Solar energy is one of the most promising energy sources as it its significantly reduce greenhouse gas (GHG) emissions compared to fossil fuels. In this study, we employ the meta frontier framework to estimate US solar energy performance in 2019 using stochastic non-parametric envelopment of data (StoNED) under the convex and non-convex frameworks. This estimation allows us to monitor operating inefficiencies and technological gaps in each observation. In addition, we investigate the potential impact of the specification of a convex production technology in relation to the use of a nonconvex technology in the comparative analysis. This methodological reflection is mainly supported by the recent engineering literature that provides evidence of the non-convex hypothesis. The results indicate that a multifaceted approach must be taken to ensure the supply of energy. Given that sunny states have the potential to transmit energy to other states, the drawbacks, such as environmental concerns and high investment expenses, drive policymakers to look for other alternatives, such as adapting panels that are suitable for specific conditions.
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Data envelopment analysis (DEA) is a nonparametric technique that estimates production frontier empirically [7,8]. The efficiency scores are calculated for each decision-making unit (DMU) under linear programming by conducting a loop. The DEA efficient frontier graphically looks like piecewise linear segments based on undominated DMUs (multiple inputs/outputs), yielding a set of convex production possibilities. The supporting argument regarding DEA does not demand any predefined assumptions about the geometrical shape of efficient frontier . The fundamental drawback of this method is that it does not consider noise from data; therefore, distance from the Pareto frontier is due to inefficiency exclusively. Like DEA, free disposal hull (FDH) is a nonparametric technique for assessing performance based on a production frontier . However, the distinction between these models is that DEA assumes convexity axiom, whereas FDH does not. Consequently, the FDH production possibility set is typically non-convex.  developed a mixed-integer linear programming (MILP) formulation with a simple algorithm.Alternatively, stochastic frontier analysis (SFA) proposed by Refs. [12,13] is an econometric approach in productivity and efficiency analysis. For the survey of this parametric strand of production-efficiency literature, see Ref. . Parametric methods assume some predefined assumption regarding the shape of the frontier that is considered a weakness . The supporting argument regarding SFA is that the composite error term is a summation of one-sided disturbance (inefficiency) and two-sided disturbance term (noise). In order to combine previous methodologies, a significant amount of research has been done on efficiency analysis. Recently, designing a model that incorporates both the nonparametric characteristics, i.e., axiomatic frontier estimation from DEA- alongside the stochastic component from SFA has been a controversial issue among economics.  were pioneers who proposed a two-step pseudo-likelihood estimator. They applied semi-parametric kernel regression to evaluate an average production frontier and maximize a pseudo-likelihood function for the remaining parameters, which are two favorable properties of these frameworks. The generalized form of  developed by Ref.  based on the local maximum likelihood principle ; or  from the nonparametric aspect and localizing the parameters of the stochastic component, through one-step maximization procedure. Further contributions to this unified framework include the model by Ref.  proposed to estimate the production frontier. This methodology provides a statistical foundation for estimating nonparametric frontier and avoiding any specific functional form. For an accurate comparison of some earlier approaches to these frameworks, see Vaninsky, (2010), . However, most of these models require some further assumptions that make them computationally challenging to use. Stochastic nonparametric envelopment of data (StoNED) is another framework that integrates SFA and DEA models [22–24]. This model's notable characteristics that discriminate it compared with the previous model  are that it excels in different Monte Carlo simulations, mainly when the data is subject to significant noise.
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