A Multilevel Stochastic Efficiency Estimation Model With Application | Chapter 8 | Mathematics and Computer Science: Research Updates Vol. 4

A two-component error term stochastic frontier model was independently, which was followed by various attempts to evaluate the efficiency of production processes and cost functions. The traditional single-level stochastic frontier model ignores the hierarchical structure of data. This leads to inaccurate efficiency scores. In contrast, multilevel models, a member of random coefficients models, account for data structure but are not frontier. These models remain largely unfamiliar to researchers, particularly in terms of practical application. Despite efforts to integrate this model into various fields, success has been limited. This paper examines the extent to which multilevel models have been used in efficiency analysis. Therefore, the goal of this research is to develop an appropriate model for hierarchical data.

 

To highlight the impact of ignoring data structure in efficiency analysis, clustered data is generated using RStudio and Limdep, alongside real data collection. The data was paneled, with five observations coming from each of the three hundred individuals. This resulted in 1500 observations. Variable p1 was generated in such a way that it took three hundred values, with each value being repeated five times. Each set of five equal values was meant for each of the three hundred individuals described. A multilevel stochastic frontier model is proposed and fitted to both simulated and real datasets in Limdep. Additionally, three versions of the conventional single-level stochastic frontier model are fitted to the same datasets for comparison.

 

Results indicate that ignoring data structure distorts efficiency levels and subject rankings in both simulated and real scenarios.  The proposed model yields significantly higher efficiency estimates than any of the conventional models, suggesting that current efficiency estimates in hierarchical organizations, such as municipalities, is underestimated. Ignoring the structure of data does not only lead to the underestimation of standard errors but also falsifies the efficiency levels of the subjects. The study's findings serve as evidence supporting the idea that implementing the proposed model in hierarchical organizations will effectively address this discrepancy.

 

Author (s) Details

Peter Chimwanda
Department of Mathematics, Chinhoyi University of Technology, Zimbabwe.

 

 

Please see the book here:- https://doi.org/10.9734/bpi/mcsru/v4/4966