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Efficiency Measurement

William Greene Stern School of Business New York University. Efficiency Measurement. Session 2. Frontier Functions. Deterministic Frontier: Programming Estimators. Estimating Inefficiency. Statistical Problems with Programming Estimators. They do correspond to MLEs.

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Efficiency Measurement

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  1. William Greene Stern School of Business New York University Efficiency Measurement

  2. Session 2 Frontier Functions

  3. Deterministic Frontier: Programming Estimators

  4. Estimating Inefficiency

  5. Statistical Problems with Programming Estimators • They do correspond to MLEs. • The likelihood functions are “irregular” • There are no known statistical properties – no estimable covariance matrix for estimates. • They might be “robust,” like LAD. • Noone knows for sure. • Never demonstrated.

  6. An Orthodox Frontier Modelwith a Statistical Basis

  7. Extensions • 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.

  8. Data Envelopment Analysis

  9. Methodological Problems with DEA • Measurement error • Outliers • Specification errors • The overall problem with the deterministic frontier approach

  10. DEA and SFA: Same Answer? • Christensen and Greene data • N=123 minus 6 tiny firms • X = capital, labor, fuel • Y = millions of KWH • Cobb-Douglas Production Function vs. DEA • (See Coelli and Perelman (1999).)

  11. Comparing the Two Methods.

  12. Total Factor Productivity

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