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

Application to Spanish Dairy Farms InputUnitsMeanStd. Dev. MinimumMaximum MilkMilk production (liters) 131,108 92,539 14,110727,281 Cows# of milking cows Labor# man-equivalent units LandHectares of land devoted to pasture and crops FeedTotal amount of feedstuffs fed to dairy cows (tons) 57,94147,9813, ,732 N = 247 farms, T = 6 years ( )

Using Farm Means of the Data

OLS vs. Frontier/MLE

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).

Confidence Intervals for Technical Inefficiency, u(i)

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

Compare SF and DEA

Similar, but different with a crucial pattern

The Dreaded Error 315 – Wrong Skewness

Cost Frontier Model

Linear Homogeneity Restriction

Translog vs. Cobb Douglas

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]

Estimated Cost Frontier: C&G

Cost Frontier Inefficiencies

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.

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.)

Truncated Normal Model ; Model = T

Truncated Normal vs. Half Normal

Multiple Output Cost Function

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