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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 InputUnitsMeanStd. Dev. MinimumMaximum MilkMilk production (liters) 131,108 92,539 14,110727,281 Cows# of milking cows 2.12 11.27 4.5 82.3 Labor# man-equivalent units 1.67 0.55 1.0 4.0 LandHectares of land devoted to pasture and crops. 12.99 6.17 2.0 45.1 FeedTotal amount of feedstuffs fed to dairy cows (tons) 57,94147,9813,924.14 376,732 N = 247 farms, T = 6 years (1993-1998)
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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)]
![Prediction Intervals for Technical Efficiency, Exp[-u(i)]](http://images.slideplayer.com/26/8762199/slides/slide_16.jpg "Prediction Intervals for Technical Efficiency, Exp[-u(i)]")
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Compare SF and DEA
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Similar, but different with 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 $ ε(i) = v(i) + u (i) [u(i) is still positive]
![Cost Frontier Command FRONTIER ; COST ; LHS = the variable ; RHS = ONE, the variables ; EFF = the new variable $ ε(i) = v(i) + u (i) [u(i) is still positive]](http://images.slideplayer.com/26/8762199/slides/slide_25.jpg "Cost Frontier Command FRONTIER ; COST ; LHS = the variable ; RHS = ONE, the variables ; EFF = the new variable $ ε(i) = v(i) + u (i) [u(i) is still positive]")
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Estimated Cost Frontier: C&G
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Cost Frontier Inefficiencies
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Normal-Truncated Normal Frontier 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.
![Normal-Truncated Normal Frontier 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.](http://images.slideplayer.com/26/8762199/slides/slide_28.jpg "Normal-Truncated Normal Frontier 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.")
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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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