We propose a kernel-based nonparametric estimator for a smooth coefficient panel data model with fixed effects. Without requiring a zero sum of fixed effects, we propose an estimator that is easy to construct and computationally efficient. Eliminating the fixed effects through a local within transformation, we perform a local linear estimation for the coefficient functions associated with time-varying variables and associated derivatives. We further estimate the intercept coefficient function, if present, through a difference of kernel-weighted averages. We characterize the estimator's asymptotic properties under a large-n and large-T framework. We demonstrate that the estimator is not asymptotically equivalent to the standard kernel estimator that ignores fixed effects. Through extensive simulation studies, we highlight the estimator's encouraging numerical performance and computational advantages over existing kernel estimators in the literature. We showcase the empirical applicability by estimating a smooth coefficient model for the Environmental Kuznets Curve through a panel of OECD countries.

We propose a semiparametric Bayesian estimator for copula density, formulated as a generalized exponential family that combines a parametric baseline copula with a flexible adjustment modeled by a Gaussian Process (GP). The baseline captures the main features of dependence and accommodates possibly unbounded densities, while the GP component introduces nonparametric refinement. To modulate the influence of the baseline, we further introduce a tuning parameter that adjusts its weight in the final estimate. Both the GP hyperparameters and this tuning parameter are inferred jointly within a Bayesian framework. We also present a posterior sampler based on importance sampling, with the baseline copula serving as a natural approximating distribution. Simulations demonstrate the efficacy of the proposed estimator and the efficiency of the sampler. The method is further illustrated with an application to commodity futures markets.

This paper develops a complementary estimation approach for functional coefficient panel data models with sample selection and fixed effects. We propose a pairwise differencing strategy that avoids imposing restrictions on the fixed effects at the cost of not directly estimating level coefficients on time-invariant regressors. We derive the estimator’s asymptotic properties and show via simulations that it performs competitively relative to existing methods. Eliminating the need to estimate individual fixed effects yields considerable computational savings, making the approach suitable for large datasets.

A kernel-based estimator is proposed for identifying the underlying structure of a nonparametric regression model from a wide range of alternatives known up to second-order derivatives. The estimator with modifications can further select relevant variables in the model. Under mild conditions, the estimator is shown to be consistent for both model structure and variable selection. The estimator is computationally efficient, can be easily deployed on a parallel computing system, and exhibits appealing finite sample performance through simulation studies. An empirical application is given to illustrate how the unknown underlying structure of a production function can be identified in practice.

Recent stochastic frontier models eschew distributional assumptions to robustify model misspecification. However, such models are potentially subject to several restrictions, particularly for identification of inefficiency mean function under general conditions. This paper proposes a new semiparametric stochastic frontier models with fixed effects to resolve all the restrictions with four new features. First, we specify a nonparametric conditional mean function of inefficiency, estimate it separately from frontier functions, and impose its non-negativity constraint. Second, we relax conventional assumption on the separability between inefficiency and frontier determinants and allow time-varying environmental variables to affect both frontier and inefficiency functions. Third, we generalize commonly used parametric frontier to a semiparametric smooth coefficient frontier, improving model flexibility and uncovering heterogeneous effects of inputs. Fourth, our model circumvents the curse of dimensionality problem by adopting single-index structures, which effectively incorporates potentially large number of frontier and inefficiency determinants to mitigate omitted variable bias. We employ a three-step nonparametric estimator and demonstrate its appealing finite-sample performance through simulations. By conducting an empirical analysis within the Italian banking sector, we demonstrate the superiority of our model compared to existing ones.

Recently, there has been a surge in interest in exploring how common macroeconomic factors impact different economic results. We propose a semiparametric dynamic panel model to analyze the impact of common regressors on the conditional distribution of the dependent variable (global output growth distribution in our case). Our model allows conditional mean, variance, and skewness to be influenced by common regressors, whose effects can be nonlinear and time-varying driven by contextual variables. By incorporating dynamic structures and individual unobserved heterogeneity, we propose a consistent two-step estimator and showcase its attractive theoretical and numerical properties. We apply our model to investigate the impact of US financial uncertainty on the global output growth distribution. We find that an increase in US financial uncertainty significantly shifts the output growth distribution leftward during periods of market pessimism. In contrast, during periods of market optimism, the increased uncertainty in the US financial markets expands the spread of the output growth distribution without a significant location change, indicating increased future uncertainty.

Empirical studies often use the residuals from ordinary least squares regression models to represent certain discretionary or unexpected components and then regress these residuals on potential determinants. However, this two-step approach has been criticized for leading to biased estimates, invalid inferences, and unreliable empirical results. This paper shows that the shortcomings of the two-step approach and alternative existing methodologies are retained and even more pronounced when analyzing inefficient corporate investment. To address these shortcomings, we propose a novel semiparametric model tailored for investment efficiency analysis. Our model effectively mitigates estimation bias caused by inappropriate model design or misspecified model structure, and accurately discerns overinvestment, underinvestment, and efficient investment along with their respective probabilities. Applying our model to a sample of Chinese listed firms reveals significant, previously obscured nonlinear impacts of Tobin's q and sales on investment. Our results reveal pronounced tendencies towards overinvestment, contradictory to existing models which reveal opposite tendencies towards underinvestment. Our model is applicable to various types of efficiency analysis, where each firm may exhibit different performance outcomes with associated probabilities.

Green innovation is crucial for environmental issues and long-term business sustainability. To remain competitive and comply with regulations, firms need prioritize operational capacity in supporting these initiatives. As one of the key concepts in operations management, operational efficiency (OE) measures a firm's ability to utilize its resources effectively. However, the impact of this operational capacity on sustainable practices remains unclear in the literature. Also, conventional methods may yield inconsistent OE estimates, limiting their applicability in empirical studies. To investigate the impact of OE on green innovation, we refine the OE estimation by proposing a semiparametric stochastic frontier model with flexible features, which incorporates interactive fixed effects, specifies an additive frontier with interactions, and avoids distributional assumptions. Using this framework, we provide robust evidence that OE negatively affects green innovation, as reflected in a decrease in green invention and utility model patent applications. Further mechanism analysis shows that focusing on higher OE results in reduced financial flexibility and intensified pressure effects. These findings suggest that an excessive emphasis on OE can undermine a firm's environmental activities.

We show that the international credit channel is an important channel through which US financial uncertainty spills over internationally. Moreover, we find the asymmetric responses of domestic and international credit conditions to US financial uncertainty shocks, contingent upon market participants' expectations. During periods of pessimism regarding future economic conditions, the impact of US financial uncertainty on both domestic and international credit conditions intensifies significantly, leading to a severe global economic slowdown. Elevated US financial uncertainty disproportionately affects the left tails of the distribution more than the right tails, heightening the likelihood of negative global output growth. Conversely, in times of optimism, heightened US financial uncertainty exerts modest effects on international credit conditions and global economic conditions. Yet it stretches the conditional distribution substantially, signaling an increasingly uncertain future.

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.

We investigated the excessive external financing problem in Chinese industrial firms by examining the potential threshold effect of the leverage ratio on the total factor productivity of firms. We hypothesized the existence of a turning point in leverage ratio at which the productivity of these firms is maximized, and this point may vary by firm ownership type. To test our hypotheses, we proposed a nonparametric panel threshold regression model. From a modeling perspective, our approach contributes to the literature by allowing the threshold variable to be endogenous, accounting for unobserved firm heterogeneities, and imposing no restrictions on the functional form of regression. We employed a two-step estimation procedure, first estimating the threshold using an extreme kernel estimator and then conducting local linear regression based on the estimated threshold. We obtained standard errors via bootstrapping and demonstrated the favorable numerical performance of our estimator through simulation studies. Consistent with our hypotheses, we found that excessive leverage relative to the identified turning point significantly restrains productivity growth. Additionally, the estimated turning point varies by ownership type, particularly in state-owned enterprises (SOEs), where leverage exceeding the threshold negatively impacts productivity. Consequently, regions with a higher concentration of SOEs experience stagnant productivity growth. Our results were statistically supported by nonparametric tests and remained consistent when using leverage growth rate as an alternative measure of external financing.

Summary We propose a flexible stochastic production frontier model with fixed effects for the panel data in which the semiparametric frontier is additive with bivariate interactions. To avoid potential misspecification and/or “wrong skew problem” due to distributional assumptions, we model the conditional mean of the inefficiency to depend on environmental variables and to be known up to a vector of parameters. We propose a difference‐based estimator for parameters characterizing the conditional mean of the inefficiency term, a profile series estimator, and a kernel‐based one‐step backfitting estimator for the frontier to facilitate inference. We establish their asymptotic properties and show that each component in the frontier estimated by the kernel‐based backfitting has the same asymptotic distribution as the one estimated with the true knowledge on the other components in the frontier (i.e., the oracle property). Through a Monte Carlo study, we demonstrate that the proposed estimators perform well in finite samples. Utilizing a panel of Chinese firm‐level data in 2000–2006, we apply our method to estimate the frontier and efficiency scores and conclude that export plays a significant role in reducing the efficiency of firms.

We distinguish the effects of export on labour share into a stand-alone direct effect and indirect effects, which alter the marginal impact of three key determinants of labour share found in the literature. While the direct effect of export has been extensively studied, the potential indirect effects remain unexplored. We investigate both effects of exports using micro-level Chinese firm-level data from 1998 to 2007. We employ a fixed-effect varying coefficient model to reveal the potential nonlinearity of the effects of exports while alleviating the risk of model mis-specification. Our model is estimated by a spline-backfitted kernel estimator, which is more efficient and computationally attractive than alternative estimators. We find that while exports directly increase labour share as expected, it declines labour share indirectly through intensifying the negative marginal impact of firms' capital intensity, monopoly power and capital-augmented technological progress on labour share. As a result, the net effect of exports is not beneficial to labour's share of income and varies in magnitude across firm characteristics, regions and time periods.

We propose a semiparametric varying coefficient estimator for a Cobb–Douglas production function for panel data with several practical features. First, we estimate the model without a log transformation to avoid induced non-negligible estimation bias. Second, we disentangle the impact of traditional inputs from that of environment variables, which impact output indirectly through altering the output elasticity of inputs and the state of technology via unknown functions. We introduce a linear index structure in the unknown functions to circumvent the curse of dimensionality, and allow the output elasticity of different inputs to depend on different environment variables. Third, our technology function accounts for latent heterogeneity across individual units, which can be freely correlated with inputs and/or environment variables. Our estimator combines series and kernel methods for both the unknown parameters and functions. We demonstrate that the proposed estimator exhibits promising finite-sample performance.

We propose a nonparametric test of significant variables in the partial derivative of a regression mean function. The derivative is estimated by local polynomial estimation and the test statistic is constructed through a variation-based measure of the derivative in the direction of variables of interest. We establish the asymptotic null distribution of the test statistic and demonstrate that it is consistent. Motivated by the null distribution, we propose a wild bootstrap test, and show that it exhibits the same null distribution, whether the null is valid or not. We perform a Monte Carlo study to demonstrate its encouraging finite sample performance. An empirical application is conducted showing how the test can be applied to infer certain aspects of regression structures in a hedonic price model.

We propose a varying coefficient regression model for panel data that controls for both latent heterogeneities in cross-sectional units and unobserved common shocks over time. The model allows different smoothing variables to enter through either a stand-alone function or a coefficient function. Without requiring a normalization of the fixed effects, we propose a two-step estimator. First, we estimate the varying coefficients with the pilot series-based estimators, eliminating fixed effects though differencing. Second, we perform a one-step kernel backfitting to improve the estimation efficiency. We demonstrate through Monte-Carlo simulations that our estimators are computationally efficient and perform well relative to a profile-based kernel estimator.

The excessive debt ratio of Chinese firms has raised concerns over its impact on productive efficiency. We employ a firm-level dataset over 1998–2007 to investigate the role of debt in the firm’s production frontier and technical efficiency. The impact of debt on frontier is decomposed into a stand-alone neutral effect and indirect non-neutral effects, which alter the output elasticity of production inputs. We estimate the effects through a semiparametric smooth coefficient stochastic frontier model. We allow a nonzero probability for the firms to be fully efficient and model it as a function of debt and technical progress represented by time. We observe that an increase in debt significantly shifts firms’ frontier downward across different ownerships, regions, and industries. Foreign and private firms are more efficient, with their full efficiency probability increased by debt and technical progress. By contrast, state-owned enterprises and collective firms are much less efficient and their probability of being fully efficient does not increase with more debt. Furthermore, lower efficiency levels are concentrated in the central and western regions and in the mining and public utility industries.

The cross-country declined labor share has been partially attributed to rising trade openness. However, the role of exports and imports in the literature was not studied separately and assumed to be homogeneous across countries. We propose two hypotheses for how exports and imports can affect labor share differently and nonlinearly. We empirically test the hypotheses by re-examining the trade–labor share nexus across 96 countries during 1970–2009, and we employ a partially linear model with fixed effect that allows a general functional form of trade variables to be estimated. Results are fairly consistent with our hypotheses, showing that while export (import) share significantly declines (raises) labor share, both effects diminish as the level of export or import share increases. The indicated nonlinear effects are significant and robust by controlling for related economic, social, and political factors. Also, we find a significant heterogeneous impact of export and import across OECD and non-OECD countries, with its implication also discussed.

In this paper we propose a zero-inefficiency stochastic frontier model with a simple semiparametric approach using panel data. We model the frontier with a smooth coefficient function and specify a nonzero conditional probability for firms being fully efficient to be a known function of environment variables. Following (Yao et al., 2017) we propose a three step semiparametric estimator which is computationally efficient. The simulation results reveal encouraging finite sample properties. We illustrate the applicability of our model using country level data from the Penn World Table. (C) 2018 Elsevier B.V. All rights reserved.