Frontier Models and Efficiency Measurement

Lab Session 4: Panel Data

William Greene

Stern School of Business

New York University

0 Introduction1 Efficiency Measurement2 Frontier Functions3 Stochastic Frontiers4 Production and Cost5 Heterogeneity6 Model Extensions7 Panel Data8 Applications

Group Size Variables for Unbalanced Panels

Farm Milk Cows FarmPrds1 23.3 10.7 3

1 23.3 10.6 3

1 25 9.4 3

2 19.6 11 2

2 22.2 11 2

3 24.7 11 4

3 25.4 12 4

3 25.3 13.5 4

3 26.1 14.5 4

4 55.4 22 2

4 63.5 22 2

Creating a Group Size Variable Requires an ID variable (such as FARM)

(1) Set the full sample exactly as desired

(2) SETPANEL ; Group = the id variable ; Pds = the name you want limdep to use for the periods variable $

SETPANEL ; Group = farm ; pds = ti $

Application to Spanish Dairy Farms

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

N = 247 farms, T = 6 years (1993-1998)

Exploring a Panel Data Set: Dairy

REGRESS ; Lhs = YIT

; RHS = COBBDGLS

; PANEL $

REGRESS ; Lhs = YIT ; RHS = COBBDGLS ; PANEL ; Het = Group $

Initiating a Panel Data Model

Nonlinear Panel Data Models

MODEL NAME ; Lhs = …

; RHS = …

; Panel

; … any other model parts … $

ALL PANEL DATA MODEL COMMANDS ARE THE SAME

Panel Data Frontier Model Commands

FRONTIER ; LHS = … [ ; COST ] ; RHS = … [; TECHEFF = …] ; Panel ; ... the rest of the model ; any other options $

Pitt and Lee Random Effects

FRONTIER ; LHS = … [ ; COST ] ; RHS = … [; EFF = …] ; Panel ; any other options $

This is the default panel model.

Pitt and Lee Model

Pitt and Lee Random Effects with Heteroscedasticity and Time Invariant Inefficiency

FRONTIER ; LHS = … [ ; COST ] ; RHS = … [; EFF = …] ; Panel ; HET ; HFU = … ; HFV = … $

Pitt and Lee Random Effectswith Heteroscedasticity and Truncation

Time Invariant Inefficiency

FRONTIER ; LHS = … [ ; COST ] ; RHS = … [; EFF = …] ; Panel ; HET ; HFU = … ; HFV = … ; MODEL = T

; RH2 = One,… $

Pitt and Lee Random Effectswith Heteroscedasticity

Time Invariant Inefficiency

FRONTIER ; LHS = … [ ; COST ] ; RHS = … [; EFF = …] ; Panel ; HET ; HFU = … ; HFV = … $

Schmidt and Sickles Fixed Effects

REGRESS ; LHS = … ; RHS = … ; PANEL ; PAR ; FIXED $CREATE ; AI = ALPHAFE ( id ) $CALC ; MAXAI = Max(AI) $CREATE ; UI = MAXAI – AI $

(Use Minimum and AI – MINAI for cost)

True Random EffectsTime Varying Inefficiency

FRONTIER ; LHS = … [ ; COST ] ; RHS = … $FRONTIER ; LHS = … [ ; COST ] ; RHS = … ; Panel ; Halton (a good idea)

; PTS = number for the simulations ; RPM ; FCN = ONE (n) ; EFF = … $

Note, first and second FRONTIER commands are identical. This sets up the starting values.

True Fixed EffectsTime Varying Inefficiency

FRONTIER ; LHS = … [ ; COST ] ; RHS = … $FRONTIER ; LHS = … [ ; COST ] ; RHS = … ; Panel ; FEM ; EFF = … $

Note, first and second FRONTIER commands are identical. This sets up the starting values.

Battese and CoelliTime Varying Inefficiency

FRONTIER ; LHS = … [ ; COST ] ; RHS = … ; Panel ; MODEL = BC ; EFF = … $This is the default specification,

u(i,t) = exp[h(t-T)] |U(i)|To use the extended specification,

u(i,t)=exp[d’z(i)] |U(i)| ; Het ; HFU = variables

Other Models

There are many other panel models with time varying and time invariant inefficiency, heteroscedasticity, heterogeneity, etc.

Latent class,Random parametersSample selection,And so on….

Frontier Models and Efficiency Measurement

Lab Session 4: Model Building

William Greene

Stern School of Business

New York University

0 Introduction1 Efficiency Measurement2 Frontier Functions3 Stochastic Frontiers4 Production and Cost5 Heterogeneity6 Model Extensions7 Panel Data8 Applications

Modeling Assignment