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	Stochastic Frontier Firm Efficiency Analysis	Malmquist Firm Productivity Index
Campo	Gestione strategica	Gestione strategica
Famiglia	Regression model	MCDM
Anno di origine	1977	1994
Ideatore	Dennis Aigner, C. A. Knox Lovell & Peter Schmidt; George Battese & Tim Coelli	Rolf Fare, Shawna Grosskopf, Mary Norris & Zhongyang Zhang; Douglas Caves, Laurits Christensen & Erwin Diewert
Tipo	Parametric composed-error regression frontier for firm efficiency	Distance-function index of total factor productivity change for firms
Fonte seminale	Aigner, D., Lovell, C. A. K., & Schmidt, P. (1977). Formulation and estimation of stochastic frontier production function models. Journal of Econometrics, 6(1), 21-37.	Fare, R., Grosskopf, S., Norris, M., & Zhang, Z. (1994). Productivity growth, technical progress, and efficiency change in industrialized countries. American Economic Review, 84(1), 66-83.
Alias	SFA Firm Technical Inefficiency, Parametric Production Frontier Estimation, Composed-Error Efficiency Model, Stochastic Frontier Production Function for Firms	Malmquist TFP Index for Firms, Firm Productivity Change Decomposition, Distance-Function Productivity Index, Malmquist Total Factor Productivity Index
Correlati	3	3
Sintesi	Stochastic frontier analysis (SFA) estimates how far a firm falls short of the best attainable output for its inputs while explicitly separating that shortfall from random noise. Aigner, Lovell and Schmidt's 1977 model introduced the defining idea: a production frontier whose error term is the sum of a symmetric, two-sided noise component and a one-sided, nonnegative inefficiency component. Because deviations below the frontier can come either from bad luck and measurement error or from genuine underperformance, SFA models both and recovers a firm-specific technical-efficiency estimate. Battese and Coelli's 1995 panel-data extension let the mean of the inefficiency term depend on firm characteristics, so analysts can simultaneously estimate the frontier and explain why some firms are more inefficient than others.	The Malmquist firm productivity index measures how a firm's total factor productivity changes between two periods and decomposes that change into two strategically meaningful parts: catching up to best practice (efficiency change) and the best-practice frontier itself shifting (technical change). The index is grounded in Caves, Christensen and Diewert's 1982 theory of productivity index numbers built from distance functions, and was made operational for empirical work by Fare, Grosskopf, Norris and Zhang in 1994, who showed how to compute it from data using linear-programming distance functions and to split it into efficiency-change and frontier-shift components. For firms, it answers whether productivity gains came from better management closing the gap to the leaders or from the whole industry's technological possibilities expanding.