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.     

Characterization of the asymptotic distribution of semiparametric M-estimators

This paper develops a concrete formula for the asymptotic distribution of two-step, possibly non-smooth semiparametric M-estimators under general misspecification. Our regularity conditions are relatively straightforward to verify and also weaker than those available in the literature. The first-stage nonparametric estimation may depend on finite dimensional parameters. We characterize: (1) conditions under which the first-stage estimation of nonparametric components do not affect the asymptotic distribution, (2) conditions under which the asymptotic distribution is affected by the derivatives of the first-stage nonparametric estimator with respect to the finite-dimensional parameters, and (3) conditions under which one can allow non-smooth objective functions. Our framework is illustrated by applying it to three examples: (1) profiled estimation of a single index quantile regression model, (2) semiparametric least squares estimation under model misspecification, and (3) a smoothed matching estimator.     

Nonparametric/semiparametric estimation and testing of econometric models with data dependent smoothing parameters

We consider nonparametric/semiparametric estimation and testing of econometric models with data dependent smoothing parameters. Most of the existing works on asymptotic distributions of a nonparametric/semiparametric estimator or a test statistic are based on some deterministic smoothing parameters, while in practice it is important to use data-driven methods to select the smoothing parameters. In this paper we give a simple sufficient condition that can be used to establish the first order asymptotic equivalence of a nonparametric estimator or a test statistic with stochastic smoothing parameters to those using deterministic smoothing parameters. We also allow for general weakly dependent data.     

Nonparametric IV estimation of local average treatment effects with covariates

In this paper nonparametric instrumental variable estimation of local average treatment effects (LATE) is extended to incorporate covariates. Estimation of LATE is appealing since identification relies on much weaker assumptions than the identification of average treatment effects in other nonparametric instrumental variable models. Including covariates in the estimation of LATE is necessary when the instrumental variable itself is confounded, such that the IV assumptions are valid only conditional on covariates. Previous approaches to handle covariates in the estimation of LATE relied on parametric or semiparametric methods. In this paper, a nonparametric estimator for the estimation of LATE with covariates is suggested that is root-n asymptotically normal and efficient.     

Nonparametric estimation and testing of fixed effects panel data models

In this paper we consider the problem of estimating nonparametric panel data models with fixed effects. We introduce an iterative nonparametric kernel estimator. We also extend the estimation method to the case of a semiparametric partially linear fixed effects model. To determine whether a parametric, semiparametric or nonparametric model is appropriate, we propose test statistics to test between the three alternatives in practice. We further propose a test statistic for testing the null hypothesis of random effects against fixed effects in a nonparametric panel data regression model. Simulations are used to examine the finite sample performance of the proposed estimators and the test statistics.     

Statistical inference for moving‐average Lévy‐driven processes: Fourier‐based approach

We consider a new method of semiparametric statistical estimation for the continuous‐time moving‐average Lévy processes. We derive the convergence rates of the proposed estimators and show that these rates are optimal in minimax sense.     

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.     

Consistent estimation of technical and allocative efficiencies for a semiparametric stochastic cost frontier with shadow input prices

Conventional parametric stochastic cost frontier models are likely to suffer from biased inferences due to misspecification and the ignorance of allocative efficiency (AE). To fill up the gap in the literature, this article proposes a semiparametric stochastic cost frontier with shadow input prices that combines a parametric portion with a nonparametric portion and that allows for the presence of both technical efficiency (TE) and AE. The introduction of AE and the nonparametric function into the cost function complicates substantially the estimation procedure. We develop a new estimation procedure that leads to consistent estimators and valid TE and AE measures, which are proved by conducting Monte Carlo simulations.     

Asymptotic inference from multi-stage samples

I develop a GMM-based framework for asymptotic inference to analyze data from surveys whose designs involve stratification and clustering. I set up the estimation problem, derive the appropriate asymptotic distribution theory as the number of clusters per stratum tends to infinity and compute asymptotic standard errors that are robust to sample-design effects. The analysis is then extended to nonparametric regression and to semiparametric estimation based on U-processes. Empirical illustrations are provided using consumption expenditure data from the complexly designed Indian national household survey.     

Efficient estimation in dynamic conditional quantile models

In this paper we consider the problem of semiparametric efficient estimation in conditional quantile models with time series data. We construct an M-estimator which achieves the semiparametric efficiency bound recently derived by Komunjer and Vuong (forthcoming). Our efficient M-estimator is obtained by minimizing an objective function which depends on a nonparametric estimator of the conditional distribution of the variable of interest rather than its density. The estimator is new and not yet seen in the literature. We illustrate its performance through a Monte Carlo experiment.     

Testing semiparametric conditional moment restrictions using conditional martingale transforms

This paper studies conditional moment restrictions that contain unknown nonparametric functions, and proposes a general method of obtaining asymptotically distribution-free tests via martingale transforms. Examples of such conditional moment restrictions are single index restrictions, partially parametric regressions, and partially parametric quantile regressions. This paper introduces a conditional martingale transform that is conditioned on the variable in the nonparametric function, and shows that we can generate distribution-free tests of various semiparametric conditional moment restrictions using this martingale transform. The paper proposes feasible martingale transforms using series estimation and establishes their asymptotic validity. Some results from a Monte Carlo simulation study are presented and discussed.     

Model specification test with correlated but not cointegrated variables

Many macroeconomic and financial variables show highly persistent and correlated patterns but are not necessarily cointegrated. Recently,  Sun et al. (2011) propose using a semiparametric varying coefficient approach to capture correlations between integrated but non cointegrated variables. Due to the complication arising from the integrated disturbance term and the semiparametric functional form, consistent estimation of such a semiparametric model requires stronger conditions than usually needed for consistent estimation for a linear (spurious) regression model, or a semiparametric varying coefficient model with a stationary disturbance. Therefore, it is important to develop a testing procedure to examine for a given data set, whether linear relationship holds or not, while allowing for the disturbance being an integrated process. In this paper we propose two test statistics for detecting linearity against semiparametric varying coefficient alternative specification. Monte Carlo simulations are used to examine the finite sample performances of the proposed tests.     

Semiparametric econometrics: A survey

Semiparametric econometric models contain both parametric and nonparametric components, reflecting in some fashion what has been learned from economic theory and previous empirical experience, and what remains unknown. They raise such questions as how well the parametric component can be estimated, and how to construct rules of inference with good statistical properties. The paper attempts to survey the econometric and most relevant statistical literature on semiparametric inference, and includes a partial bibliography.     

Statistical Inference in Nonparametric Frontier Models: The State of the Art

Efficiency scores of firms are measured by their distance to an estimated production frontier. The economic literature proposes several nonparametric frontier estimators based on the idea of enveloping the data (FDH and DEA-type estimators). Many have claimed that FDH and DEA techniques are non-statistical, as opposed to econometric approaches where particular parametric expressions are posited to model the frontier. We can now define a statistical model allowing determination of the statistical properties of the nonparametric estimators in the multi-output and multi-input case. New results provide the asymptotic sampling distribution of the FDH estimator in a multivariate setting and of the DEA estimator in the bivariate case. Sampling distributions may also be approximated by bootstrap distributions in very general situations. Consequently, statistical inference based on DEA/FDH-type estimators is now possible. These techniques allow correction for the bias of the efficiency estimators and estimation of confidence intervals for the efficiency measures. This paper summarizes the results which are now available, and provides a brief guide to the existing literature. Emphasizing the role of hypotheses and inference, we show how the results can be used or adapted for practical purposes.     

NONPARAMETRIC AND SEMIPARAMETRIC PANEL DATA MODELS: RECENT DEVELOPMENTS

In this paper, we provide an intensive review of the recent developments for semiparametric and fully nonparametric panel data models that are linearly separable in the innovation and the individual-specific term. We analyze these developments under two alternative model specifications: fixed and random effects panel data models. More precisely, in the random effects setting, we focus our attention in the analysis of some efficiency issues that have to do with the so-called working independence condition. This assumption is introduced when estimating the asymptotic variance–covariance matrix of nonparametric estimators. In the fixed effects setting, to cope with the so-called incidental parameters problem, we consider two different estimation approaches: profiling techniques and differencing methods. Furthermore, we are also interested in the endogeneity problem and how instrumental variables are used in this context. In addition, for practitioners, we also show different ways of avoiding the so-called curse of dimensionality problem in pure nonparametric models. In this way, semiparametric and additive models appear as a solution when the number of explanatory variables is large.     

Robust and consistent estimation of nonlinear errors-in-variables models

This paper considers the consistent estimation of nonlinear errors-in-variables models. It adopts the functional modeling approach by assuming that the true but unobserved regressors are random variables but making no parametric assumption on the distribution from which the latent variables are drawn. This paper shows how the information extracted from the replicate measurements can be used to identify and consistently estimate a general nonlinear errors-in-variables model. The identification is established through characteristic functions. The estimation procedure involves nonparametric estimation of the conditional density of the latent variables given the measurements using the identification results at the first stage, and at the second stage, a semiparametric nonlinear least-squares estimator is proposed. The consistency of the proposed estimator is also established. Finite sample performance of the estimator is investigated through a Monte Carlo study.     

A regularization approach to the many instruments problem

This paper focuses on the estimation of a finite dimensional parameter in a linear model where the number of instruments is very large or infinite. In order to improve the small sample properties of standard instrumental variable (IV) estimators, we propose three modified IV estimators based on three different ways of inverting the covariance matrix of the instruments. These inverses involve a regularization or smoothing parameter. It should be stressed that no restriction on the number of instruments is needed and that all the instruments are used in the estimation. We show that the three estimators are asymptotically normal and attain the semiparametric efficiency bound. Higher-order analysis of the MSE reveals that the bias of the modified estimators does not depend on the number of instruments. Finally, we suggest a data-driven method for selecting the regularization parameter. Interestingly, our regularization techniques lead to a consistent nonparametric estimation of the optimal instrument.     

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.     

Quadratic semiparametric Von Mises calculus

We discuss a new method of estimation of parameters in semiparametric and nonparametric models. The method is based on U-statistics constructed from quadratic influence functions. The latter extend ordinary linear influence functions of the parameter of interest as defined in semiparametric theory, and represent second order derivatives of this parameter. For parameters for which the matching cannot be perfect the method leads to a bias-variance trade-off, and results in estimators that converge at a slower than n ^?1/2-rate. In a number of examples the resulting rate can be shown to be optimal. We are particularly interested in estimating parameters in models with a nuisance parameter of high dimension or low regularity, where the parameter of interest cannot be estimated at n ^?1/2-rate.     

Efficient local IV estimation of an empirical auction model

In this paper we examine semiparametric efficiency bounds and efficient estimators for the case of a linear local instrument variable (LIV) model under the assumptions studied in Abadie et al. (2002). We apply the semiparametrically efficient estimation method to analyze the relation between bid dispersion and early bidding in an online auction dataset, which is collected from a natural experiment conducted in Nekipelov (2007). The results confirm the theoretical findings developed in Nekipelov (2007). The semiparametric efficient estimation procedure substantially improves the statistical significance of the effect of jump bidding on bid dispersion.