Estimation Of Sample Selection Models Research Articles

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

We study estimation of sample selection models with the spatially lagged latent dependent variable or spatial errors in both the selection and outcome equations under cross-sectional dependence. Since there is no estimation framework for the spatial-lag model and the existing estimators for the spatial-error model are computationally demanding or have poor small sample properties, we suggest to estimate these models by the partial maximum likelihood estimator. We show that the estimator is consistent and asymptotically normally distributed. To facilitate easy and precise estimation of the variance matrix, we propose the parametric bootstrap method. Simulations demonstrate the advantages of the estimators.

Nonparametric identification and estimation of sample selection models under symmetry

Under a conditional mean restriction Das et al. (2003) considered nonparametric estimation of sample selection models. However, their method can only identify the outcome regression function up to a constant. In this paper we strengthen the conditional mean restriction to a symmetry restriction under which selection biases due to selection on unobservables can be eliminated through proper matching of propensity scores; consequently we are able to identify and obtain consistent estimators for the average treatment effects and the structural regression functions. The results from a simulation study suggest that our estimators perform satisfactorily.

Binary response panel data models with sample selection and self‐selection

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.

Identification and estimation of endogenous selection models in the presence of misclassification errors

This paper shows the semi-parametric identification and estimation of sample selection models when the primary equation contains a discrete mismeasured endogenous covariate. Assuming that appropriate instruments for the presence of endogeneity are available, I apply a control function approach to remove the possible endogeneity. Based on the conditional mean independence between the model error and the selection error, the model can be regarded as a semi-parametric regression model with a discrete mismeasured covariate, thereby permitting a non-classical measurement error. Additional identification assumptions include monotonicity restrictions on the regression function and an empirical testable rank condition. I then use the identification result to construct a sieve maximum likelihood estimation estimator to estimate the model parameters consistently and recover the selection rule and joint probabilities of the accurately measured endogenous variable and the mismeasured observed variable. The proposed estimation method allows for a rather flexible functional form of the mismeasured endogenous covariate, requires only one valid instrument to control for both endogeneity and measurement errors for the variable of interest, and imposes no distribution assumptions on the selection rule.

Estimation of sample selection models with spatial dependence

SUMMARYWe consider the estimation of a sample selection model that exhibits spatial autoregressive errors (SAE). Our methodology is motivated by a two‐step strategy where in the first step we estimate a spatial probit model and in the second step (outcome equation) we include an estimated inverse Mills ratio (IMR) as a regressor to control for selection bias. Since the appropriate IMR under SAE depends on a parameter from the second step, both steps are jointly estimated employing the generalized method of moments. We explore the finite sample properties of the estimator using simulations and provide an empirical illustration. Copyright © 2010 John Wiley & Sons, Ltd.

Estimation of sample selection models with two selection mechanisms

This paper focuses on estimating sample selection models with two incidentally truncated outcomes and two corresponding selection mechanisms. The method of estimation is an extension of the Markov chain Monte Carlo (MCMC) sampling algorithm from Chib (2007) and Chib et al. (2009). Contrary to conventional data augmentation strategies when dealing with missing data, the proposed algorithm augments the posterior with only a small subset of the total missing data caused by sample selection. This results in improved convergence of the MCMC chain and decreased storage costs, while maintaining tractability in the sampling densities. The methods are applied to estimate the effects of residential density on vehicle miles traveled and vehicle holdings in California.

Semiparametric and nonparametric estimation of sample selection models under symmetry

This paper considers the semiparametric estimation of binary choice sample selection models under a joint symmetry assumption. Our approaches overcome various drawbacks associated with existing estimators. In particular, our method provides root- n consistent estimators for both the intercept and slope parameters of the outcome equation in a heteroscedastic framework, without the usual cross equation exclusion restriction or parametric specification for the error distribution and/or the form of heteroscedasticity. Our two-step estimators are shown to be consistent and asymptotically normal. A Monte Carlo simulation study indicates the usefulness of our approaches.

Two-step series estimation of sample selection models

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.

Estimation of Sample Selection Models with Spatial Dependence

We consider the estimation of sample selection (type II Tobit) models that exhibit spatial error dependence or spatial autoregressive errors (SAE). The method considered is motivated by a two-step strategy analogous to the popular heckit model. The first step of estimation is based on a spatial probit model following a methodology proposed by Pinkse and Slade (1998) that yields consistent estimates. The consistent estimates of the selection equation are used to estimate the inverse Mills ratio (IMR) to be included as a regressor in the estimation of the outcome equation (second step). Since the appropriate IMR turns out to depend on a parameter from the second step under SAE we propose to estimate the two steps jointly within a generalized method of moments (GMM) framework. We explore the finate sample properties of the proposed estimator using a Monte Carlo experiment; discuss the importance of the spatial sample selection model in applied work, and illustrate the application of our method by estimating the spatial production within a fishery with data that is censored for reasons of confidentiality.

Parametric and semiparametric estimation of sample selection models: an empirical application to the female labour force in Portugal

AbstractThis 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.

Collinearity and Two-Step Estimation of Sample Selection Models: Problems, Origins, and Remedies

This paper investigates the origins of the collinearity problems encountered in the two-step estimation method for sample selection models. The analysis reveals several critical misconceptions and deficiencies in the literature. Remedies to the collinearity problems are proposed and evaluated. Monte Carlo experiments as well as an empirical example based on Mroz's (1987) data are used to illustrate the practical relevance and importance of the analysis.

EFFICIENT SEMIPARAMETRIC SCORING ESTIMATION OF SAMPLE SELECTION MODELS

A semiparametric likelihood method is proposed for the estimation of sample selection models. The method is a two-step semiparametric scoring estimation procedure based on an index restriction and kernel estimation. Under some regularity conditions, the estimator is square-root n-consistent and asymptotically normal. The estimator is also asymptotically efficient in the sense that its asymptotic covariance matrix attains the semiparametric efficiency bound under the index restriction. For the binary choice sample selection model, it also attains the efficiency bound under the independence assumption. This method can be applied to the estimation of general sample selection models.

Estimation of sample-selection models by the maximum likelihood method

Estimation of sample-selection models by the maximum likelihood method

Two-step estimation of heteroskedastic sample selection models

This paper considers two-step estimation of a sample selection model in which there is heteroskedasticity of unknown form in the latent errors. We propose an estimator which uses recent developments in nonparametric regression estimation involving series approximations. The estimator is shown to be consistent and asymptotically normally distributed under reasonable conditions. A small Monte Carlo experiment demonstrates the usefulness of the estimator and highlights the bias inherent in the usual Heckman (1979) estimator when there is heteroskedasticity.