On Intercept Estimation in the Sample Selection Model

We provide a proof of the consistency and asymptotic normality of the estimator suggested by Heckman (1990) for the intercept of a semiparametrically estimated sample selection model. The estimator is based on "identification at infinity" which leads to non-standard convergence rate. Andrews and Schafgans (1998) derived asymptotic results for a smoothed version of the estimator. We examine the optimal bandwidth selection for the estimators and derive asymptotic MSE rates under a wide class of distributional assumptions. We also provide some comparisons of the estimators and practical guidelines.

A method of moments estimator for semiparametric index models

We propose an easy to use derivative based two-step estimation procedure for semi-parametric index models. In the first step various functionals involving the derivatives of the unknown function are estimated using nonparametric kernel estimators. The functionals used provide moment conditions for the parameters of interest, which are used in the second step within a method-of-moments framework to estimate the parameters of interest. The estimator is shown to be root N consistent and asymptotically normal. We extend the procedure to multiple equation models. Our identification conditions and estimation framework provide natural tests for the number of indices in the model. In addition we discuss tests of separability, additivity, and linearity of the influence of the indices.Semiparametric estimation, multiple index models, average derivative functionals, generalized methods of moments estimator, rank testing

Smoothness Adaptive AverageDerivative Estimation

Many important models, such as index models widely used in limiteddependent variables, partial linear models and nonparametric demand studiesutilize estimation of average derivatives (sometimes weighted) of theconditional mean function. Asymptotic results in the literature focus onsituations where the ADE converges at parametric rates (as a result ofaveraging); this requires making stringent assumptions on smoothness of theunderlying density; in practice such assumptions may be violated. We extendthe existing theory by relaxing smoothness assumptions. We consider boththe possibility of lack of smoothness and lack of precise knowledge of degreeof smoothness and propose an estimation strategy that produces the bestpossible rate without a priori knowledge of degree of density smoothness. Thenew combined estimator is a linear combination of estimators correspondingto different bandwidth/kernel choices that minimizes the trace of the part ofthe estimated asymptotic mean squared error that depends on the bandwidth.Estimation of the components of the AMSE, of the optimal bandwidths,selection of the set of bandwidths and kernels are discussed. Monte Carloresults for density weighted ADE confirm good performance of the combinedestimator.Nonparametric estimation, density weighted average derivativeestimator, combined estimator.

Inference without smoothing for large panels with cross-sectional and temporal dependence

This paper addresses inference in large panel data models in the presence of both cross-sectional and temporal dependence of unknown form. We are interested in making inferences without relying on the choice of any smoothing parameter as is the case with the often employed "HAC" estimator for the covariance matrix. To that end, we propose a cluster estimator for the asymptotic covariance of the estimators and a valid bootstrap which accommodates the nonparametric nature of both temporal and cross-sectional dependence. Our approach is based on the observation that the spectral representation of the fixed effect panel data model is such that the errors become approximately temporal uncorrelated. Our proposed bootstrap can be viewed as a wild bootstrap in the frequency domain. We present some Monte-Carlo simulations to shed some light on the small sample performance of our inferential procedure and illustrate our results using an empirical example

Multiproduct firms, income distribution, and trade

We develop a general equilibrium model of multiproduct fi…rms with quality differentiated goods. Households are characterized by an heterogeneous taste for the differentiated good and their income level. The use of non-homothetic preferences and vertical product differentiation (product quality) enables us to analyze how distributional changes in income affect the number of vertically differentiated …firms, their product range and prices in the presence of strategic interaction across …rms. The implications of lowering the barriers to trade within this setting are considered as well

A method of moments estimator for semiparametric index models

We propose an easy to use derivative based two-step estimation procedure for semi-parametric index models. In the first step various functionals involving the derivatives of the unknown function are estimated using nonparametric kernel estimators. The functionals used provide moment conditions for the parameters of interest, which are used in the second step within a method-of-moments framework to estimate the parameters of interest. The estimator is shown to be root N consistent and asymptotically normal. We extend the procedure to multiple equation models. Our identification conditions and estimation framework provide natural tests for the number of indices in the model. In addition we discuss tests of separability, additivity, and linearity of the influence of the indices

Selectivity and the gender wage gap decomposition in the presence of a joint decision process

In this paper we revisit the gender decomposition of wages in the presence of selection bias. We show that when labor market participation decisions of couples are not independent, the sample selection corrections used in the literature have been incomplete (incorrect). We derive the appropriate sample selection corrections, based on a reduced form model for the joint participation decisions of both spouses. The influence that husbands’ participation decision has on the female participation decision also highlights the importance of using data on both spouses for the analysis of the gender wage gap. Taking account of these issues might influence the outcome of the decomposition analysis and affect the evidence of discrimination. We analyze its potential impact by analyzing the gender earnings differential using Canadian census data

On intercept estimation in the sample selection model

We provide a proof of the consistency and asymptotic normality of the estimator suggested by Heckman (1990) for the intercept of a semiparametrically estimated sample selection model. The estimator is based on 'identification at infinity' which leads to non-standard convergence rate. Andrews and Schafgans (1998) derived asymptotic results for a smoothed version of the estimator. We examine the optimal bandwidth selection for the estimators and derive asymptotic MSE rates under a wide class of distributional assumptions. We also provide some comparisons of the estimators and practical guidelines

Adapting kernel estimation to uncertain smoothness

For local and average kernel based estimators, smoothness conditions ensure that the kernel order determines the rate at which the bias of the estimator goes to zero and thus allows the econometrician to control the rate of convergence. In practice, even with smoothness the estimation errors may be substantial and sensitive to the choice of the bandwidth and kernel. For distributions that do not have sufficient smoothness asymptotic theory may importantly differ from standard; for example, there may be no bandwidth for which average estimators attain root-n consistency. We demonstrate that non-convex combinations of estimators computed for different kernel/bandwidth pairs can reduce the trace of asymptotic mean square error relative even to the optimal kernel/bandwidth pair. Our combined estimator builds on these results. To construct it we provide new general estimators for degree of smoothness, optimal rate and for the biases and covariances of estimators. We show that a bootstrap estimator is consistent for the variance of local estimators but exhibits a large bias for the average estimators; a suitable adjustment is provided

Gender wage differences in Malaysia: parametric and semiparametric estimation

This paper is an empirical study on the labor force in (Peninsular) Malaysia. Parametric and semiparametric estimated wage equations, which correct for sample selection bias, are used to assess the returns to education and extent of gender ‘discrimination’. To estimate in the semiparametric case the wage equation intercept, which is needed for the Oaxaca wage decomposition, consistently we apply the newly developed Andrews–Schafgans [Andrews, D.W.K., Schafgans, M.M.A., 1998, Semiparametric estimation of the intercept of a sample selection model, Review of Economic Studies, 65: 497–518.] estimator. The results suggest that ‘discrimination’ favoring men in Malaysia is still quite prevalent, while for Malays (the ‘sons of the soil’) the strong level of ‘discrimination’ favoring Malay men is negated by the semiparametric estimation results