Semiparametric estimation of a bivariate Tobit model

The existing semiparametric estimation literature has mainly focused on univariate Tobit models and no semiparametric estimation has been considered for bivariate Tobit models. In this paper, we consider semiparametric estimation of the bivariate Tobit model proposed by Amemiya (1974), under the independence condition without imposing any parametric restriction on the error distribution. Our estimator is shown to be consistent and asymptotically normal, and simulation results show that our estimator performs well in finite samples. It is also worth noting that while Amemiya’s (1974) instrumental variables estimator (IV) requires the normality assumption, our semiparametric estimator actually outperforms his IV estimator even when normality holds. Our approach can be extended to higher dimensional multivariate Tobit models.     

On nonparametric estimation of a hedonic price function

Recently, using mixed data on Canadian housing, Parmeter, Henderson, and Kumbhakar (Journal of Applied Econometrics 2007; 22 : 695–699) found that a nonparametric approach for estimating a hedonic house price function is superior to formerly suggested parametric and semiparametric specifications. We carefully reanalyze these specifications for this dataset by applying a recent nonparametric specification test and simulation‐based prediction comparisons. For the case at issue our results suggest that a previously proposed parametric specification does not have to be rejected and we illustrate how nonparametric methods provide valuable insights during all modeling steps. Copyright © 2010 John Wiley & Sons, Ltd.     

Estimating a generalized correlation coefficient for a generalized bivariate probit model

In this paper we consider semiparametric estimation of a generalized correlation coefficient in a generalized bivariate probit model. The generalized correlation coefficient provides a simple summary statistic measuring the relationship between the two binary decision processes in a general framework. Our semiparametric estimation procedure consists of two steps, combining semiparametric estimators for univariate binary choice models with the method of maximum likelihood for the bivariate probit model with nonparametrically generated regressors. The estimator is shown to be consistent and asymptotically normal. The estimator performs well in our simulation study.     

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$n$ 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.     

Semiparametric estimation of a hedonic price function

Previous work on the preferred specification of hedonic price models usually recommended a Box-Cox model. In this paper we note that any parametric model involves implicit restrictions and they can be reduced by using a semiparametric model. We estimate a benchmark parametric model which passes several common specification tests, before showing that a semiparametric model outperforms it significantly. In addition to estimating the model, we compare the predictions of the models by deriving the distribution of the predicted log(price) and then calculating the associated prediction intervals. Our data show that the semiparametric model provides more accurate mean predictions than the benchmark parametric model.     

Does Education Matter for Economic Growth?

Empirical growth regressions typically include mean years of schooling as a proxy for human capital. However, empirical research often finds that the sign and significance of schooling depends on the sample of observations or the specification of the model. We use a non‐parametric local‐linear regression estimator and a non‐parametric variable relevance test to conduct a rigorous and systematic search for significance of mean years of schooling by examining five of the most comprehensive schooling databases. Contrary to a few recent articles that have identified significant nonlinearities between education and growth, our results suggest that mean years of schooling is not a statistically relevant variable in growth regressions. However, we do find evidence (within a cross‐sectional framework), that educational achievement, measured by mean test scores, may provide a more reliable measure of human capital than mean years of schooling.     

A Semi‐Parametric Analysis of Two‐Sided Markets: An Application to the Local Daily Newspapers in the USA

This paper considers an empirical semiparametric model for two‐sided markets. Contrary to existing empirical literature on two‐sided markets, we specify network effects and probability distribution functions of net benefits of the two sides nonparametrically. We then estimate the model by nonparametric instrumental variables regression for local daily newspapers from the USA. We show that semiparametric specification is supported by the data and the network effects are neither linear nor monotonic. With a numerical illustration we demonstrate that the mark‐up of the newspaper on each side changes drastically with the nonlinearly specified network effects from the case with linear network effects. Copyright © 2015 John Wiley & Sons, Ltd.     

Estimation and model selection of semiparametric multivariate survival functions under general censorship

We study estimation and model selection of semiparametric models of multivariate survival functions for censored data, which are characterized by possibly misspecified parametric copulas and nonparametric marginal survivals. We obtain the consistency and root-n$n$ asymptotic normality of a two-step copula estimator to the pseudo-true copula parameter value according to KLIC, and provide a simple consistent estimator of its asymptotic variance, allowing for a first-step nonparametric estimation of the marginal survivals. We establish the asymptotic distribution of the penalized pseudo-likelihood ratio statistic for comparing multiple semiparametric multivariate survival functions subject to copula misspecification and general censorship. An empirical application is provided.     

Specification Sensitivity in Right‐Tailed Unit Root Testing for Explosive Behaviour

This article aims to provide some empirical guidelines for the practical implementation of right‐tailed unit root tests, focusing on the recursive right‐tailed ADF test of Phillips et al. (2011b). We analyze and compare the limit theory of the recursive test under different hypotheses and model specifications. The size and power properties of the test under various scenarios are examined and some recommendations for empirical practice are given. Some new results on the consistent estimation of localizing drift exponents are obtained, which are useful in assessing model specification. Empirical applications to stock markets illustrate these specification issues and reveal their practical importance in testing.     

Local multiplicative bias correction for asymmetric kernel density estimators

We consider semiparametric asymmetric kernel density estimators when the unknown density has support on [0,∞)$[0,\infty )$. We provide a unifying framework which relies on a local multiplicative bias correction, and contains asymmetric kernel versions of several semiparametric density estimators considered previously in the literature. This framework allows us to use popular parametric models in a nonparametric fashion and yields estimators which are robust to misspecification. We further develop a specification test to determine if a density belongs to a particular parametric family. The proposed estimators outperform rival non- and semiparametric estimators in finite samples and are easy to implement. We provide applications to loss data from a large Swiss health insurer and Brazilian income data.     

Estimating Engel curves under unit and item nonresponse

This paper estimates food Engel curves using data from the first wave of the Survey on Health, Aging and Retirement in Europe (SHARE). Our statistical model simultaneously takes into account selectivity due to unit and item nonresponse, endogeneity problems, and issues related to flexible specification of the relationship of interest. We estimate both parametric and semiparametric specifications of the model. The parametric specification assumes that the unobservables in the model follow a multivariate Gaussian distribution, while the semiparametric specification avoids distributional assumptions about the unobservables. Copyright © 2011 John Wiley & Sons, Ltd.     

Semiparametric hedonic price models: assessing the effects of agricultural nonpoint source pollution

In the area of environmental analysis using hedonic price models, we investigate the performance of various nonparametric and semiparametric specifications. The proposed model specifications are made up of two parts: a linear component for house characteristics and a non‐(semi)parametric component representing the nonlinear influence of environmental indicators on house prices. We adopt a general‐to‐specific search procedure, based on recent specification tests comparing the proposed specifications with a fully nonparametric benchmark model, to select the best model specification. An application of these semiparametric models to rural districts indicates that pollution resulting from intensive livestock farming has a significant nonlinear impact on house prices. Copyright © 2008 John Wiley & Sons, Ltd.     

Interval censored regression with fixed effects

This paper considers identification and estimation of a fixed-effects model with an interval-censored dependent variable. In each time period, the researcher observes the interval (with known endpoints) in which the dependent variable lies but not the value of the dependent variable itself. Two versions of the model are considered: a parametric model with logistic errors and a semiparametric model with errors having an unspecified distribution. In both cases, the error disturbances can be heteroskedastic over cross-sectional units as long as they are stationary within a cross-sectional unit; the semiparametric model also allows for serial correlation of the error disturbances. A conditional-logit-type composite likelihood estimator is proposed for the logistic fixed-effects model, and a composite maximum-score-type estimator is proposed for the semiparametric model. In general, the scale of the coefficient parameters is identified by these estimators, meaning that the causal effects of interest are estimated directly in cases where the latent dependent variable is of primary interest (e.g., pure data-coding situations). Monte Carlo simulations and an empirical application to birthweight outcomes illustrate the performance of the parametric estimator.     

Nonlinear regression models with single‐index heteroscedasticity

We consider nonlinear heteroscedastic single‐index models where the mean function is a parametric nonlinear model and the variance function depends on a single‐index structure. We develop an efficient estimation method for the parameters in the mean function by using the weighted least squares estimation, and we propose a “delete‐one‐component” estimator for the single‐index in the variance function based on absolute residuals. Asymptotic results of estimators are also investigated. The estimation methods for the error distribution based on the classical empirical distribution function and an empirical likelihood method are discussed. The empirical likelihood method allows for incorporation of the assumptions on the error distribution into the estimation. Simulations illustrate the results, and a real chemical data set is analyzed to demonstrate the performance of the proposed estimators.     

Bayesian semiparametric stochastic volatility modeling

This paper extends the existing fully parametric Bayesian literature on stochastic volatility to allow for more general return distributions. Instead of specifying a particular distribution for the return innovation, nonparametric Bayesian methods are used to flexibly model the skewness and kurtosis of the distribution while the dynamics of volatility continue to be modeled with a parametric structure. Our semiparametric Bayesian approach provides a full characterization of parametric and distributional uncertainty. A Markov chain Monte Carlo sampling approach to estimation is presented with theoretical and computational issues for simulation from the posterior predictive distributions. An empirical example compares the new model to standard parametric stochastic volatility models.     

Parametric bootstrap tests for continuous and discrete distributions

Statistical procedures based on the estimated empirical process are well known for testing goodness of fit to parametric distribution families. These methods usually are not distribution free, so that the asymptotic critical values of test statistics depend on unknown parameters. This difficulty may be overcome by the utilization of parametric bootstrap procedures. The aim of this paper is to prove a weak approximation theorem for the bootstrapped estimated empirical process under very general conditions, which allow both the most important continuous and discrete distribution families, along with most parameter estimation methods. The emphasis is on families of discrete distributions, and simulation results for families of negative binomial distributions are also presented.     

Efficient estimation of a multivariate multiplicative volatility model

We propose a multivariate generalization of the multiplicative volatility model of Engle and Rangel (2008), which has a nonparametric long run component and a unit multivariate GARCH short run dynamic component. We suggest various kernel-based estimation procedures for the parametric and nonparametric components, and derive the asymptotic properties thereof. For the parametric part of the model, we obtain the semiparametric efficiency bound. Our method is applied to a bivariate stock index series. We find that the univariate model of Engle and Rangel (2008) appears to be violated in the data whereas our multivariate model is more consistent with the data.     

Partially varying coefficient instrumental variables models

In this article, we study a new class of semiparametric instrumental variables models, in which the structural function has a partially varying coefficient functional form. Under this specification, the model is linear in the endogenous/exogenous components with unknown constant or functional coefficients. As a result, the ill‐posed inverse problem in a general non‐parametric model with continuous endogenous variables can be avoided. We propose a three‐step estimation procedure for estimating both constant and functional coefficients and establish their asymptotic properties such as consistency and asymptotic normality. We develop consistent estimators for their error variances. We demonstrate that the constant coefficient estimators achieve the optimal ‐convergence rate, and the functional coefficient estimators are oracle. In addition, efficiency issue of the parameter estimation is discussed and a simple efficient estimator is proposed. The proposed procedure is illustrated via a Monte Carlo simulation and an application to returns to education.     

Estimation of copula-based semiparametric time series models

This paper studies the estimation of a class of copula-based semiparametric stationary Markov models. These models are characterized by nonparametric marginal distributions and parametric copula functions, while the copulas capture all the scale-free temporal dependence of the processes. Simple estimators of the marginal distribution and the copula parameter are provided, and their asymptotic properties are established under easily verifiable conditions. These results are used to obtain root-n consistent and asymptotically normal estimators of important features of the transition distribution such as the (nonlinear) conditional moments and conditional quantiles. The semiparametric conditional quantile estimators are automatically monotonic across quantiles, which is attractive for portfolio conditional value-at-risk calculations.     

Conducting inference in semiparametric duration models under inequality restrictions on the shape of the hazard implied by job search theory

Using a four-month panel of revised Current Population Survey data from September–December 1993, we extend the class of semiparametric hazard models of the type first studied by Prentice and Gloeckler ( 1978 ), and brought to the attention of economists by Meyer ( 1988 , 1990 ), to incorporate inequality restrictions on the shape of the hazard. This extension enables us to test hypotheses regarding the shape of the hazard implied by search theory using duration data alone. These tests provide another link between the empirical and theoretical literatures on unemployment duration and job search. The GHK probability simulator makes it straightforward to generate approximate hypothesis test results, as simulation estimates of the probability under the null hypothesis are generated using the asymptotic normal approximation to the distribution of the hazard parameters obtained from maximum likelihood estimation. Importance sampling is used to conduct inference under the null and obtain exact finite sample estimates of the probability the null is satisfied. A new algorithm for maintaining stability of the importance weights is also developed. Copyright © 1999 John Wiley & Sons, Ltd.