Endogeneity in Semiparametric Binary Response Models

This paper develops and implements semiparametric methods for estimating binary response (binary choice) models with continuous endogenous regressors. It extends existing results on semiparametric estimation in single-index binary response models to the case of endogenous regressors. It develops a control function approach to account for endogeneity in triangular and fully simultaneous binary response models. The proposed estimation method is applied to estimate the income effect in a labour market participation problem using a large micro data-set from the British Family Expenditure Survey. The semiparametric estimator is found to perform well, detecting a significant attenuation bias. The proposed estimator is contrasted to the corresponding probit and linear probability specifications.     

Intrafirm human capital externalities and selection bias

This article investigates the existence of intrafirm human capital externalities in the Spanish economy. In doing so, it focusses on two estimation issues. First, a semiparametric methodology is used to estimate externalities in a more flexible way that allows to affect all parameters in the equation. Second, two approaches to control for selection bias are designed for use in cross-section data. Our results show a higher externality effect on wages when using the semi parametric approach as compared to the standard estimation approach. Additionally, the estimations even when controlling for selection bias give evidence of externalities.     

Semiparametric Bayesian estimation of mixed count regression models

This paper develops semiparametric Bayesian estimation approach for Poisson regression models with unobserved heterogeneity of unknown density. This approach is computationally efficient and allows automatic adaptation of the approximating density to data during estimation. Simulations show the estimator performs well.     

12034/8GraphicAbstract.png

1 School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an, China 2 State IJR Center of Aerospace Design and Additive Manufacturing, Northwestern Polytechnical University, Xi’an, China 3 School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an, China     

Matching using semiparametric propensity scores

This paper considers the application of semiparametric methods to estimate propensity scores or probabilities of program participation, which are central to certain program evaluation methods. To evaluate the practical benefits, we first conduct a Monte Carlo study. Second, we use data from the NSW experiment, CPS, and PSID. We compare treatment effect and evaluation bias estimates using propensity scores estimated from parametric logit, semiparametric single index, and semiparametric binary quantile regression models. Our results suggest that it is important to account for very general forms of heterogeneity in (semiparametric) estimation of the propensity score, particularly when the treatment effects vary in an unsystematic manner with the true propensity score.     

Efficient Estimation of Additive Partially Linear Models

I consider the problem of estimating an additive partially linear model using general series estimation methods with polynomial and splines as two leading cases. I show that the finite-dimensional parameter is identified under weak conditions. I establish the root-n-normality result for the finite-dimensional parameter in the linear part of the model and show that it is asymptotically more efficient than a semiparametric estimator that ignores the additive structure. When the error is conditional homoskedastic, my finite-dimensional parameter estimator reaches the semiparametric efficiency bound. Efficient estimation when the error is conditional heteroskedastic is also discussed.     

Estimation of nonparametric inefficiency effects stochastic frontier models with an application to British manufacturing

The purpose of this paper is to propose a simple stochastic frontier model with a non-parametric specification for covariates affecting the mean of technical inefficiency. We derive a simple two-step semiparametric estimation procedure to estimate the frontier parameters as well as the mean of the technical inefficiency. The consistency of the estimator and its asymptotic normality are shown. The proposed method is illustrated using a large panel data set of British manufacturing firms.     

The asymptotic efficiency of semiparametric estimators for censored linear regression models

This paper presents numerical comparisons of the asymptotic mean square estimation errors of semiparametric generalized least squares (SGLS), quantite, symmetrically censored least squares (SCLS), and tobit maximum likelihood estimators of the slope parameters of censored linear regression models with one explanatory variable. The results indicate that the SCLS estimator is less efficient than the other two semiparametric estimators. The SGLS estimator is more efficient than quantile estimators when the tails of the distribution of the random component of the model are not too thick and the probability of censoring is not too large. The most efficient semiparametric estimators usually have smaller mean square estimation errors than does the tobit estimator when the random component of the model is not normally distributed and the sample size is 500–1,000 or more.     

Regulatory design and technical efficiency: public transport in France

The provision of local public transport in France involves private and public firms and the use of incentive contracts to regulate them. We study the effect of these institutional features on the sector’s efficiency using a long panel data of firms, with a two-stage estimation procedure. First, we use nonparametric data envelopment analysis techniques to estimate input usage efficiency, following a conditional approach that controls for differences in the environments in which the firms operate. Second, we estimate semiparametric censored regressions, using fixed effects to control for unobserved sources of heterogeneity. Our results point to a differential effect of private and mixed public-private companies. In particular, having the performance of public operators as the benchmark, efficiency is relatively higher for private firms, but lower when the service is delegated to a mixed public-private firm. In the latter case, the effects diverge by contract type: when the contract is of the cost reimbursement type, performance is lower than the public firm benchmark, while for other contract types, there are no statistically significant differences.     

A NOTE ON SEMIPARAMETRIC ESTIMATION OF FINITE MIXTURES OF DISCRETE CHOICE MODELS WITH APPLICATION TO GAME THEORETIC MODELS*

We view a game abstractly as a semiparametric mixture distribution and study the semiparametric efficiency bound of this model. Our results suggest that a key issue for inference is the number of equilibria compared to the number of outcomes. If the number of equilibria is sufficiently large compared to the number of outcomes, root‐n consistent estimation of the model will not be possible. We also provide a simple estimator in the case when the efficiency bound is strictly above zero.     

Semiparametric Estimation of Simultaneous-Equation Microeconometric Models with Index Restrictions

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.     

Likelihood Inference on Semiparametric Models: Average Derivative and Treatment Effect

Over the past few decades, much progress has been made in semiparametric modelling and estimation methods for econometric analysis. This paper is concerned with inference (i.e. confidence intervals and hypothesis testing) in semiparametric models. In contrast to the conventional approach based on t‐ratios, we advocate likelihood‐based inference. In particular, we study two widely applied semiparametric problems, weighted average derivatives and treatment effects, and propose semiparametric empirical likelihood and jackknife empirical likelihood methods. We derive the limiting behaviour of these empirical likelihood statistics and investigate their finite sample performance through Monte Carlo simulation. Furthermore, we extend the (delete‐1) jackknife empirical likelihood toward the delete‐d version with growing d and establish general asymptotic theory. This extension is crucial to deal with non‐smooth objects, such as quantiles and quantile average derivatives or treatment effects, due to the well‐known inconsistency phenomena of the jackknife under non‐smoothness.     

SEMINONPARAMETRIC MAXIMUM LIKELIHOOD ESTIMATION OF CONDITIONAL MOMENT RESTRICTION MODELS*

This article studies estimation of a conditional moment restriction model with the seminonparametric maximum likelihood approach proposed by Gallant and Nychka (Econometrica 55 (March 1987), 363–90). Under some sufficient conditions, we show that the estimator of the finite dimensional parameter θ is asymptotically normally distributed and attains the semiparametric efficiency bound and that the estimator of the density function is consistent under L₂ norm. Some results on the convergence rate of the estimated density function are derived. An easy to compute covariance matrix for the asymptotic covariance of the θ estimator is presented.     

ESTIMATION WITH CENSORED REGRESSORS: BASIC ISSUES*

We study issues that arise for estimation of a linear model when a regressor is censored. We discuss the efficiency losses from dropping censored observations, and illustrate the losses for bound censoring. We show that the common practice of introducing a dummy variable to “correct for” censoring does not correct bias or improve estimation. We show how censored observations generally have zero semiparametric information, and we discuss implications for estimation. We derive the likelihood function for a parametric model of mixed bound‐independent censoring, and apply that model to the estimation of wealth effects on consumption.     

Semiparametric Bayesian inference of the Kuznets hypothesis

In contrast to the parametric (quadratic) specification used for examining the Kuznets hypothesis, this study relies on the semiparametric Bayesian inference of the partially linear regression to re-assess the validity of an inverted-U shape of the Kuznets curve. The simple framework permits us to perform estimation and model comparison in a unified way. Empirical results using cross-sectional data on 75 countries indicate that there exists an (approximately) inverted-√, hence, asymmetric relation between inequality and per capita GDP. Moreover, judged by the Bayes factor, overwhelming evidence is found in favor of our semiparametric specification. Finally, robustness check using alternative measure of inequality and pool data confirms our findings.     

Nonlinearity in dynamic adjustment: Semiparametric estimation of panel labor supply

We estimate a semiparametric dynamic panel data model by the local linear kernel method and we interpret the slope of the nonparametric component function as a varying slope coefficient. Thus, the slope coefficient is a smooth, but otherwise unknown, function of some of the regressors. A Monte Carlo experiment is reported to examine the finite sample performance of the local linear estimator. We apply the estimation method to a labor supply equation for men from the triannual Survey of Income and Program Participation (SIPP). Specification tests based on the estimated labor supply elasticities, partial adjustment coefficients, and residuals demonstrate the improvements from a semiparametric partially linear model. Our empirical results point to a need by economists to revisit the issue of the speed of labor market adjustment to policy induced shifts in labor demand and to take more formal econometric account of heterogeneity in wage effects when studying the distributional consequences of tax reforms for labor supply earnings. First version received: July 2000/Final version received: January 2001     

Poverty analysis with missing data: alternative estimators compared

Poverty models are generally estimated by using sample surveys affected by missing data problems. Most methods proposed to take account of missing data problems consider point estimators which typically impose restrictive assumptions. However, it is possible to identify a range of logically possible values for the poverty probability, an identification interval, without imposing any assumption. It is then of interest to check whether the point estimates lie within the identification interval. This is a way to check the validity of the assumptions imposed by point estimators. Using the ECHP we perform this check to assess different estimation methods.     

Semiparametric versus parametric hedonic wine price models: an empirical investigation

In this article, we conduct formal statistical tests to compare a semiparametric hedonic wine price model with its parametric counterpart using a Canadian data set. The relevant test results turn out to be overwhelmingly in favour of the semiparametric specification. The estimated semiparametric model also provides clear evidence of nonlinearity between wine prices and quality when other wine attributes are controlled for.     

Testing for structural breaks in panel varying coefficient models: with an application to OECD health expenditure

In this article, we propose a model selection approach for testing structural breaks in a semiparametric panel varying coefficient model. Monte Carlo evidence shows that the proposed model selection approach performs well in finite sample settings. Applying the method to an empirical data, we find evidence of structural breaks in Organisation for Economic Co-operation and Development (OECD) health expenditure data by allowing for income elasticity to be state (income)-dependent. The relationship between health expenditure and income is subject to two types of structural changes: smooth changes over income and structural breaks in the time dimension. The findings hold for both foreign exchange rate-converted and Purchasing Power Parity-converted expenditure and GDP.     

Semiparametric estimation of conditional mean functions with missing data

A new semiparametric estimator for estimating conditional expectation functions from incomplete data is proposed, which integrates parametric regression with nonparametric matching estimators. Besides its applicability to missing data situations due to non-response or attrition, the estimator can also be used for analyzing treatment effect heterogeneity and statistical treatment rules, where data on potential outcomes is missing by definition. By combining moments from a parametric specification with nonparametric estimates of mean outcomes in the non-responding population within a GMM framework, the estimator seeks to balance a good fit in the responding population with low bias in the non-responding population. The estimator is applied to analyzing treatment effect heterogeneity among Swedish rehabilitation programmes.

---