Lab Session 2 Stochastic Frontier William Greene Stern School of Business New York University 0 Introduction 1 Efficiency Measurement 2 Frontier Functions 3 Stochastic Frontiers 4 Production and Cost ID: 656273
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Frontier Models and Efficiency MeasurementLab Session 2: Stochastic Frontier
William GreeneStern School of BusinessNew York University
0 Introduction1 Efficiency Measurement2 Frontier Functions3 Stochastic Frontiers4 Production and Cost5 Heterogeneity6 Model Extensions7 Panel Data8 ApplicationsSlide2
Application to Spanish Dairy Farms
Input
Units
Mean
Std. Dev.
Minimum
Maximum
Milk
Milk production (liters)
131,108 92,539 14,110727,281Cows# of milking cows 2.12 11.27 4.5 82.3Labor# man-equivalent units 1.67 0.55 1.0 4.0LandHectares of land devoted to pasture and crops. 12.99 6.17 2.0 45.1FeedTotal amount of feedstuffs fed to dairy cows (tons) 57,94147,9813,924.14 376,732
N = 247 farms, T = 6 years (1993-1998)Slide3
Using Farm Means of the DataSlide4Slide5Slide6
OLS vs. Frontier/MLESlide7Slide8
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).Slide9Slide10Slide11Slide12Slide13Slide14
Confidence Intervals for Technical Inefficiency, u(i)Slide15
Prediction Intervals for Technical Efficiency, Exp[-u(i)]Slide16
Prediction Intervals for Technical Efficiency, Exp[-u(i)]Slide17
Compare SF and DEASlide18
Similar, but differentwith a crucial patternSlide19Slide20
The Dreaded Error 315 – Wrong SkewnessSlide21
Cost Frontier ModelSlide22
Linear Homogeneity RestrictionSlide23
Translog vs. Cobb DouglasSlide24
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]Slide25
Estimated Cost Frontier: C&GSlide26
Cost Frontier InefficienciesSlide27
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.Slide28
Observations about Truncation Model
Truncation Model estimation is often unstableOften estimation is not possibleWhen possible, estimates are often wildEstimates of u(i) are usually only moderately affectedEstimates of u(i) are fairly stable across models (exponential, truncation, etc.)Slide29
Truncated Normal Model ; Model = TSlide30
Truncated Normal vs. Half NormalSlide31
Multiple Output Cost FunctionSlide32
Ranking Observations
CREATE ; newname = Rnk ( Variable ) $ Creates the set of ranks. Use in any subsequent analysis.Slide33