Efficiency Measurement

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Efficiency Measurement

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

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Lab Session 2

• Stochastic Frontier Estimation

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Application to Spanish Dairy Farms
N 247 farms, T 6 years (1993-1998)
Input Units Mean Std. Dev. Minimum Maximum
Milk Milk production (liters) 131,108 92,539 14,110 727,281
Cows of milking cows 2.12 11.27 4.5 82.3
Labor man-equivalent units 1.67 0.55 1.0 4.0
Land Hectares of land devoted to pasture and crops. 12.99 6.17 2.0 45.1
Feed Total amount of feedstuffs fed to dairy cows (tons) 57,941 47,981 3,924.14 376,732
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Using Farm Means of the Data
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OLS vs. Frontier/MLE
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JLMS Inefficiency Estimator

• FRONTIER LHS the variable
• RHS ONE, the variables
• EFF the new variable
• Creates a new variable in the data set.
• FRONTIER LHS YIT RHS X EFF U_i
• Use Techeff variable to compute exp(-u).

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Confidence Intervals for Technical
Inefficiency, u(i)
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Prediction Intervals for Technical Efficiency,
Exp-u(i)
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Prediction Intervals for Technical Efficiency,
Exp-u(i)
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Compare SF and DEA
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Similar, but differentwith a crucial pattern
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The Dreaded Error 315 Wrong Skewness
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Cost Frontier Model
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Linear Homogeneity Restriction
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Translog vs. Cobb Douglas
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Cost Frontier Command

• FRONTIER COST
• LHS the variable
• RHS ONE, the variables
• EFF the new variable
• e(i) v(i) u(i) u(i) is still positive

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Estimated Cost Frontier CG
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Cost Frontier Inefficiencies
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Normal-Truncated NormalFrontier Command

• FRONTIER COST
• LHS the variable
• RHS ONE, the variables
• Model Truncation
• EFF the new variable
• e(i) v(i) /- u(i)
• u(i) U(i), U(i) Nµ,?2
• The half normal model has µ 0.

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Observations

• Truncation Model estimation is often unstable
• Often estimation is not possible
• When possible, estimates are often wild
• Estimates of u(i) are usually only moderately
  affected
• Estimates of u(i) are fairly stable across models
  (exponential, truncation, etc.)

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Truncated Normal Model
Model T
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Truncated Normal vs. Half Normal
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Multiple Output Cost Function
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Ranking Observations

• CREATE newname Rnk ( Variable )
• Creates the set of ranks. Use in any
  subsequent analysis.

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