Smooth Constrained Frontier Analysis

Parmeter, Christopher F.; Racine, Jeffrey S.

doi:10.1007/978-1-4614-1653-1_18

Cited by 27 publications

(16 citation statements)

References 40 publications

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“…To separate them, the empirical studies have been assuming asymmetric distribution to the efficiencies (usually a half-normal), while they used to assume that random errors follow a symmetric distribution (usually the standard normal) (Aigner et al , 1977). Even though the SFA is traditionally parametric, the latter improvements have given it some degrees of convergence with non-parametric models, which are referred as the non-parametric or semiparametric SFA (Banker and Maindiratta, 1992; Fan et al , 1996; Kneip and Simar, 1996; Kumbhakar et al , 2017; Kuosmanen and Kortelainen, 2012; Noh, 2014; Parmeter and Racine, 2013). Essentially, Fan et al (1996) and Kneip and Simar (1996) provided the baseline studies for these methodologies.…”

Section: Literature Reviewmentioning

confidence: 99%

Efficiency analysis of viticulture systems in the Portuguese Douro region

Santos

Rodríguez

Marta-Costa

2020

IJWBR

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Purpose The purpose of this paper is to estimate and analyse the technical efficiency (TE) component of productivity for a sample of winegrowers from the Douro Demarcated Region in Portugal. Design/methodology/approach The data were collected through face-to-face surveys and includes a sample of 110 farmers’ vineyards with specific input-output information and other data about production systems during the year of 2017. The authors use a two-stage data envelopment analysis using bootstrap techniques to obtain TE scores in the farmers’ vineyards and to examine the determinants of its efficiency. Findings The results show that some farmers’ vineyards have a low efficiency level and that there are essential determinants of the production system, which can influence its efficiency. This suggests considerable opportunities for improvement of wine grape productivity through better use of available resources considering the state of technology. Originality/value This work has overcome the lack of data in the farmers’ vineyards, the lack of efficiency studies in the region and also allowed to evaluate the production systems and to assess their impact on efficiency.

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Section: Literature Reviewmentioning

confidence: 99%

Efficiency analysis of viticulture systems in the Portuguese Douro region

Santos

Rodríguez

Marta-Costa

2020

IJWBR

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“…Another feasible option under multiple shape constraints is to adapt the elegant kernel regression device of Hall and Huang (2001) and Du et al (2013). This idea has recently been implemented by Parmeter and Racine (2013) and improved in Noh (2014) by developing kernel-type boundary smoothers computed via quadratic programming, with suitably selected bandwidths. A drawback of this method so far is, however, that it does not ensure perfectly the desired monotonicity or monotone concavity constraints.…”

Section: Discussionmentioning

confidence: 99%

“…This justifies the concavity property of the frontier function ϕ.x/, which is known in economics as diminishing marginal returns. Thus, the differentiability of ϕ.x/ across the support of the covariate is a desirable microeconomic feature if one is interested in measuring the responsiveness of output to changes in the input (see, for example, Parmeter and Racine (2013)). This is particularly important if one is interested in returns to scale, which are defined as the sum of input elasticities, which in turn rely on the second derivative ϕ .x/.…”

Section: Data Examplesmentioning

confidence: 99%

Data Envelope Fitting with Constrained Polynomial Splines

Daouia

Noh

Park

2014

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary Estimation of support frontiers and boundaries often involves monotone and/or concave edge data smoothing. This estimation problem arises in various unrelated contexts, such as optimal cost and production assessments in econometrics and master curve prediction in the reliability programmes of nuclear reactors. Very few constrained estimators of the support boundary of a bivariate distribution have been introduced in the literature. They are based on simple envelopment techniques which often suffer from lack of precision and smoothness. Combining the edge estimation idea of Hall, Park and Stern with the quadratic spline smoothing method of He and Shi, we develop a novel constrained fit of the boundary curve which benefits from the smoothness of spline approximation and the computational efficiency of linear programmes. Using cubic splines is also feasible and more attractive under multiple shape constraints; computing the optimal spline smoother is then formulated as a second‐order cone programming problem. Both constrained quadratic and cubic spline frontiers have a similar level of computational complexity to those of the unconstrained fits and inherit their asymptotic properties. The utility of this method is illustrated through applications to some real data sets and simulation evidence is also presented to show its superiority over the best‐known methods.

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“…(Du, Parmeter and Racine 2013) extend this estimation to further impose convexity useful for production function applications. For a useful discussion, see (Henderson and Parmeter 2009), (Parmeter and Racine 2013) and (Yagi, Johnson and Kuosmanen 2016). In this paper we are focused on developing a hinge function formulation and do not consider the kernel regression based approaches.…”

Section: Introductionmentioning

confidence: 99%

An improved Afriat–Diewert–Parkan nonparametric production function estimator

Olesen

Ruggiero

2018

European Journal of Operational Research

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Recent developments in the production frontier literature include nonparametric estimators with shape constraints. A few of these estimators rely on the Afriat inequalities to provide piecewise linear approximations to the production function/frontier. We show in this paper that these Afriat-Diewert-Parkan (ADP) estimators have deficiencies in the presence of moderate statistical noise including overfitting and a relatively high estimator variance. We propose new estimators with lower variance and a relatively low bias. We consider such alternative estimators based on (weighted) averages of random hinge functions with parameter restrictions. Small sample properties of the estimators are presented that show our new estimators outperform the existing ADP estimators when moderate to large amounts of noise are present.

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Smooth Constrained Frontier Analysis

Cited by 27 publications

References 40 publications

Efficiency analysis of viticulture systems in the Portuguese Douro region

Efficiency analysis of viticulture systems in the Portuguese Douro region

Data Envelope Fitting with Constrained Polynomial Splines

An improved Afriat–Diewert–Parkan nonparametric production function estimator

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