Distance Function Estimation Research Articles

Towards a better measure of productivity in India: a case of chemical and chemical products industry

PurposeA brief review of earlier studies on the productivity scenario of Indian industry shows that most of the studies analysed are confined to either parametric approach or growth accounting approach of measuring productivity. At the same time, the few studies based on the non-parametric [namely, Malmquist productivity index (MPI)] overlook the returns to scale conditions as well as the bias involved in the estimation of distance functions. Given this backdrop, this study aims to provide a robust measure of productivity, which considers the returns to scale assumptions and correct for the bias involved in the estimation of productivity.Design/methodology/approachThis study empirically tests for the returns to scale that exists in the chemical and chemical products industry in India. The test result suggests that Ray and Desli (1997) approach of MPI is the appropriate one for the present context. Initially, the conventional Ray and Desli (1997) estimation and decomposition of MPI for the period 2001 to 2017 is being used. Subsequently, to correct for the bias in the estimation of efficiency scores used for the estimation of MPI, the bootstrapping algorithm of Simar and Wilson (2007) has been extended into the context of MPI estimation.FindingsThe results from the conventional Malmquist productivity estimates testifies to an improvement of total factor productivity (TFP) in seven out of 16 years under consideration. On the contrary, TFP growth is recorded only in the four years throughout the period after the bias correction. A greater discrepancy between the two measures has been found in the case of scale change factor component of MPI.Practical implicationsThe technical change (TC) component positively influences TFP, whereas scale change factor (SCF) deteriorates the TFP condition of this industry. It will be appropriate for these firms to identify and operate under an optimal scale of operation, along with reaping the benefits of technological change. From a methodological perspective, researchers should consider the potential bias that arise in estimation of TFP and use a larger sample whenever possible.Originality/valueThis paper brings in a new perspective to the existing literature on industrial productivity. As against earlier studies, this study empirically tests the returns to scale of the sector under consideration and uses the most appropriate approach to measure productivity. The effect of sampling bias on TFP and its components is analysed.

Redefine carbon footprint performance with the total factor productivity: A case from a regional food production system

By observing the disturbance of indicators, models, and samples variability to the robustness of low carbon performance evaluation, the importance of random errors and heterogeneity of sample data is clarified. The carbon footprint joint total factor productivity conceptual framework is proposed in this study, then we apply it to a food production system in a region of China to reasonably judge the carbon footprint performance level of peasant households. With regard to the single-output production frontier, the internal method changes did not cause significant changes in the level of crop production technical efficiency in the deterministic and stochastic estimation strategies respectively. Although the results of partial low-carbon economic technical efficiency are consistent in the two estimation strategies, a significant difference is obvious for the low-carbon technical efficiency; The total low-carbon economic technical efficiency is significantly different between deterministic non-parametric slacks-based measure and parameterized random distance function estimation strategies under the framework of the multi-output production frontier; Ultimately, the total factor productivity including the carbon footprint of the food system in our research area close to the technical level of the industry, as well as the technical efficiency of the sample is at an efficient level.

Addressing endogeneity when estimating stochastic ray production frontiers: a Bayesian approach

We propose a Bayesian approach for inference in the stochastic ray production frontier (SRPF), which can model multiple-input–multiple-output production technologies even in case of zero output quantities, i.e., if some outputs are not produced by some of the firms. However, the econometric estimation of the SRPF—as the estimation of distance functions in general—is susceptible to endogeneity problems. To address these problems, we apply a profit-maximizing framework to derive a system of equations after incorporating technical inefficiency. As the latter enters non-trivially into the system of equations and as the Jacobian is highly complicated, we use Monte Carlo methods of inference. Using US banking data to illustrate our innovative approach, we also address the problems of missing prices and the dependence on the ordering of the outputs via model averaging.

On Variational and PDE-Based Methods for Accurate Distance Function Estimation

A new variational problem for accurate approximation of the distance from the boundary of a domain is proposed and studied. It is shown that the problem can be efficiently solved by the alternating direction method of multipliers. Links between this problem and $$p$$-Laplacian diffusion are established and studied. Advantages of the proposed distance function estimation method are demonstrated by numerical experiments.

An ADMM-based scheme for distance function approximation

A novel variational problem for approximating the distance function (to a domain boundary) is proposed. It is shown that this problem can be efficiently solved by ADMM. A review of several other variational and PDE-based methods for distance function estimation is presented. Advantages of the proposed distance function estimation method are demonstrated by numerical experiments. Applications of the method to the problems of surface curvature estimation and computing the skeleton of a binary image are shown.

Nonparametric Identification and Estimation of Distance Functions in Network Formation Models with Fixed Effects

The second chapter of the dissertation discusses the non-parametric extension of the network formation model in Toth (2018), when the researcher does not assume the functional form of the distance function. An intuitive way for the non-parametric extension is to use the parametric estimator for linear indices coupled with a series expansion. While the technique is generally applicable, it comes with the caveat that the identification of the models must be assured a priori. After demonstrating the applicability of the method on classical models of Manski (1987) and Han (1987), we prove the nonparametric identification of the distance function for the network formation model, and define the corresponding series estimator. We give a proof for consistency, and also analyze the rate of convergence.

Reducing CO2 emissions from drinking water treatment plants: A shadow price approach

The water industry is currently facing the challenge to reduce its carbon footprint. Although the majority of previous studies have focused on wastewater treatment energy issues, a non-negligible quantity of energy is consumed in drinking water treatment plants (DWTPs). To develop environmental policies aimed to reduce CO2 emissions, it is essential to estimate the shadow price of CO2 because this can provide information about the marginal abatement cost of CO2. This paper computes the shadow price of CO2 for a sample of Chilean DWTPs using directional distance function estimation. The potential reduction of CO2 emissions for each DWTP is also calculated. Finally, applying a non-parametric hypothesis test, factors that affect CO2 shadow prices are investigated. The results indicated that the Chilean DWTPs evaluated have notable room to reduce CO2 emissions. Moreover, the average shadow price of CO2 for DWTPs is 5.7% of the drinking water price. The methodology and results of this study are of great interest for water companies and policy makers to introduce incentives for promoting the transition towards an urban water cycle with a low carbon footprint.

Profitability development of Czech dairy farms

The paper deals with the development and main determinants of the profitability of Czech dairy farms. The aim of the paper is to evaluate the differences in the dynamics of profitability for two types of milk producers - specialized dairy farms and mixed farms - within the context of the agricultural policy changes. This aim is achieved by decomposing profitability into output growth, output and input price changes, changes in decoupled subsidies, technical change, scale, mark-up, and technical efficiency change components based on input distance function estimation. Based on the panel data obtained from the FADN database in the time period 2004-2011, it was found that the change in profitability was positive in the analysed time period, and slightly higher for the specialized dairy farms than for the mixed ones. The changes in output price, mark-up component and technical change are the main determinants of the development of profitability. Agricultural policy measures had different effects on these components. The strongest correlation was between the operational subsidies and the technical change and technical efficiency change, and this correlation was negative.

On Variational and PDE‐Based Distance Function Approximations

AbstractIn this paper, we deal with the problem of computing the distance to a surface (a curve in two dimensional) and consider several distance function approximation methods which are based on solving partial differential equations (PDEs) and finding solutions to variational problems. In particular, we deal with distance function estimation methods related to the Poisson‐like equations and generalized double‐layer potentials. Our numerical experiments are backed by novel theoretical results and demonstrate efficiency of the considered PDE‐based distance function approximations.

Econometric estimation of distance functions and associated measures of productivity and efficiency change

Multi-input multi-output production technologies can be represented using distance functions. Econometric estimation of these functions typically involves factoring out one of the outputs or inputs and estimating the resulting equation using maximum likelihood methods. A problem with this approach is that the outputs or inputs that are not factored out may be correlated with the composite error term. Fernandez et al. (J Econ 98:47–79, 2000) show how to solve this so-called ‘endogeneity problem’ using Bayesian methods. In this paper I use the approach to estimate an output distance function and an associated index of total factor productivity (TFP) change. The TFP index is a new index that satisfies most, if not all, economically-relevant axioms from index number theory. It can also be exhaustively decomposed into a measure of technical change and various measures of efficiency change. I illustrate the methodology using state-level data on U.S. agricultural input and output quantities (no prices are needed). Results are summarized in terms of the characteristics (e.g., means) of estimated probability density functions for measures of TFP change, technical change and efficiency change.

A Real Time Morphological Snakes Algorithm

Active contours, or snakes, are computer-generated curves that move within images to find out salient image structures like object boundaries. Energy based formulations using a level set approach have been successfully used to model the snake evolution. The Euler-Lagrange equation associated to such energies yields to partial differential equations (PDE) which are usually solved using level set methods which involve contour distance function estimation and standard methods to discretize the PDE. Recently we have proposed a morphological approach to snake evolution. First, we observe that the differential operators used in the standard PDE snake models can be approached using morphological operations. By combining the morphological operators associated to the PDE components we achieve a new morphological approach to the PDE snakes evolution. This new approach is based on numerical methods which are very simple and fast. Moreover, since the level set is just a binary piecewise constant function, this approach does not require to estimate a contour distance function to define the level set. In this paper we present an algorithm to compute morphological snake evolution in real time.

A Comparison of Distance Function Estimation Methods for Analyzing Production Characteristics and Efficiency

A Comparison of Distance Function Estimation Methods for Analyzing Production Characteristics and Efficiency

Vector Quantization for Arbitrary Distance Function Estimation

In this article we apply the concepts of vector quantization for the evaluation of arbitrary distance functions—a problem which has important applications in logistics and location analysis. The input to our problem is the set of coordinates of a large number of nodes whose internode arbitrary “distances” have to be estimated. To render the problem interesting, nontrivial and realistic, we assume that the explicit form of this distance function is both unknown and uncomputable. Unlike traditional operations research methods, which compute aggregate parameters of functional estimators according to certain goodness-of-fit criteria, we have utilized vector quantization principles to first adaptively polarize the nodes into subregions. Subsequently, the parameters characterizing the subregions are learned by using a variety of methods (including, for academic purposes a vector quantization strategy in the metadomain). The algorithms have been rigorously tested for the actual roadtravel distances involving cities in Turkey. The results obtained are not only conclusive, but also the best currently available from any single or hybrid strategy.