Stochastic Frontier Models Frontier Functions Part 2 17

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

Stochastic Frontier. Models Frontier Functions [Part 2] Deterministic Frontier: Programming Estimators 2/7

Stochastic Frontier. Models Frontier Functions [Part 2] Estimating Inefficiency 3/7

Stochastic Frontier. Models Frontier Functions [Part 2] 4/7 Statistical Problems with Programming Estimators They do correspond to MLEs. p The likelihood functions are “irregular” p There are no known statistical properties – no estimable covariance matrix for estimators. p They might be “robust, ” like LAD. p n n Noone knows for sure. Never demonstrated.

Stochastic Frontier. Models Frontier Functions [Part 2] An Orthodox Frontier Model with a Statistical Basis 5/7

Stochastic Frontier. Models Frontier Functions [Part 2] Extensions p p Cost frontiers, based on duality results: ln y = f(x) – u ln C = g(y, w) + u’ u > 0. u’ > 0. Economies of scale and allocative inefficiency blur the relationship. Corrected and modified least squares estimators based on the deterministic frontiers are easily constructed. 6/7

Stochastic Frontier. Models Frontier Functions [Part 2] Data Envelopment Analysis 7/7