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Frontier Models and Efficiency Measurement Lab Session 2: Stochastic Frontier

William Greene Stern School of Business New York University. Frontier Models and Efficiency Measurement Lab Session 2: Stochastic Frontier. 0 Introduction 1 Efficiency Measurement 2 Frontier Functions 3 Stochastic Frontiers 4 Production and Cost 5 Heterogeneity 6 Model Extensions

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Frontier Models and Efficiency Measurement Lab Session 2: Stochastic Frontier

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  1. William Greene Stern School of Business New York University Frontier Models and Efficiency MeasurementLab Session 2: Stochastic Frontier 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

  2. Application to Spanish Dairy Farms N = 247 farms, T = 6 years (1993-1998)

  3. Using Farm Means of the Data

  4. OLS vs. Frontier/MLE

  5. 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).

  6. Confidence Intervals for Technical Inefficiency, u(i)

  7. Prediction Intervals for Technical Efficiency, Exp[-u(i)]

  8. Prediction Intervals for Technical Efficiency, Exp[-u(i)]

  9. Compare SF and DEA

  10. Similar, but differentwith a crucial pattern

  11. The Dreaded Error 315 – Wrong Skewness

  12. Cost Frontier Model

  13. Linear Homogeneity Restriction

  14. Translog vs. Cobb Douglas

  15. Cost Frontier Command FRONTIER ; COST ; LHS = the variable ; RHS = ONE, the variables ; TechEFF = the new variable $ ε(i) = v(i) + u(i) [u(i) is still positive]

  16. Estimated Cost Frontier: C&G

  17. Cost Frontier Inefficiencies

  18. Normal-Truncated NormalFrontier Command FRONTIER ; COST ; LHS = the variable ; RHS = ONE, the variables ; Model = Truncation ; EFF = the new variable $ ε(i) = v(i) +/- u(i) u(i) = |U(i)|, U(i) ~ N[μ,2] The half normal model has μ = 0.

  19. Observations about Truncation Model • 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.)

  20. Truncated Normal Model ; Model = T

  21. Truncated Normal vs. Half Normal

  22. Multiple Output Cost Function

  23. Ranking Observations CREATE ; newname = Rnk ( Variable ) $ Creates the set of ranks. Use in any subsequent analysis.

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