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This chapter proposes a simple procedure to estimate average derivatives in nonparametric regression models with incomplete responses. The method consists of replacing the responses with an appropriately weighted version and then use local polynomial estimation for the average derivatives. The resulting estimator is shown to be asymptotically normal, and an estimator of its asymptotic variance–covariance matrix is also shown to be consistent. Monte Carlo experiments show that the proposed estimator has desirable finite sample properties.

Peers and friends are among the most influential social forces affecting adolescent behavior. In this chapter, the authors investigate peer effects on post high school career decisions and on school choice. The authors define peers as students who are in the same classes and social clubs and measure peer effects as spatial dependence among them. Utilizing recent developments in spatial econometrics, the authors formalize a spatial multinomial choice model in which individuals are spatially dependent in their preferences. The authors estimate the model via pseudo maximum likelihood using data from the Texas Higher Education Opportunity Project. The authors do find that individuals are positively correlated in their career and college preferences and examine how such dependencies impact decisions directly and indirectly as peer effects are allowed to reverberate through the social network in which students reside.

Applied econometric analysis is often performed using data collected from large-scale surveys. These surveys use complex sampling plans in order to reduce costs and increase the estimation efficiency for subgroups of the population. These sampling plans result in unequal inclusion probabilities across units in the population. The purpose of this paper is to derive the asymptotic properties of a design-based nonparametric regression estimator under a combined inference framework. The nonparametric regression estimator considered is the local constant estimator. This work contributes to the literature in two ways. First, it derives the asymptotic properties for the multivariate mixed-data case, including the asymptotic normality of the estimator. Second, I use least squares cross-validation for selecting the bandwidths for both continuous and discrete variables. I run Monte Carlo simulations designed to assess the finite-sample performance of the design-based local constant estimator versus the traditional local constant estimator for three sampling methods, namely, simple random sampling, exogenous stratification and endogenous stratification. Simulation results show that the estimator is consistent and that efficiency gains can be achieved by weighting observations by the inverse of their inclusion probabilities if the sampling is endogenous.

We investigate the evolution of corporate risk management practices in Slovenian non-financial firms in the period 2004–2009 and compare the findings several surveys conducted for other countries. We mail questionaires to non-financial companies, where the target group included non-financial companies listed on Ljubljana Stock Exchange and the largest exporting companies in Slovenia. We find that the current use of derivatives for hedging purposes is still at a lower level than in the majority of developed countries. The great expansion of Slovenian economy in the period 2004–2008, the development of Slovenian financial system, the convergence of Slovenian and EU accounting standards and recent financial crisis did not sufficiently induce Slovenian firms to adopt risk management practices. The most often stated reasons for the low use of derivatives are (1) insufficient risk exposure, (2) problems with the evaluation and monitoring of derivatives and (3) the costs associated with the implementation of derivatives programme. In our opinion, the institutional environment in Slovenia does not induce managers to undertake proper risk management activities. We argue that not only managers, but also owners and creditors should be more accountable for the decisions they take (or do not take).

For kernel-based estimators, smoothness conditions ensure that the asymptotic rate at which the bias goes to zero is determined by the kernel order. In a finite sample, the leading term in the expansion of the bias may provide a poor approximation. We explore the relation between smoothness and bias and provide estimators for the degree of the smoothness and the bias. We demonstrate the existence of a linear combination of estimators whose trace of the asymptotic mean-squared error is reduced relative to the individual estimator at the optimal bandwidth. We examine the finite-sample performance of a combined estimator that minimizes the trace of the MSE of a linear combination of individual kernel estimators for a multimodal density. The combined estimator provides a robust alternative to individual estimators that protects against uncertainty about the degree of smoothness.

The asymptotic bias and variance of a general class of local polynomial estimators of M-regression functions are studied over the whole compact support of the multivariate covariate under a minimal assumption on the support. The support assumption ensures that the vicinity of the boundary of the support will be visited by the multivariate covariate. The results show that like in the univariate case, multivariate local polynomial estimators have good bias and variance properties near the boundary. For the local polynomial regression estimator, we establish its asymptotic normality near the boundary and the usual optimal uniform convergence rate over the whole support. For local polynomial quantile regression, we establish a uniform linearization result which allows us to obtain similar results to the local polynomial regression. We demonstrate both theoretically and numerically that with our uniform results, the common practice of trimming local polynomial regression or quantile estimators to avoid “the boundary effect” is not needed.

Estimators for derivatives associated with a density function can be useful in identifying its modes and inflection points. In addition, these estimators play an important role in plug-in methods associated with bandwidth selection in nonparametric kernel density estimation. In this paper, we extend the nonparametric class of density estimators proposed by Mynbaev and Martins-Filho (2010) to the estimation of m-order density derivatives. Contrary to some existing derivative estimators, the estimators in our proposed class have a full asymptotic characterization, including uniform consistency and asymptotic normality. An expression for the bandwidth that minimizes an asymptotic approximation for the estimators’ integrated squared error is provided. A Monte Carlo study sheds light on the finite sample performance of our estimators and contrasts it with that of density derivative estimators based on the classical Rosenblatt–Parzen approach.

We consider a semiparametric panel stochastic frontier model where one-sided firm effects representing inefficiencies are correlated with the regressors. A form of the Chamberlain-Mundlak device is used to relate the logarithm of the effects to the regressors resulting in a lognormal distribution for the effects. The function describing the technology is modeled nonparametrically using penalized splines. Both Bayesian and non-Bayesian approaches to estimation are considered, with an emphasis on Bayesian estimation. A Monte Carlo experiment is used to investigate the consequences of ignoring correlation between the effects and the regressors, and choosing the wrong functional form for the technology.

This paper examines Aman Ullah’s contributions to robust inference, finite sample econometrics, nonparametrics and semiparametrics, and panel and spatial models. His early works on robust inference and finite sample theory were mostly motivated by his thesis advisor, Professor Anirudh Lal Nagar. They eventually led to his most original rethinking of many statistics and econometrics models that developed into the monograph Finite Sample Econometrics published in 2004. His desire to relax distributional and functional-form assumptions lead him in the direction of nonparametric estimation and he summarized his views in his most influential textbook Nonparametric Econometrics (with Adrian Pagan) published in 1999 that has influenced a whole generation of econometricians. His innovative contributions in the areas of seemingly unrelated regressions, parametric, semiparametric and nonparametric panel data models, and spatial models have also inspired a larger literature on nonparametric and semiparametric estimation and inference and spurred on research in robust estimation and inference in these and related areas.

We present a new procedure for nonparametric Bayesian estimation of regression functions. Specifically, our method makes use of an idea described in Frühwirth-Schnatter and Wagner (2010) to impose linearity exactly (conditional upon an unobserved binary indicator), yet also permits departures from linearity while imposing smoothness of the regression curves. An advantage of this approach is that the posterior probability of linearity is essentially produced as a by-product of the procedure. We apply our methods in both generated data experiments as well as in an illustrative application involving the impact of body mass index (BMI) on labor market earnings.