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This paper gives a selective review on some recent developments of nonparametric methods in both continuous and discrete time finance, particularly in the areas of nonparametric estimation and testing of diffusion processes, nonparametric testing of parametric diffusion models, nonparametric pricing of derivatives, nonparametric estimation and hypothesis testing for nonlinear pricing kernel, and nonparametric predictability of asset returns. For each financial context, the paper discusses the suitable statistical concepts, models, and modeling procedures, as well as some of their applications to financial data. Their relative strengths and weaknesses are discussed. Much theoretical and empirical research is needed in this area, and more importantly, the paper points to several aspects that deserve further investigation.

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.

This chapter discusses new developments in nonparametric econometric approaches related to empirical modeling of demand decisions. It shows how diverse recent approaches are, and what new modeling options arise in practice. We review work on nonparametric identification using nonseparable functions, semi- and nonparametric estimation approaches involving inverse problems, and nonparametric testing approaches. We focus on classical consumer demand systems with continuous quantities, and do not consider approaches that involve discrete consumption decisions as are common in empirical industrial organization. Our intention is to give a subjective account on the usefulness of these various methods for applications in the field.

Hausman (1978) represented a tectonic shift in inference related to the specification of econometric models. The seminal insight that one could compare two models which were both consistent under the null spawned a test which was both simple and powerful. The so-called ‘Hausman test’ has been applied and extended theoretically in a variety of econometric domains. This paper discusses the basic Hausman test and its development within econometric panel data settings since its publication. We focus on the construction of the Hausman test in a variety of panel data settings, and in particular, the recent adaptation of the Hausman test to semiparametric and nonparametric panel data models. We present simulation experiments which show the value of the Hausman test in a nonparametric setting, focusing primarily on the consequences of parametric model misspecification for the Hausman test procedure. A formal application of the Hausman test is also given focusing on testing between fixed and random effects within a panel data model of gasoline demand.

In this paper, we study a partially linear dynamic panel data model with fixed effects, where either exogenous or endogenous variables or both enter the linear part, and the lagged-dependent variable together with some other exogenous variables enter the nonparametric part. Two types of estimation methods are proposed for the first-differenced model. One is composed of a semiparametric GMM estimator for the finite-dimensional parameter θ and a local polynomial estimator for the infinite-dimensional parameter m based on the empirical solutions to Fredholm integral equations of the second kind, and the other is a sieve IV estimate of the parametric and nonparametric components jointly. We study the asymptotic properties for these two types of estimates when the number of individuals N tends to ∞ and the time period T is fixed. We also propose a specification test for the linearity of the nonparametric component based on a weighted square distance between the parametric estimate under the linear restriction and the semiparametric estimate under the alternative. Monte Carlo simulations suggest that the proposed estimators and tests perform well in finite samples. We apply the model to study the relationship between intellectual property right (IPR) protection and economic growth, and find that IPR has a non-linear positive effect on the economic growth rate.

Equilibrium job search models allow for labor markets with homogeneous workers and firms to yield nondegenerate wage densities. However, the resulting wage densities do not accord well with empirical regularities. Accordingly, many extensions to the basic equilibrium search model have been considered (e.g., heterogeneity in productivity, heterogeneity in the value of leisure, etc.). It is increasingly common to use nonparametric forms for these extensions and, hence, researchers can obtain a perfect fit (in a kernel smoothed sense) between theoretical and empirical wage densities. This makes it difficult to carry out model comparison of different model extensions. In this paper, we first develop Bayesian parametric and nonparametric methods which are comparable to the existing non-Bayesian literature. We then show how Bayesian methods can be used to compare various nonparametric equilibrium search models in a statistically rigorous sense.

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.

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.

The purpose of this paper is to present a nonparametric comparative study on the HCMS consumption of urban and rural households in China.

This paper applies the panel data for China's thirty provinces in 1991‐2007 as a sample and presents a local linear estimation to the nonparametric Working‐Leser panel data models on the HCMS consumption of the rural and urban households in China. The nonparametric Hausman test is applied to test the random effects specification against the fixed effects.

Both the parametric and nonparametric estimation of the Working‐Leser panel data models give us a similar result: that the HCMS commodity is quite elastic in both the rural and urban China. Nonparametric estimate also shows that the urban‐rural difference of the HCMS expenditure share in the total expenditure is mainly due to the large urban‐rural difference of total expenditure. Under the same total expenditure, the HCMS is more elastic in the urban than in the rural regions.

To decrease the urban‐rural difference in the HCMS consumption, the government should enhance the income or total expenditure level of the rural households, especially in the impoverished and remote areas in China. Urbanization plays a critical role in access to health care and can help make substantial changes in rural health care in China.

Compared to the parametric estimation, the nonparametric estimation gives us the added information that the expenditure elasticity of the HCMS consumption in China gradually declines as one moves up the per capita total expenditure distribution. The paper could make a contribution to the relatively thin literature on the Chinese medical and health consumption market.

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.