Transcript Document 7700466

Efficiency Measurement
William Greene
Stern School of Business
New York University
Lab Session 2
Stochastic Frontier
Estimation
Application to Spanish Dairy Farms
N = 247 farms, T = 6 years (1993-1998)
Input
Units
Mean
Std.
Dev.
Minimum
Maximum
Milk
Milk production (liters)
131,108
92,539
14,110
727,281
Cows
# of milking cows
2.12
11.27
4.5
82.3
Labor
# man-equivalent units
1.67
0.55
1.0
4.0
Land
Hectares
of
land
devoted to pasture and
crops.
12.99
6.17
2.0
45.1
Feed
Total
amount
of
feedstuffs fed to dairy
cows (tons)
57,941
47,981
3,924.14
376,732
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)]
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
Cost=C(Output, Input Prices)
C = C(Q, P1 , P2 ,... PK )
Frontier Model
logC = logC(Q, P1 , P2 ,... PK ) + v + u
Linear Homogeneity Restriction
C(Q, aP1 , aP2 ,... aPM ) = aC(Q, P1 , P2 ,... PM )
Cobb-Douglas Form
logC = 0  1logP1  2logP2  ...  M logPM  logQ
Homogeneity: 1  2  ...  M  1
Normalized CD Cost Function with Homogeneity Imposed
logC/PM = 0 
1log(P1 /PM )  2log(P2 /PM )  ...  M-1 (PM-1 /PM ) +
logQ
Translog vs. Cobb Douglas
Normalized TranslogCost Function with Homogeneity Imposed
logC/PM = 0 
1log(P1/PM )  2log(P2 /PM )  ...  M-1 (PM-1/PM ) +
 Q logQ +
11 12 log 2 (P1/PM )  22 12 log 2 (P2 /PM )  ...  M-1,M-1 12 log 2 (PM-1/PM ) +
12 log(P1/PM )log(P2 /PM )  ...  (all unique cross products)
 QQ 12 log 2Q 
1log(P1/PM )logQ   2log(P2 /PM )logQ  ...   M-1log(PM-1/PM )logQ
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
C(Q1 ,Q 2 ,...,Q L , aP1 , aP2 ,... aPM ) = aC(Q1 ,Q 2 ,...,Q L , P1 , P2 ,... PM )
Cobb-Douglas Form
logC = 0  1logP1  2 logP2  ...  M logPM   lL1 l logQl
Homogeneity: 1  2  ...  M  1
Normalized CD Multiple Output Cost Function with Homogeneity
logC/PM = 0 
1log(P1 /PM )  2log(P2 /PM )  ...  M-1 (PM-1 /PM ) +
lL1 l logQ l
Ranking Observations
CREATE
; newname = Rnk ( Variable ) $
Creates the set of ranks. Use in any
subsequent analysis.