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

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

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)

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