Efficiency Measurement

William GreeneStern School of BusinessNew York University

Lab Session 3

Heterogeneity

WHO Data

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)

Heterogeneous Frontier Model

FRONTIER ; LHS = LDALE ; RHS = ONE,LHEXP,LHEXP2,LEDUC,

VOICE,GEFF,LPOPDEN,TROPICS

; EFF = UI_WHO $

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

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 $

Efficiency Estimates|Load Factor

Model Command for Heteroscedasticity

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

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

Parametric vs. Nonparametric

Latent Class Model