frontier models and efficiency measurement lab session 3: heterogeneity
DESCRIPTION
William Greene Stern School of Business New York University. Frontier Models and Efficiency Measurement Lab Session 3: Heterogeneity. 0Introduction 1 Efficiency Measurement 2 Frontier Functions 3 Stochastic Frontiers 4 Production and Cost 5 Heterogeneity 6 Model Extensions - PowerPoint PPT PresentationTRANSCRIPT
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Frontier Models and Efficiency Measurement
Lab Session 3: Heterogeneity
William Greene
Stern School of Business
New York University
0 Introduction1 Efficiency Measurement2 Frontier Functions3 Stochastic Frontiers4 Production and Cost5 Heterogeneity6 Model Extensions7 Panel Data8 Applications
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WHO Data
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Heterogeneous Frontier Command
FRONTIER [; COST] ; LHS = the variable
; RHS = ONE, the variables, the additional variables ; EFF = the new variable $
ε(i) = v(i) +/- u(i)
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Heterogeneous Frontier Model
FRONTIER ; LHS = LDALE ; RHS = ONE,LHEXP,LHEXP2,LEDUC,
VOICE,GEFF,LPOPDEN,TROPICS
; EFF = UI_WHO $
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Heteroscedasticity
ui u i
vi v i
Either or both of
exp[ ]
(heteroscedasticity in inefficiency)
exp[ ]
(heteroscedasticity in random shift)
Variables may be the same or different.
w
w
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Effects of Environmental Variable on Efficiency
? Frontier cost function with environmental? Variables, load factor, points served, stage? Length.FRONTIER ; Cost ; Lhs = lc ; Rhs = one,…, loadfctr,log(points),log(stage) $
? How does load factor affect efficiency?SIMULATE ; scenario: & loadfctr = .4(.025).95 ; plot $
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Efficiency Estimates|Load Factor
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Model Command for Heteroscedasticity
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Heterogeneity in the Mean of u(i)
i
i i
2i
i
Mean of u depends on measured variables
u | U |
U ~ N[ , ] (may be heteroscedastic)
= i u
iz
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Nonparametric Frontier
Frontier with local
Compute residuals then estimate and given the set of residuals from the nonparametric frontier
Compute efficiencies using residuals and and
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Parametric vs. Nonparametric
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Latent Class Model
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