human development index (HDI) is an indicator used to monitor the government's success in developing the quality of human life. East Java Province's HDI is the lowest compared to other provinces on Java Island. Therefore, it is necessary to improve human development in this province. Attention must be paid to all aspects of human development, including the relationship between neighboring regions. The spatial regression method is an analysis method that considers the spatial dependency of the data. Ensemble spatial regression combines several spatial models by adding noise to the response variable, which is expected to reduce the diversity in the data. This research aims to use ensemble spatial regression to examine the East Java HDI. East Java HDI has spatial lag and spatial error dependence, modeled with SAR and SEM. Queen contiguity is used as a spatial weight. The SEM model does not fulfill the homogeneity assumption, so it is continued with the ensemble method. The ensemble method is proven to reduce diversity, so SEM Ensemble fulfills the assumption of homoscedasticity. After analysis using SAR and SEM Ensemble, the SAR model was chosen as the best model with the largest and lowest AIC value. Significant variables on East Java HDI are life expectancy, expected years of schooling, average years of schooling, and expenditure per capita.

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.

We develop a fully parametric estimation procedure for unbalanced panel data models with unobserved effects that allow for a common binary endogenous variable in both the selection equation and the outcome equation. We test the finite sample properties of the estimator using Monte Carlo simulations and find that our estimator performs better in the presence of high endogeneity and high sample selection compared to the estimators that ignore either or both of these issues. In addition, our estimator is also robust to distributional misspecification. We apply our econometric methodology to estimate the effect of fertility decisions on wages for white women using the National Longitudinal Survey of Youth 1979 (NLSY79) data from 1982 to 2006.

Spatial regression, particularly the Spatial Error Model (SERM), was utilized in prior studies to analyze Human Development Index (HDI) modeling. However, the studies were unable to determine which dimension among the three defined by the UN and BPS had the significant impact on HDI, as they constructed models based on the indicators used for the interpretation of the dimensions. Therefore, a comprehensive analysis combining spatial regression and Structural Equation Modeling (SEM), known as spatial SEM, was deemed necessary. This is the reason the current study aimed to develop SERM-SEM modeling holistically. The model parameters were estimated using the Generalized Method of Moments (GMM). To assess spatial dependency, the Lagrange Multiplier (LM) method was employed, with a distinct model error distribution compared to the error distribution of the traditional spatial model. The result of the LM test development showed that, under the null hypothesis, the LM test statistics followed a distribution. The results of the SERM-SEM model development were applied to HDI modeling using data in 2022 with three latent variables, namely a Long and Healthy Life (LHL), Knowledge (Know_L), and a Decent Standard of Living (DLS) (based on UN standards). The assessment of the outer model in SEM was based on the loading factor values that exceed 0.5 and their significance. This evaluation aimed to identify indicators that effectively explained or measured latent variables, so it got the revised model in SEM. These indicators are LHL2 and LHL 4 to form LHL. DLS1 and DLS3 are indicators to make up DLS, and for Know_L, they are K2 and K3. The revised SEM model was analyzed using spatial. The results of the spatial dependency test showed that the HDI model significantly led to the SERM-SEM model. Knowledge and a decent standard of living variables significantly influence HDI.

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.

The problem of specification errors in sample selection models has received considerable attention both theoretically and empirically. Originally proposed in Heckman (1979) within a fully parametric context, Ahn and Powell (1993) have proposed a semiparametric alternative that is claimed to be asymptotically robust against several misspecification errors. However, very few is known about the finite sample behavior of these estimators. In this paper we investigate theoretically and by simulations both bias and finite sample distribution of these estimators when ignoring heteroskedasticity in the sample selection mechanism.