Nonparametric Frontier Estimation Research Articles

Double hedonic price-characteristics frontier estimation for IoT service providers in the industry 5.0 era: A nonconvex perspective accommodating ratios

The advent of advanced digital technologies, including the Internet of Things (IoT), image processing, artificial intelligence (AI), blockchain, robotics and cognitive computing that have been embedded in Industry 5.0, is considerably improving the sustainability, resilience, and human-centric performance of industrial organizations. Despite the increasing use of Industry 5.0 technologies in smart product platforming in industrial organizations, a critical issue remains how to assess the providers/suppliers of such technologies in highly competitive markets to fulfil personalized products and services. Following Lancaster's characteristics approach to consumer theory, in this study we contribute to assess digital technologies service providers in the Industry 5.0 era by focusing on both theoretical and empirical evidence inquiring about the convexity of conventional nonparametric frontier estimation methods. To do so, a nonparametric double frontier estimation of the hedonic price characteristics relation is developed from both the buyer's and seller's perspectives. Moreover, a separable directional distance function-based optimization model is developed for the efficiency estimation. Furthermore, a comparable estimation of the convex and nonconvex hedonic price function is proposed. We also explicitly test the impact of convexity in evaluating the efficiency of IoT service providers in the Industry 5.0 context. In this study, we also show that the hypothesis of convexity in assessing the efficiency of IoT service providers is rejected using the Li-test comparing entire densities in the case of the seller's perspective without ratio data. Differences are less pronounced for the buyer's perspective and in the case with ratio data.

Modeling the effect of competition on US manufacturing sectors’ efficiency: an order-m frontier analysis

The study applies the probabilistic framework of nonparametric frontier estimation to model the effect of competitive conditions on sectors’ production efficiency levels. We utilize conditional order-m robust frontiers to model the dynamic effects of competition on a sample of U.S. manufacturing sectors over the period 1958–2009. Contrary to the existing studies, we apply for the first time in the Industrial Organization literature the latest advances of robust nonparametric frontier analysis to disentagle the dynamic effects alongside the effects of competition on sectors’ productive efficiency levels. The results derived from the time-dependent robust conditional estimators unveil a non-linear relationship between product market competition and productive efficiency. Our findings suggest that for higher competition levels the effect is positive up to a certain threshold after which the effect becomes negative.

Technological Change and Catching-Up in the Indian Banking Sector: A Time-Dependent Nonparametric Frontier Approach

This paper investigates whether there has been any improvement in efficiency convergence of banks in India during the post-reform period considering bank ownership structures, using a balanced panel for 73 banks over the time period 1996–2014. Utilizing nonparametric frontier estimators, we compute time-dependent bank efficiency scores, which allow us to examine the dynamics of technological frontier and catch-up levels of Indian banks, and to explore the convergence patterns in the estimated efficiency levels. Our results signify that the state-owned banks, which dominate the banking activity in India, establish themselves as the best performers, ahead of the private, foreign and cooperative banks during post-2005. Even during the recent global financial crisis period, we find that bank efficiency levels increased, except for foreign banks which have had the greatest adverse impact. The convergence results show that heterogeneity is present in bank efficiency convergence, which points to the presence of club formation suggesting that Indian banks’ efficiency convergence is partly driven by the ownership structure.

Economic growth and environmental degradation: a conditional nonparametric frontier analysis

This paper examines the effect of economic growth and the association of environmental degradation on economies’ technological change and technological catch-up. Using a conditional nonparametric frontier analysis to a sample of 73 economies over the time period 1980–2014, empirical evidence of the examined relationship is provided both under full and partial frontiers in the constant and variable returns to scale (VRS) models. Specifically, the newly proposed time-dependent conditional nonparametric frontier estimators have been applied. In our case the time-dependent conditional efficiency estimators allow us to model directly the effects of growth and time on economies’ estimated performance without requiring any specification of the production functional form and without assuming the separability condition between time, economic growth and the support of inputs and outputs. The overall results reveal that the efficiency results of full and partial frontiers tend to lead to the same results, except in the cases of full VRS models where energy use and carbon dioxide emissions are incorporated as an additional input and output, respectively. The results demonstrate that countries with a higher environmental efficiency are those that have signed the first agreement between nations (Kyoto Protocol) to mandate country-by-country reductions in greenhouse-gas emissions, while countries that have not signed are relatively inefficient. Ultimately, the empirical findings also suggest that the effect of economic growth is determined by economies’ development stage and geographical region.

Financial Development and Countries’ Production Efficiency: A Nonparametric Analysis

This paper examines the effect of financial development on countries’ production efficiency levels. By applying a probabilistic framework it develops robust (Order-m) time-dependent conditional nonparametric frontier estimators in order to measure 87 countries’ production efficiency levels over the period 1970–2014. In order to examine the effect of time and domestic credit on countries’ production efficiency levels, a second-stage nonparametric econometric analysis is performed. Specifically, generalized additive models with tensor products and cubic spline penalties are applied in order to investigate the potential nonlinear behavior of financial development on countries’ production efficiency levels. The results reveal that the effect of financial development on production efficiency is nonlinear. Specifically, the effect is positive up to a certain credit level after which it becomes negative. Finally, the evidence suggests that the effect is influenced by a country’s financial system, institutional, and development characteristics.

Robust frontier estimation from noisy data: A Tikhonov regularization approach

In stochastic frontier models, the regression function defines the production frontier and the regression errors are assumed to be composite. The actually observed outputs are assumed to be contaminated by a stochastic noise. The additive regression errors are composed from this noise term and the one-sided inefficiency term. The aim is to construct a robust nonparametric estimator for the production function. The main tool is a robust concept of partial, expected maximum production frontier, defined as a special probability-weighted moment. In contrast to the deterministic one-sided error model where robust partial frontier modeling is fruitful, the composite error problem requires a substantial different treatment based on deconvolution techniques. To ensure the identifiability of the model, it is sufficient to assume an independent Gaussian noise. In doing so, the frontier estimation necessitates the computation of a survival function estimator from an ill-posed equation. A Tikhonov regularized solution is constructed and nonparametric frontier estimation is performed. The asymptotic properties of the obtained survival function and frontier estimators are established. Practical guidelines to effect the necessary computations are described via a simulated example. The usefulness of the approach is discussed through two concrete data sets from the sector of Delivery Services.

Measuring the efficiency of grid companies in China: A bootstrapping non-parametric meta-frontier approach

The unbundling policy reform of power industry has become a worldwide trend since 1980s. There are quite many studies focusing on the efficiency changes of transmission and distribution sectors in European and Latin American countries while few reports on China's issues have been found. This paper employs a nonparametric frontier estimation combined with meta-frontier and bootstrapping method to measure the productive efficiency and changes in the decomposition index for China's 31 grid companies from 2004 to 2013. In addition, it further employs Tobit regression model to analyze the influences of relevant policies and heterogeneity factors, such as natural conditions and economic development. The results indicate that the grouping approach extends the application of non-parametric data envelopment analysis, which may decrease the assumption of homogeneity for the decision making units and provide better efficiency estimates by increasing the credibility of the evaluation results. Overall productive efficiency increased during the whole study period, with technology progress the main contributor to this improvement. Efficiency trends fluctuated with changes in economic development and power supply situation, and the economics and customer density had positive effects on productive efficiency while the influence of clean power proportion is negative.

Non-parametric frontier estimation of health care efficiency among US states, 2002–2008

This paper examines cross-state health care efficiency rankings using modern non-parametric estimators. Cross-state efficiency rankings are robust to minor modifications in the input–output combinations used for estimation. This paper finds that there is no clear relationship between health care efficiency rankings and per capita health care expenditures in that state in the models used for this paper, even though this is a key variable that policymakers target. It also finds that Massachusetts, in one dataset, has shown significant productivity improvement from 2005 to 2008, the time period during which its health care reform was launched. In a second dataset, from 2002 to 2007, productivity regressed in Massachusetts. This may hint that efficiency gains from structural health care reform can outweigh population behavioral inefficiencies from using the ER as a source of primary care with insurance coverage expansion. I also find that states that chose to expand Medicaid were less efficient, on average, than states that did not choose to expand Medicaid. Simple variable comparisons suggest that this is an artifact of the data and political decision making, rather than people migrating for Medicaid or productive inefficiency.

Comparing Malmquist and Hicks–Moorsteen productivity indices: Exploring the impact of unbalanced vs. balanced panel data

We explore the effect of balancing unbalanced panel data when estimating primal productivity indices using non-parametric frontier estimators. First, we list a series of pseudo-solutions aimed at making an unbalanced panel balanced. Then, we discuss some intermediate solutions (e.g., balancing 2-years by 2years). Furthermore, we link this problem with a variety of literatures on infeasibilities, statistical inference of non-parametric frontier estimators, and the index theory literature focusing on the dynamics of entry and exit in industries. We then empirically illustrate these issues comparing both Malmquist and Hicks–Moorsteen productivity indices on two data sets. In particular, we test for the differences in distribution when comparing balanced and unbalanced results for a given index and when comparing Malmquist and Hicks–Moorsteen productivity indices for a given type of data set. The latter tests are crucial in answering the question to which extent the Malmquist index can approximate the Hicks–Moorsteen index that has a Total Factor Productivity (TFP) interpretation. Finally, we draw up a list of remaining issues that could benefit from further exploration.

Regularization of nonparametric frontier estimators

In production theory and efficiency analysis, we estimate the production frontier, the locus of the maximal attainable level of an output (the production), given a set of inputs (the production factors). In other setups, we estimate rather an input (or cost) frontier, the minimal level of the input (cost) attainable for a given set of outputs (goods or services produced). In both cases the problem can be viewed as estimating a surface under shape constraints (monotonicity, …). In this paper we derive the theory of an estimator of the frontier having an asymptotic normal distribution. It is based on the order-m partial frontier where we let the order m to converge to infinity when n→∞ but at a slow rate. The final estimator is then corrected for its inherent bias. We thus can view our estimator as a regularized frontier. In addition, the estimator is more robust to extreme values and outliers than the usual nonparametric frontier estimators, like FDH and than the unregularized order-mn estimator of Cazals et al. (2002) converging to the frontier with a Weibull distribution if mn→∞ fast enough when n→∞. The performances of our estimators are evaluated in finite samples and compared to other estimators through some Monte-Carlo experiments, showing a better behavior (in terms of robustness, bias, MSE and achieved coverage of the resulting confidence intervals). The practical implementation and the robustness properties are illustrated through simulated data sets but also with a real data set.

Comparing efficiency across markets: An extension and critique of the methodology

Abstract The use of non-parametric frontier methods for the evaluation of product market efficiency in heterogeneous markets seems to have gained some popularity recently. However, the statistical properties of these frontier estimators have been largely ignored. The main point is that non-parametric frontier estimators are biased and that the degree of bias depends on specific sample properties, most importantly sample size and number of dimensions of the model. To investigate the effect of this bias on comparing market efficiency, this contribution estimates the efficiency for several datasets for two main product categories. Following (Zhang, Y., Bartels, R., 1998. The effect of sample size on the mean efficiency in DEA with an application to electricity distribution in Australia, Sweden and New Zealand. Journal of Productivity Analysis, 9(3), 187-204.), these results comprise re-estimates for the larger samples limiting their size to that of the smaller samples when the model dimensions for different samples are identical. Furthermore, sample sizes are adjusted to mitigate the eventual differences in dimensions in specification. This allows comparing market efficiency for different markets on a more equal footing, since it reduces the bias effect to a minimum making the comparison of market efficiency possible. However, the article also points out the critical limitations of this [Zhang, Y., Bartels, R., (1998). The effect of sample size on the mean efficiency in DEA with an application to electricity distribution in Australia, Sweden and New Zealand. Journal of Productivity Analysis 9 (3), 187–204] approach in certain respects. Apart from reporting these negative results, we also offer some suggestions for future work.

Large deviation properties for empirical quantile-type production functions

In standard microeconomic theory of the firm, the production frontier is used to describe the geometric locus of the optimal production. Most limitations of the conventional estimators of this efficient frontier stem from its reliance on estimation of the upper surface of the joint support of (X, Y), where X∈ℝ p + represents the inputs-usage and Y∈ℝ+ is the produced output. Instead, a recent approach involving the estimation of a partial quantile-type frontier of the joint support, lying close to its full boundary, has emerged in the literature as an attractive alternative. In this paper, we present a new and simple proof of the asymptotic normality of the resulting nonparametric frontier estimators and provide an estimate for the accuracy of the normal approximation. We also propose a Kiefer-type asymptotic representation for these estimators. The main results concern the study of some weak, moderate and strong large deviation properties of the quantile-based frontier estimators.

Performance of French intensive care units: A directional distance function approach at the patient level

By using a novel adaptation of the free-disposable hull analysis of productivity, we assess the medical and technical efficiency of patient care in 25 Parisian intensive care units (ICUs) during 2000. The robust free disposable hull (RFDH) as defined by [Cazals et al., 2002. Nonparametric frontier estimation: a robust approach. Journal of Econometrics 106, 1–25] reduces the impact outliers may have on findings by employing Monte-Carlo techniques and repeated sample selection. Among our key findings, there was no overall significant correlation between medical and technical efficiencies for all the ICUs, therefore performing well in one does not guarantee good performance in the other. We also found that over 80% of inefficiency is concentrated in less than 20% of the sampled patients.

ASYMPTOTIC PROPERTIES OF NONPARAMETRIC FRONTIER ESTIMATORS

Aragon, Daouia, and Thomas-Agnan (2005, Econometric Theory 21, 358–389) introduced a new nonparametric frontier estimation. We prove the weak convergence of the empirical conditional quantile function. The distribution of the limit depends on the unknown conditional quantile density function. We provide a method to construct uniform confidence bands without estimating the conditional quantile density.

Efficiency and productivity change in Ukrainian health care

The study analyses technical efficiency and efficiency change of 193 community hospitals and polyclinics across Ukraine, for the years 1997–2001. These facilities are a subset of the medical institutions in rural Ukraine; they are identical w.r.t. their function in the health system and share the same departmental structure. The data comprise the number of beds in the hospitals, the number of staff employed in the hospitals as well as the polyclinics connected to the hospitals, the number of inpatient and outpatient admissions as well as the number of surgical procedures, lab tests, X-rays performed and the number of deaths and deaths after surgery. Because of the known sensitivity of traditional nonparametric frontier estimators to outlier observations, we employ an order-m estimator, a robust technique, to assess the efficiency of these health care providers as well as changes of their productivity time. The efficiency scores are calculated with an output-oriented model; they are close to unity for hospitals whereas polyclinics seem somewhat less efficient. The Malmquist-indices averaged over all observations are close to unity indicating that productivity does not change over during our observation period. But, depending on the period and the region, substantial deviations from unity can be observed.

A smooth nonparametric conditional quantile frontier estimator

Traditional estimators for nonparametric frontier models (DEA, FDH) are very sensitive to extreme values/outliers. Recently, Aragon et al. [2005. Nonparametric frontier estimation: a conditional quantile-based approach. Econometric Theory 21, 358–389] proposed a nonparametric α -frontier model and estimator based on a suitably defined conditional quantile which is more robust to extreme values/outliers. Their estimator is based on a nonsmooth empirical conditional distribution. In this paper, we propose a new smooth nonparametric conditional quantile estimator for the α -frontier model. Our estimator is a kernel based conditional quantile estimator that builds on early work of Azzalini [1981. A note on the estimation of a distribution function and quantiles by a kernel method. Biometrika 68, 326–328]. It is computationally simple, resistant to outliers and extreme values, and smooth. In addition, the estimator is shown to be consistent and n asymptotically normal under mild regularity conditions. We also show that our estimator's variance is smaller than that of the estimator proposed by Aragon et al. A simulation study confirms the asymptotic theory predictions and contrasts our estimator with that of Aragon et al.

Functional convergence of quantile-type frontiers with application to parametric approximations

Nonparametric estimators of the upper boundary of the support of a multivariate distribution are very appealing because they rely on very few assumptions. But in productivity and efficiency analysis, this upper boundary is a production (or a cost) frontier and a parametric form for it allows for a richer economic interpretation of the production process under analysis. On the other hand, most of the parametric approaches rely on often too restrictive assumptions on the stochastic part of the model and are based on standard regression techniques fitting the shape of the center of the cloud of points rather than its boundary. To overcome these limitations, Florens and Simar [2005. Parametric approximations of nonparametric frontiers. J. Econometrics 124 (1), 91–116] propose a two-stage approach which tries to capture the shape of the cloud of points near its frontier by providing parametric approximations of a nonparametric frontier. In this paper we propose an alternative method using the nonparametric quantile-type frontiers introduced in Aragon, Daouia and Thomas-Agnan [2005. Nonparametric frontier estimation: a conditional quantile-based approach. Econometric Theory 21, 358–389] for the nonparametric part of our model. These quantile-type frontiers have the superiority of being more robust to extremes. Our main result concerns the functional convergence of the quantile-type frontier process. Then we provide convergence and asymptotic normality of the resulting estimators of the parametric approximation. The approach is illustrated through simulated and real data sets.

A robust nonparametric approach to evaluate and explain the performance of mutual funds

The topic of the measurement of mutual funds’ performance is receiving an increasing interest both from an applied and a theoretical perspective. Beside the traditional financial literature, a growing body of studies has started to apply the tools of frontier analysis for benchmarking comparisons in portfolio analysis. Our paper contributes to this literature proposing a robust nonparametric approach for analysing mutual funds. It is based on the concept of order- m frontier [Cazals, C., Florens, J.P., Simar, L., 2002. Nonparametric frontier estimation: A robust approach. Journal of Econometrics 106, 1–25] and on a probabilistic approach [Daraio, C., Simar, L., 2005. Introducing environmental variables in nonparametric frontier models: A probabilistic approach. Journal of Productivity Analysis 24 (1), 93–121] to find out the factors explaining mutual funds’ performance. Within this framework, a decomposition of conditional efficiency is proposed, and its usefulness for economic interpretation analysed. Our approach is illustrated by using US mutual funds data, grouped for category by objective. Economies of scale, slacks and market risks are investigated. A comparison of traditional, nonparametric and robust performance measures is also offered.

Robust Non-Parametric Quantile Estimation of Efficiency and Productivity Change in U.S. Commercial Banking, 1985-2004

This paper describes a non-parametric, unconditional, hyperbolic quantile estimator that unlike traditional non-parametric frontier estimators is both robust to data outliers and has a root-n convergence rate. We use this estimator to examine changes in the efficiency and productivity of U.S. banks between 1985 and 2004. We find that larger banks experienced larger efficiency and productivity gains than small banks, consistent with the presumption that recent changes in regulation and information technology have favored larger banks.

The Efficiency of Public Employment Services: A Nonparametric Matching Function Analysis for Switzerland

This study develops a methodology for assessing the efficiency of job placement services based on the matching function. Unlike most previous estimates of the matching function, based on aggregate time-series regressions and parametric functional forms, this study employs micro cross-sectional data and uses nonparametric frontier estimation techniques (DEA). The methodology is applied to 126 regional placement offices operating in Switzerland in the period 1997–98. In contrast to time-series regressions, our results point to sizable increasing returns-to-scale. Our findings also suggest that counseling is more effective than other active labor market measures or disciplining actions in increasing matching efficiency.