Carlos Martins-Filho

Nonparametric regression estimation with general parametric error covariance

The asymptotic distribution for the local linear estimator in nonparametric regression models is established under a general parametric error covariance with dependent and heterogeneously distributed regressors. A two-step estimation procedure that incorporates the parametric information in the error covariance matrix is proposed. Sufficient conditions for its asymptotic normality are given and its efficiency relative to the local linear estimator is established. We give examples of how our results are useful in some recently studied regression models. A Monte Carlo study confirms the asymptotic theory predictions and compares our estimator with some recently proposed alternative estimation procedures.

Estimation of Value-at-Risk and Expected Shortfall based on Nonlinear Models of Return Dynamics and Extreme Value Theory

We propose an estimation procedure for value-at-risk (VaR) and expected shortfall (TailVaR) for conditional distributions of a time series of returns on a financial asset. Our approach combines a local polynomial estimator of conditional mean and volatility functions in a conditional heterocedastic autoregressive nonlinear (CHARN) model with Extreme Value Theory for estimating quantiles of the conditional distribution. We investigate the finite sample properties of our method and contrast them with alternatives, including the method recently proposed by McNeil and Frey (2000), in an extensive Monte Carlo study. The method we propose outperforms the estimators currently available in the literature. An evaluation based on backtesting was also performed.

Demand and Pricing of Telecommunications Services: Evidence and Welfare Implications

Although telephone pricing has received increasing attention in recent years, the geographic patterns of telephone pricing and the corresponding economic consequences of those patterns have remained perplexing to consumers and policymakers and largely unaddressed by economists. In this article we first specify a model of the demand for short (intraLATA) long distance calling. We then draw upon data made available by the recent adoption of extended area service (EAS) in four metropolitan areas to empirically measure the structure of inter-exchange telephone demand. Given these estimates, and a conceptual framework for analyzing the economic welfare effects, we were able to quantify the consumer-surplus effects of alternative pricing policies. The empirical results indicate that consumer surplus is noticeably enhanced by adopting EAS. But the net economic welfare effects are shown to be sensitive to, among other things, the level of price-cost margins prevailing prior to the implementation of EAS.

A CLASS OF IMPROVED PARAMETRICALLY GUIDED NONPARAMETRIC REGRESSION ESTIMATORS

In this article we define a class of estimators for a nonparametric regression model with the aim of reducing bias. The estimators in the class are obtained via a simple two-stage procedure. In the first stage, a potentially misspecified parametric model is estimated and in the second stage the parametric estimate is used to guide the derivation of a final semiparametric estimator. Mathematically, the proposed estimators can be thought as the minimization of a suitably defined Cressie–Read discrepancy that can be shown to produce conventional nonparametric estimators, such as the local polynomial estimator, as well as existing two-stage multiplicative estimators, such as that proposed by Glad (1998). We show that under fairly mild conditions the estimators in the proposed class are asymptotically normal and explore their finite sample (simulation) behavior.

Seemingly unrelated regressions under additive heteroscedasticity Theory and share equation applications

Abstract We derive consistent, asymptotically efficient, and asymptotically normal estimators for SUR systems that have additive heteroscedastic contemporaneous correlation. Both our estimator for the location vector and the parameters of the covariance matrix possess these properties. The procedure is superior to other methods because we use GLS to estimate the parameters of the covariance matrix. Our method also permits the use of cross-equation parameter restrictions. We discuss how this type of heteroscedasticity arises naturally in share equation systems and random coefficient models, and how these models can be uniquely estimated with our two-step estimation technique.

A model of vertical differentiation, brand loyalty, and persuasive advertising

In this paper, we analyze the impact of advertising and quality decisions on price competition in a duopoly setting. Firms are able to differentiate their products vertically and use persuasive advertising to increase consumer brand loyalty. The model predicts that the high quality firm will advertise more intensively than the low quality firm in both covered and uncovered markets. Because consumers are assumed to be informed about product characteristics, advertising neither signals high quality nor discourages firms from lowering product quality unexpectedly. Instead, advertising is persuasive and is used to dampen price competition, enabling firms to avoid the Bertrand Paradox. This model provides one explanation for the coexistence of name (heavily advertised) and generic (sparsely advertised) brands.

Semiparametric Stochastic Frontier Estimation via Profile Likelihood

We consider the estimation of a nonparametric stochastic frontier model with composite error density which is known up to a finite parameter vector. Our primary interest is on the estimation of the parameter vector, as it provides the basis for estimation of firm specific (in)efficiency. Our frontier model is similar to that of Fan et al. (1996), but here we extend their work in that: a) we establish the asymptotic properties of their estimation procedure, and b) propose and establish the asymptotic properties of an alternative estimator based on the maximization of a conditional profile likelihood function. The estimator proposed in Fan et al. (1996) is asymptotically normally distributed but has bias which does not vanish as the sample size n → ∞. In contrast, our proposed estimator is asymptotically normally distributed and correctly centered at the true value of the parameter vector. In addition, our estimator is shown to be efficient in a broad class of semiparametric estimators. Our estimation procedure provides a fast converging alternative to the recently proposed estimator in Kumbhakar et al. (2007). A Monte Carlo study is performed to shed light on the finite sample properties of these competing estimators.

A Unified Approach to Asymptotic Equivalence of Aitken and Feasible Aitken Instrumental Variables Estimators

Asymptotic equivalence of Aitken and feasible Aitken estimators in linear models with nonscalar identity error covariance matrices is usually established in a tedious case-by-case manner. Some general sufficient conditions for this equivalence exist but there are problems with the extant conditions. These problems are discussed and new widely applicable sufficient conditions are presented and applied to a variety of error structures. Copyright 1994 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

High order conditional quantile estimation based on nonparametric models of regression

We consider the estimation of a high order quantile associated with the conditional distribution of a regressand in a nonparametric regression model. Our estimator is inspired by Pickands (1975) where it is shown that arbitrary distributions which lie in the domain of attraction of an extreme value type have tails that, in the limit, behave as generalized Pareto distributions (GPD). Smith (1987) has studied the asymptotic properties of maximum likelihood (ML) estimators for the parameters of the GPD in this context, but in our paper the relevant random variables used in estimation are standardized residuals from a first stage kernel based nonparametric estimation. We obtain convergence in probability and distribution of the residual based ML estimator for the parameters of the GPD as well as the asymptotic distribution for a suitably defined quantile estimator. A Monte Carlo study provides evidence that our estimator behaves well in finite samples and is easily implementable. Our results have direct application in finance, particularly in the estimation of conditional Value-at-Risk, but other researchers in applied fields such as insurance will also find the results useful.

On Asymptotic Normality of the Local Polynomial Regression Estimator with Stochastic Bandwidths

Nonparametric density and regression estimators commonly depend on a bandwidth. The asymptotic properties of these estimators have been widely studied when bandwidths are non stochastic. In practice, however, in order to improve finite sample performance of these estimators, bandwidths are selected by data driven methods, such as cross-validation or plug-in procedures. As a result, nonparametric estimators are usually constructed using stochastic bandwidths. In this article, we establish the asymptotic equivalence in probability of local polynomial regression estimators under stochastic and nonstochastic bandwidths. Our result extends previous work by Boente and Fraiman (1995) and Ziegler (2004).