1. William Greene Stern School of Business New York University
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

3. WHO Data

4. 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)

5. Heterogeneous Frontier Model
FRONTIER ; LHS = LDALE
; RHS = ONE,LHEXP,LHEXP2,LEDUC,
VOICE,GEFF,LPOPDEN,TROPICS
; EFF = UI_WHO $

7. Heteroscedasticity

8. 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 $

10. Efficiency Estimates|Load Factor

12. Model Command for Heteroscedasticity

15. Heterogeneity in the Mean of u(i)

18. 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 

19. Parametric vs. Nonparametric

22. Latent Class Model