Frontier Models and Efficiency Measurement Lab Session 3: Heterogeneity

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Frontier Models and Efficiency Measurement Lab Session 3: Heterogeneity William Greene Stern School of Business New York University 0 Introduction 1 Efficiency Measurement 2 Frontier Functions 3 Stochastic Frontiers 4 Production and Cost 5 Heterogeneity 6 Model Extensions 7 Panel Data 8 Applications

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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 Presentation

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Page 1: Frontier Models and Efficiency Measurement Lab Session 3: Heterogeneity

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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Page 3: Frontier Models and Efficiency Measurement Lab Session 3: Heterogeneity

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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Page 7: Frontier Models and Efficiency Measurement Lab Session 3: Heterogeneity

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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Page 10: Frontier Models and Efficiency Measurement Lab Session 3: Heterogeneity

Efficiency Estimates|Load Factor

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Page 12: Frontier Models and Efficiency Measurement Lab Session 3: Heterogeneity

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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Page 17: Frontier Models and Efficiency Measurement Lab Session 3: Heterogeneity
Page 18: Frontier Models and Efficiency Measurement Lab Session 3: Heterogeneity

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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