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This chapter proposes semiparametric estimation of the relationship between growth rate of GDP per capita, growth rates of physical and human capital, labor as well as other covariates and common trends for a panel of 23 OECD countries observed over the period 1971–2015. The observed differentiated behaviors by country reveal strong heterogeneity. This is the motivation behind using a mixed fixed- and random coefficients model to estimate this relationship. In particular, this chapter uses a semiparametric specification with random intercepts and slopes coefficients. Motivated by Lee and Wand (2016), the authors estimate a mean field variational Bayes semiparametric model with random coefficients for this panel of countries. Results reveal nonparametric specifications for the common trends. The use of this flexible methodology may enrich the empirical growth literature underlining a large diversity of responses across variables and countries.

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.

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.

A semiparametric stochastic frontier model is proposed for panel data, incorporating several flexible features. First, a constant elasticity of substitution (CES) production frontier is considered without log-transformation to prevent induced non-negligible estimation bias. Second, the model flexibility is improved via semiparameterization, where the technology is an unknown function of a set of environment variables. The technology function accounts for latent heterogeneity across individual units, which can be freely correlated with inputs, environment variables, and/or inefficiency determinants. Furthermore, the technology function incorporates a single-index structure to circumvent the curse of dimensionality. Third, distributional assumptions are eschewed on both stochastic noise and inefficiency for model identification. Instead, only the conditional mean of the inefficiency is assumed, which depends on related determinants with a wide range of choice, via a positive parametric function. As a result, technical efficiency is constructed without relying on an assumed distribution on composite error. The model provides flexible structures on both the production frontier and inefficiency, thereby alleviating the risk of model misspecification in production and efficiency analysis. The estimator involves a series based nonlinear least squares estimation for the unknown parameters and a kernel based local estimation for the technology function. Promising finite-sample performance is demonstrated through simulations, and the model is applied to investigate productive efficiency among OECD countries from 1970–2019.

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.

Public management researchers commonly model dichotomous dependent variables with parametric methods despite their relatively strong assumptions about the data generating process. Without testing for those assumptions and consideration of semiparametric alternatives, such as maximum score, estimates might be biased, or predictions might not be as accurate as possible.

To guide researchers, this paper provides an evaluative framework for comparing parametric estimators with semiparametric and nonparametric estimators for dichotomous dependent variables. To illustrate the framework, the article estimates the factors associated with the passage of school district bond referenda in all Texas school districts from 1998 to 2015.

Estimates show that the correct prediction of a bond passing increases from 77.2 to 78%, with maximum score estimation relative to a commonly used parametric alternative. While this is a small increase, it is meaningful in comparison to the random prediction base model.

Future research modeling any dichotomous dependent variable can use the framework to identify the most appropriate estimator and relevant statistical programs.

The purpose of this paper is to investigate the nonlinear relationship between shadow economy and income inequality and determine whether the size of shadow economy can influence the level of income inequality.

Both parametric (panel OLS) and nonparametric/semiparametric regression suggested by Robinson (1988) will be used to capture the dynamic nonlinear relationship between these variables using unbalanced panel data of 154 countries from 2000 to 2007. Additionally, the relationship between income inequality and shadow economy on both developed and developing countries will be analyzed and compared.

First, semiparametric analysis and nonparametric analysis are significantly different than parametric analysis and better in nonlinear analysis between income inequality and shadow economy. Second, income inequality and shadow economy resemble an inverted-N relationship. Third, the relationship between income inequality and shadow economy is different in developed countries (OECD countries) and developing countries, where OECD countries have similar inverted-N relationship as before. However, for developing countries, income inequality and shadow economy show an inverted-U relationship, similar to the original Kuznets hypothesis.

This study suggests that there is a possible trade-off between income inequality and shadow economy and helps policy makers in solving both problems effectively.

Despite the growing importance of income inequality and shadow economy, literature linking the two variables is scarce. To the best of the authors’ knowledge, there is no literature that nonlinearly links these two variables. Furthermore, the dynamics of the relationship between these two variables in developed countries and developing countries will be explored as well.

This chapter studies the large sample properties of a subclassification-based estimator of the dose–response function under ignorability. Employing standard regularity conditions, it is shown that the estimator is root-n consistent, asymptotically linear, and semiparametric efficient in large samples. A consistent estimator of the standard-error is also developed under the same assumptions. In a Monte Carlo experiment, we investigate the finite sample performance of this simple and intuitive estimator and compare it to others commonly employed in the literature.

This chapter re-examines the determinants of health care expenditure (HCE), using a panel of 32 Organization for Economic Cooperation and Development (OECD) countries from 1990 to 2012. In particular, a panel semiparametric technique (i.e., a partially linear model) is employed, with cross-sectional dependence allowed. Beside the study of coefficients, this chapter investigates the trending functions of HCE. After the common and individual trends of HCE are estimated via semiparametric methods, the authors calibrate them with polynomial specifications, leading to out-of-sample forecasting. The validities of the calibration are tested as well. Contrary to those studies that do not take into account time series properties, our finding suggests that medical care is not a luxury commodity. Other determinants, such as public financing, and the supply of doctors, are all positively related to HCE. Moreover, the calibrated trending models perform well in out-of-sample forecasting.

In this chapter we consider the “Regularization of Derivative Expectation Operator” (Rodeo) of Lafferty and Wasserman (2008) and propose a modified Rodeo algorithm for semiparametric single index models (SIMs) in big data environment with many regressors. The method assumes sparsity that many of the regressors are irrelevant. It uses a greedy algorithm, in that, to estimate the semiparametric SIM of Ichimura (1993), all coefficients of the regressors are initially set to start from near zero, then we test iteratively if the derivative of the regression function estimator with respect to each coefficient is significantly different from zero. The basic idea of the modified Rodeo algorithm for SIM (to be called SIM-Rodeo) is to view the local bandwidth selection as a variable selection scheme which amplifies the coefficients for relevant variables while keeping the coefficients of irrelevant variables relatively small or at the initial starting values near zero. For sparse semiparametric SIM, the SIM-Rodeo algorithm is shown to attain consistency in variable selection. In addition, the algorithm is fast to finish the greedy steps. We compare SIM-Rodeo with SIM-Lasso method in Zeng et al. (2012). Our simulation results demonstrate that the proposed SIM-Rodeo method is consistent for variable selection and show that it has smaller integrated mean squared errors (IMSE) than SIM-Lasso.