**Stochastic frontier analysis** (SFA) is a method of economic modeling. It has its starting point in the stochastic production frontier models simultaneously introduced by Aigner, Lovell and Schmidt (1977) and Meeusen and Van den Broeck (1977).

Extensions: The two-tier stochastic frontier model

Polacheck & Yoon (1987) have introduced a three-component error structure, where one non-negative error term is added to, while the other is subtracted from, the zero-mean symmetric random disturbance. This modeling approach attempts to measure the impact of informational inefficiencies (incomplete and imperfect information) on the prices of realized transactions, inefficiencies that in most cases characterize both parties in a transaction (hence the two inefficiency components, to disentangle the two effects).

Recently, various non-parametric and semi-parametric approaches were proposed in the literature, where no parametric assumption on the functional form of production relationship is made, see for example Parmeter and Kumbhakar (2014) and Park, Simar and Zelenyuk (2015) ^{[1]} and references cited therein.

References

**^**Park, B., Simar, L. and V. Zelenyuk (2015) “Categorical data in local maximum likelihood: theory and applications to productivity analysis,” Journal of Productivity Analysis 43:2, pp. 199-214.

- Aigner, D.J.; Lovell, C.A.K.; Schmidt, P. (1977) Formulation and estimation of stochastic frontier production functions. Journal of Econometrics, 6:21–37.
- Baltas, G., (2005). Exploring Consumer Differences in Food Demand: A Stochastic Frontier Approach. British Food Journal, 107(9): 685-692.
- Coelli, T.J.; Rao, D.S.P.; O’Donnell, C.J.; Battese, G.E. (2005) An Introduction to Efficiency and Productivity Analysis, 2nd Edition. Springer, ISBN 978-0-387-24266-8.`
- Greene, W. H. (2008) The Econometric Approach to Efficiency Analysis. In Fried, H. O., Knox Lovell, C. A., and Schmidt, P., editors, The Measurement of Productive Efficiency. Oxford University Press, New York and Oxford.
- Parmeter, C.F., Kumbhakar, S.C., (2014) “Efficiency Analysis: A Primer on Recent Advances,” Foundations and Trends in Econometrics, 7(3-4), 191-385.
- Polachek, S. W. ; Yoon, B. J. (1987). A two-tiered earnings frontier estimation of employer and employee information in the labor market. Review of Economics and Statistics, 69(2), 296-302.