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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.

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.

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.

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.

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.

Small- and medium-sized enterprises can be highly affected by losses caused by exchange rate changes. The aim of this paper was to find the optimal Value-at-Risk (VaR) method for estimating future exchange rate losses within one year.

The analysis focuses on five VaR methods, some of them traditional and some of them more up to date with integrated EVT or GARCH. The analysis of VaR methods was concentrated on a time horizon (1–12 months), overestimation predictions and six scenarios based on trends and variability of exchange rates. This study used three currency pairs EUR/CZK, EUR/USD and EUR/JPY for backtesting.

In compliance with the backtesting results, the parametric VaR with random walk has been chosen, despite its shortcomings, as the most accurate for estimating future losses in a medium-term period. The Nonparametric VaR confirmed insensitivity to the current exchange rate development. The EVT-based methods showed overconservatism (overestimation predictions). Every parametric or semiparametric method revealed a severe increase of liberality with increasing time.

This research is limited to the analysis of suitable VaR models in a long- and short-run period without using artificial intelligence.

The result of this paper is the choice of a proper VaR method for the online application for estimating the future exchange rate for enterprises.

The orientation of medium-term period makes the research original and useful for small- and medium-sized enterprises.

The purpose of this paper is to study performance and market timing ability of equity real estate investment trusts (REITs).

The authors use classical regression‐based framework and their multi‐index, multifactor, and conditional extensions to jointly detect asset selectivity and market timing ability of equity REITs and their subcategories. These results are then validated by a nonparametric test.

It is found that equity REITs in aggregate have some housing market timing ability. Various equity REIT subcategories perform differently: office REITs can discover underpriced properties, while retail, industrial, and office REITs have poor timing ability. Nonparametric tests confirm that equity REITs do not have ability to predict real estate market movements.

Research in REIT performance evaluation is still limited to the asset selectivity aspect. This paper intends to fill this gap by providing empirical evidence of market timing ability of equity REITs using an array of parametric and nonparametric methods.

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.

Although the theoretical trade-off between the quantity and quality of children is well established, empirical evidence supporting such a causal relationship is limited. This chapter applies a recently developed nonparametric estimator of the conditional local average treatment effect to assess the sensitivity of the quantity–quality trade-off to functional form and parametric assumptions. Using data from the Indonesia Family Life Survey and controlling for the potential endogeneity of fertility, we find mixed evidence supporting the trade-off.