Download presentation
Presentation is loading. Please wait.
1
Frontier Models and Efficiency Measurement Lab Session 2: Stochastic Frontier William Greene Stern School of Business New York University 0Introduction 1Efficiency Measurement 2Frontier Functions 3Stochastic Frontiers 4Production and Cost 5Heterogeneity 6Model Extensions 7Panel Data 8Applications
2
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)
3
Using Farm Means of the Data
6
OLS vs. Frontier/MLE
8
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).
14
Confidence Intervals for Technical Inefficiency, u(i)
15
Prediction Intervals for Technical Efficiency, Exp[-u(i)]
![Prediction Intervals for Technical Efficiency, Exp[-u(i)]](http://images.slideplayer.com./26/8762232/slides/slide_15.jpg "Prediction Intervals for Technical Efficiency, Exp[-u(i)]")
17
Compare SF and DEA
18
Similar, but different with a crucial pattern
20
The Dreaded Error 315 – Wrong Skewness
21
Cost Frontier Model
22
Linear Homogeneity Restriction
23
Translog vs. Cobb Douglas
24
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]
![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]](http://images.slideplayer.com./26/8762232/slides/slide_24.jpg "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]")
25
Estimated Cost Frontier: C&G
26
Cost Frontier Inefficiencies
27
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./26/8762232/slides/slide_27.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.")
28
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.)
29
Truncated Normal Model ; Model = T
30
Truncated Normal vs. Half Normal
31
Multiple Output Cost Function
32
Ranking Observations CREATE ; newname = Rnk ( Variable ) $ Creates the set of ranks. Use in any subsequent analysis.
Similar presentations
![[Part 5] 1/53 Stochastic FrontierModels Heterogeneity Stochastic Frontier Models William Greene Stern School of Business New York University 0Introduction.](/11/3189205/big_thumb.jpg "[Part 5] 1/53 Stochastic FrontierModels Heterogeneity Stochastic Frontier Models William Greene Stern School of Business New York University 0Introduction.>")
![[Part 4] 1/25 Stochastic FrontierModels Production and Cost Stochastic Frontier Models William Greene Stern School of Business New York University 0Introduction.](/11/3189255/big_thumb.jpg "[Part 4] 1/25 Stochastic FrontierModels Production and Cost Stochastic Frontier Models William Greene Stern School of Business New York University 0Introduction.>")
![[Part 3] 1/49 Stochastic FrontierModels Stochastic Frontier Model Stochastic Frontier Models William Greene Stern School of Business New York University.](/15/4666432/big_thumb.jpg "[Part 3] 1/49 Stochastic FrontierModels Stochastic Frontier Model Stochastic Frontier Models William Greene Stern School of Business New York University.>")
![[Part 8] 1/27 Stochastic FrontierModels Applications Stochastic Frontier Models William Greene Stern School of Business New York University 0Introduction.](/19/5854682/big_thumb.jpg "[Part 8] 1/27 Stochastic FrontierModels Applications Stochastic Frontier Models William Greene Stern School of Business New York University 0Introduction.>")
![[Part 7] 1/68 Stochastic FrontierModels Panel Data Stochastic Frontier Models William Greene Stern School of Business New York University 0Introduction.](/18/6142499/big_thumb.jpg "[Part 7] 1/68 Stochastic FrontierModels Panel Data Stochastic Frontier Models William Greene Stern School of Business New York University 0Introduction.>")
