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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.

This chapter builds up a simple general equilibrium trade model where, in the absence of a credit market for human capital formation, initial distribution of capital endowment and relevant factor prices determine the size of the three income classes. The poor, with little capital, invests in traditional manufacturing, the middle-income group invests solely in human capital and the rich invests in both. Chances are that such an economy will export both high- and low-skilled goods, importing the middle one. Conventional wisdom suggests that greater skill premium encourages skill formation. In contrast, we show that higher unskilled wage and lower degree of income inequality are consistent with greater skill formation. We also show that protection discourages skill formation and may aggravate inequality.

The chapter reviews and extends the theory of exact and superlative index numbers. Exact index numbers are empirical index number formula that are equal to an underlying theoretical index, provided that the consumer has preferences that can be represented by certain functional forms. These exact indexes can be used to measure changes in a consumer's cost of living or welfare. Two cases are considered: the case of homothetic preferences and the case of nonhomothetic preferences. In the homothetic case, exact index numbers are obtained for square root quadratic preferences, quadratic mean of order r preferences, and normalized quadratic preferences. In the nonhomothetic case, exact indexes are obtained for various translog preferences.

This paper deals with estimation of risk and the risk preference function when producers face uncertainties in production (usually labeled as production risk) and output price. These uncertainties are modeled in the context of production theory where the objective of the producers is to maximize expected utility of normalized anticipated profit. Models are proposed to estimate risk preference of individual producers under (i) only production risk, (ii) only price risk, (iii) both production and price risks, (iv) production risk with technical inefficiency, (v) price risk with technical inefficiency, and (vi) both production and price risks with technical inefficiency. We discuss estimation of the production function, the output risk function, and the risk preference functions in some of these cases. Norwegian salmon farming data is used for an empirical application of some of the proposed models. We find that salmon farmers are, in general, risk averse. Labor is found to be risk decreasing while capital and feed are found to be risk increasing.

This chapter suggests a robust Hausman and Taylor (1981), hereafter HT, estimator that deals with the possible presence of outliers. This entails two modifications of the classical HT estimator. The first modification uses the Bramati and Croux (2007) robust Within MS estimator instead of the Within estimator in the first stage of the HT estimator. The second modification uses the robust Wagenvoort and Waldmann (2002) two-stage generalized MS estimator instead of the 2SLS estimator in the second step of the HT estimator. Monte Carlo simulations show that, in the presence of vertical outliers or bad leverage points, the robust HT estimator yields large gains in MSE as compared to its classical Hausman–Taylor counterpart. We illustrate this robust version of the HT estimator using an empirical application.

To fully accommodate the correlations between semiconductor product demands and external information such as the end market trends or regional economy growth, a linear dynamic system is introduced in this chapter to improve forecasting performance in supply chain operations. In conjunction with the generic Gaussian noise assumptions, the proposed state-space model leads to an expectation-maximization (EM) algorithm to estimate model parameters and predict production demands. Since the set of external indicators is of high dimensionality, principal component analysis (PCA) is applied to reduce the model order and corresponding computational complexity without loss of substantial statistical information. Experimental study on certain real electronic products demonstrates that this forecasting methodology produces more accurate predictions than other conventional approaches, which thereby helps improve the production planning and the quality of semiconductor supply chain management.

In response to common criticisms on the appropriateness of mean-variance in asset allocation decisions involving hedge funds, we offer a mean-Gini framework as an alternative. The mean-Gini framework does not require the usual normality assumption concerning return distributions. We also evaluate empirically the differences in allocation outcomes between the two frameworks using historical data. The differences turn out to be significant. The evidence thus confirms the inappropriateness of the mean-variance framework and enhances the attractiveness of mean-Gini for this asset class.

This paper proposes the Student's t Dynamic Linear Regression (St-DLR) model as an alternative to the various extensions/modifications of the ARCH type volatility model. The St-DLR differs from the latter models of volatility because it can incorporate exogenous variables in the conditional variance in a natural way. Moreover, it also addresses the following issues: (i) apparent long memory of the conditional variance, (ii) distributional assumption of the error, (iii) existence of higher moments, and (iv) coefficient positivity restrictions. The model is illustrated using Dow Jones data and the three-month T-bill rate. The empirical results seem promising, as the contemporaneous variable appears to account for a large portion of the volatility.

In empirical research, panel (and multinomial) probit models are leading examples for the use of maximum simulated likelihood estimators. The Geweke–Hajivassiliou–Keane (GHK) simulator is the most widely used technique for this type of problem. This chapter suggests an algorithm that is based on GHK but uses an adaptive version of sparse-grids integration (SGI) instead of simulation. It is adaptive in the sense that it uses an automated change-of-variables to make the integration problem numerically better behaved along the lines of efficient importance sampling (EIS) and adaptive univariate quadrature. The resulting integral is approximated using SGI that generalizes Gaussian quadrature in a way such that the computational costs do not grow exponentially with the number of dimensions. Monte Carlo experiments show an impressive performance compared to the original GHK algorithm, especially in difficult cases such as models with high intertemporal correlations.