Efficiency Measurement

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Efficiency Measurement

• William Greene
• Stern School of Business
• New York University

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Session 2

• Frontier Functions

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Deterministic Frontier Programming Estimators
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Estimating Inefficiency
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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.

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An Orthodox Frontier Modelwith a Statistical
Basis
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Extensions

• Cost frontiers, based on duality results
• ln y f(x) u ?? ln C g(y,w) u
• u gt 0. u gt 0. Economies of scale and
• allocative inefficiency blur the relationship.
• Corrected and modified least squares estimators
  based on the deterministic frontiers are easily
  constructed.

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Data Envelopment Analysis
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Methodological Problems with DEA

• Measurement error
• Outliers
• Specification errors
• The overall problem with the deterministic
  frontier approach

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DEA and SFA Same Answer?

• Christensen and Greene data
• N123 minus 6 tiny firms
• X capital, labor, fuel
• Y millions of KWH
• Cobb-Douglas Production Function vs. DEA
• (See Coelli and Perelman (1999).)

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Comparing the Two Methods.
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Total Factor Productivity