1. Frontier Models and Efficiency Measurement Lab Session 4: Panel Data 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

2. Group Size Variables for Unbalanced Panels FarmMilkCowsFarmPrds 123.310.73 123.310.63 1259.43 219.6112 222.2112 324.7114 325.4124 325.313.54 326.114.54 455.4222 463.5222

3. 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 $

4. Application to Spanish Dairy Farms InputUnitsMeanStd. Dev. MinimumMaximum MilkMilk production (liters) 131,108 92,539 14,110727,281 Cows# of milking cows 2.12 11.27 4.5 82.3 Labor# man-equivalent units 1.67 0.55 1.0 4.0 LandHectares of land devoted to pasture and crops. 12.99 6.17 2.0 45.1 FeedTotal amount of feedstuffs fed to dairy cows (tons) 57,94147,9813,924.1 4 376,732 N = 247 farms, T = 6 years (1993-1998)

5. Exploring a Panel Data Set: Dairy REGRESS ; Lhs = YIT ; RHS = COBBDGLS ; PANEL $ REGRESS ; Lhs = YIT ; RHS = COBBDGLS ; PANEL ; Het = Group $

6. Initiating a Panel Data Model

7. Nonlinear Panel Data Models MODEL NAME ; Lhs = … ; RHS = … ; Panel ; … any other model parts … $ ALL PANEL DATA MODEL COMMANDS ARE THE SAME

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

9. Pitt and Lee Random Effects FRONTIER ; LHS = … [ ; COST ] ; RHS = … [; EFF = …] ; Panel ; any other options $ This is the default panel model.

10. Pitt and Lee Model

11. Pitt and Lee Random Effects with Heteroscedasticity and Time Invariant Inefficiency FRONTIER ; LHS = … [ ; COST ] ; RHS = … [; EFF = …] ; Panel ; HET ; HFU = … ; HFV = … $

12. Pitt and Lee Random Effects with Heteroscedasticity and Truncation Time Invariant Inefficiency FRONTIER ; LHS = … [ ; COST ] ; RHS = … [; EFF = …] ; Panel ; HET ; HFU = … ; HFV = … ; MODEL = T ; RH2 = One,… $

13. Pitt and Lee Random Effects with Heteroscedasticity Time Invariant Inefficiency FRONTIER ; LHS = … [ ; COST ] ; RHS = … [; EFF = …] ; Panel ; HET ; HFU = … ; HFV = … $

14. 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)

15. True Random Effects Time 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.

16. True Fixed Effects Time 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.

17. Battese and Coelli Time 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

21. Other Models There are many other panel models with time varying and time invariant inefficiency, heteroscedasticity, heterogeneity, etc. Latent class, Random parameters Sample selection, And so on….

23. Frontier Models and Efficiency Measurement Lab Session 4: Model Building 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

24. Modeling Assignment