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The R environment for statistical computing and graphics (R Development Core Team, 2008) offers practitioners a rich set of statistical methods ranging from random number generation and optimization methods through regression, panel data, and time series methods, by way of illustration. The standard R distribution (base R) comes preloaded with a rich variety of functionality useful for applied econometricians. This functionality is enhanced by user-supplied packages made available via R servers that are mirrored around the world. Of interest in this chapter are methods for estimating nonparametric and semiparametric models. We summarize many of the facilities in R and consider some tools that might be of interest to those wishing to work with nonparametric methods who want to avoid resorting to programming in C or Fortran but need the speed of compiled code as opposed to interpreted code such as Gauss or Matlab by way of example. We encourage those working in the field to strongly consider implementing their methods in the R environment thereby making their work accessible to the widest possible audience via an open collaborative forum.

The link between the magnitude of a bandwidth and the relevance of the corresponding covariate in a regression has recently garnered theoretical attention. Theory suggests that variables included erroneously in a regression will be automatically removed when bandwidths are selected via cross-validation procedure. However, the connections between the bandwidths of the variables that are smoothed away and the insights from these same variables when properly tested for statistical significance have not been previously studied. This paper proposes a variety of simulation exercises to examine the relative performance of both cross-validated bandwidths and individual and joint tests of significance. We focus on settings where the hypothesis of interest may focus on a single data type (e.g., continuous only) or a mix of discrete and continuous variables. Moreover, we propose an extension of a well-known kernel smoothing significance test to handle mixed data types. Our results suggest that individual tests of significance and variable-specific bandwidths are very close in performance, but joint tests and joint bandwidth recognition produce substantially different results. This underscores the importance of testing for joint significance when one is trying to arrive at the final nonparametric model of interest.

We propose a local linear functional coefficient estimator that admits a mix of discrete and continuous data for stationary time series. Under weak conditions our estimator is asymptotically normally distributed. A small set of simulation studies is carried out to illustrate the finite sample performance of our estimator. As an application, we estimate a wage determination function that explicitly allows the return to education to depend on other variables. We find evidence of the complex interacting patterns among the regressors in the wage equation, such as increasing returns to education when experience is very low, high return to education for workers with several years of experience, and diminishing returns to education when experience is high. Compared with the commonly used parametric and semiparametric methods, our estimator performs better in both goodness-of-fit and in yielding economically interesting interpretation.

Economic conditions such as convexity, homogeneity, homotheticity, and monotonicity are all important assumptions or consequences of assumptions of economic functionals to be estimated. Recent research has seen a renewed interest in imposing constraints in nonparametric regression. We survey the available methods in the literature, discuss the challenges that present themselves when empirically implementing these methods, and extend an existing method to handle general nonlinear constraints. A heuristic discussion on the empirical implementation for methods that use sequential quadratic programming is provided for the reader, and simulated and empirical evidence on the distinction between constrained and unconstrained nonparametric regression surfaces is covered.

There is a growing literature in nonparametric econometrics in the recent two decades. Given the space limitation, it is impossible to survey all the important recent developments in nonparametric econometrics. Therefore, we choose to limit our focus on the following areas. In Section 2, we review the recent developments of nonparametric estimation and testing of regression functions with mixed discrete and continuous covariates. We discuss nonparametric estimation and testing of econometric models for nonstationary data in Section 3. Section 4 is devoted to surveying the literature of nonparametric instrumental variable (IV) models. We review nonparametric estimation of quantile regression models in Section 5. In Sections 2–5, we also point out some open research problems, which might be useful for graduate students to review the important research papers in this field and to search for their own research interests, particularly dissertation topics for doctoral students. Finally, in Section 6 we highlight some important research areas that are not covered in this paper due to space limitation. We plan to write a separate survey paper to discuss some of the omitted topics.

Classical unit root tests are known to suffer from potentially crippling size distortions, and a range of procedures have been proposed to attenuate this problem, including the use of bootstrap procedures. It is also known that the estimating equation’s functional form can affect the outcome of the test, and various model selection procedures have been proposed to overcome this limitation. In this chapter, the authors adopt a model averaging procedure to deal with model uncertainty at the testing stage. In addition, the authors leverage an automatic model-free dependent bootstrap procedure where the null is imposed by simple differencing (the block length is automatically determined using recent developments for bootstrapping dependent processes). Monte Carlo simulations indicate that this approach exhibits the lowest size distortions among its peers in settings that confound existing approaches, while it has superior power relative to those peers whose size distortions do not preclude their general use. The proposed approach is fully automatic, and there are no nuisance parameters that have to be set by the user, which ought to appeal to practitioners.

Local polynomial regression is extremely popular in applied settings. Recent developments in shape-constrained nonparametric regression allow practitioners to impose constraints on local polynomial estimators thereby ensuring that the resulting estimates are consistent with underlying theory. However, it turns out that local polynomial derivative estimates may fail to coincide with the analytic derivative of the local polynomial regression estimate which can be problematic, particularly in the context of shape-constrained estimation. In such cases, practitioners might prefer to instead use analytic derivatives along the lines of those proposed in the local constant setting by Rilstone and Ullah (1989). Demonstrations and applications are considered.

Identification and inference are central to applied analysis, and two papers examine these issues, the first being theoretical in nature and the second being simulation based.

This is a survey paper of the recent literature on the application of semiparametric–econometric advances to testing for functional form of the environmental Kuznets curve (EKC). The EKC postulates that there is an inverted U-shaped relationship between economic growth (typically measured by income) and pollution; that is, as economic growth expands, pollution increases up to a maximum and then starts declining after a threshold level of income. This hypothesized relationship is simple to visualize but has eluded many empirical investigations. A typical application of the EKC uses panel data models, which allows for heterogeneity, serial correlation, heteroskedasticity, data pooling, and smooth coefficients. This vast literature is reviewed in the context of semiparametric model specification tests. Additionally, recent developments in semiparametric econometrics, such as Bayesian methods, generalized time-varying coefficient models, and nonstationary panels are discussed as fruitful areas of future research. The cited literature is fairly complete and should prove useful to applied researchers at large.