Efficiency Measurement William Greene Stern School of Business New York University

Lab Session 2 Stochastic Frontier Estimation

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 ; EFF = 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  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.