Frontier Models and Efficiency MeasurementLab Session 1

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

Executing the Lab Scripts

Frontier Models and Efficiency Measurement

Lab Session 1: Operating NLOGIT

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

Lab Session 1

Operating NLOGIT Basic Commands - Transformations Linear Regression/Panel Data Application:

Panel data on Spanish Dairy Farms Estimating the linear model Testing a hypothesis Examining residuals

Desktop

Entering Data for Analysis IMPORT: ASCII, Excel Spreadsheets, other

formats: .txt, .csv, .txt READ: other programs.dta (stata), .xls (excel) LOAD existing data sets in the form of

LIMDEP/NLOGIT ‘Project Files’ – SAVED from earlier sessions or data preparations.lpj (nlogit, limdep, Stat Transfer)

Internal data editor

Sample data set: dairy.lpj

Panel Data on Spanish Dairy Farms Use for a Production Function Study Raw: Milk,Cows,Land, Labor, Feed Transformed

yit = log(Milk) x1, x2, x3, x4 = logs of inputs x11 = .5*x12, x12 = x1*x2, etc. year93 = dummy variable for year,…

Data on 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)

Locate file Dairy.lpj

Project Window

Project window displays the data set currently being analyzed:

Variables

Matrices

Other program related results

Instructing LIMDEP to do something

Menus – available but we will generally not use them

Command language – entered in an editor then ‘submitted’ to the program

Use File:New/OK for an Editing Window

Text Editing Window

Commands will be entered in this window and submitted from here

Typing Commands in the Editor

Spacing and capitalization never matter. Just type instructions so they are easily readable and contain the right information.

When you open a .lim file, it creates a new editing window for you. Submit the existing commands, modify them then submit, or type new commands in the same window.

“Submitting” Commands

One line command Place cursor on that line Press “Go” button

More than one command or command on more than one line Highlight all lines (like any text editor) Press “Go” button

The GO Button

There is a STOP button also. You can use it to interrupt iterations that seem to be going nowhere. It is red (active) during iterations.

Where Do Results Go?

On the screen in a third window that is opened automatically

In a text file if you request it.

To an Excel CSV file if you EXPORT them

Internally to matrices, variables, etc.

Project window shows variables in the data set

Results appear in output window

Commands typed in editing window

Standard Three Window Operation

Command Structure

VERB ; instruction ; … ; … $ Verb must be present Semicolons always separate subcommands ALL commands end with $

Case never matters in commands Spaces are always ignored Use as many lines as desired, but commands

must begin on a new line

Important Commands: CREATE ; Variable = transformation $

Create ; LogMilk = Log(Milk) $ Create ; LMC = .5*Log(Milk)*Log(Cosw) $ Create ; … any algebraic transformation $

SAMPLE ; first - last $ Sample ; 1 – 1000 $ Sample ; All $

REJECT ; condition $ Reject ; Cows < 20 $

Model Command Model ; Lhs = dependent variable

; Rhs = list of independent variables $ Regress ; Lhs=Milk ; Rhs=ONE,Feed,Labor,Land $ ONE requests the constant term - mandatory Typically many optional variations

Models are REGRESS, FRONTIER, PROBIT, POISSON, LOGIT, TOBIT, … and over 100 others. All have the same form. Variants of models such as Poisson / NegBinomial Several hundred different models altogether

Model Command with Sample Definition

Model ; If [ condition ] ; Lhs = … ; Rhs = … ; etc. $

FRONTIER ; If [Year = 1988] ; Lhs = yit ; Rhs = one,x1,x2,x3,x4 ; Model = Rayleigh $

Name Conventions

CREATE ; Name = any function desired $

Name is the name of a new variable No more than 8 characters in a name The first character must be a letter May not contain -,+,*,/. Use letters A – Z, digits 0 – 9 and _ May contain _.

Two Useful FeaturesNAMELIST ; listname = a group of names $

Listname is any new name. After the command, it is a synonym for the list

NAMELIST ; CobbDgls=One,LogK,LogL $ REGRESS ;Lhs = LogY ; Rhs = CobbDgls $

* = All names

DSTAT ; RHS = * $ REGRESS ; Lhs = Q ; Rhs = One, LOG* $

A Useful Tool - Calculator

CALC ; List ; any expression $ CALC ; List ; 1 + 1 $ CALC ; List ; FTB ( .95,3,1482) $ (Critical point from F table)

CALC ; List ; Name = any expression $ Saves result with name so it can be used later. CALC ; Chisq=2*(LogL – Logl0) $

;LIST may be omitted. Then result is computed but not displayed

Matrix Algebra

Large package; integrated into the program.

NAMELIST ; X = One,X1,X2,X3,X4 $

MATRIX ; bols = <X’X> * X’y $

CREATE ; e = y – X’bols $

CALC ; s2 = e’e / (N – Col(X)) $

MATRIX ; Vols =s2 * <X’X> ;Stat(bols,Vols,X) $

Over 100 matrix functions and all of matrix algebra are supported. Use with CREATE, CALC, and model estimators.

Regression Results

Model estimates on screen in the output window Matrices B and VARB Scalar results New Variables if requested, e.g., residuals Retrievable table of regression results

Results on the Screen in the Output Window

Matrices B and VARB. Double click names to open windows. Use B and VARB in other MATRIX computations and commands.

Scalar results from a regression can also be used in later computations

Regression Analysis: Testing Cobb-Douglas vs. Translog

NAMELIST ; cobbdgls = one,x1,x2,x3,x4 $NAMELIST ; quadrtic =x11,x22,x33,x44,x12,x13,x14,x23,x24,x34 $NAMELIST ; translog = cobbdgls,quadrtic $DSTAT ; Rhs=*$REGRESS ; Lhs = yit ; Rhs = cobbdgls $CALC ; loglcd = logl ; rsqcd = rsqrd $REGRESS ; Lhs = yit ; Rhs= translog $CALC ; logltl = logl ; rsqtl = rsqrd $CALC ; dfn = Col(translog) – Col(cobbdgls) $CALC ; dfd = n – Col(translog) $CALC ; list ; f=((rsqtl – rsqcd)/dfn) / ((1 - rsqtl)/dfd)$CALC ; list ; cf = ftb(.95,dfn,dfd) $CALC ; list ; chisq = 2*(logltl – loglcd) $CALC ; list ; cc = Ctb(.95,dfn) $

Built in F and Chi squared tests

REGRESS ; Lhs = yit ; Rhs = translog ; test: quadrtic $

Exiting the Program

Save Your Work When You Exit

Lab Exercises with Dairy Farm Data

Fit a linear regression with robust covariance matrix

Fit the linear model using least absolute deviations and quantile regression

Test for time effects in the model Use a Wald test for the translog model Test for constant returns to scale Analyze residuals for nonnormality