Spatial Econometric Analysis Using GAUSS

1
Spatial Econometric Analysis Using GAUSS

• 2
• Kuan-Pin LinPortland State University

2
GAUSSMathematical and Statistical System

• Windows Interface
• Windows
• Command, Error, Log,
• Menu
• File, Edit, Run, , Help
• Operation
• Interactive Mode
• Command (Input / Output)
• Batch Mode
• Writing Program
• Online Help

3
GAUSS Basics

• Basic Operations on Matrices -    .   ./
      !     / .lt   .lt   .   .gt   .gt   ./  
    lt   lt     gt   gt   / .not  .and   .or  
  .xor   not  and or   xor     ..  
• Special Operators       .   '(transpose)
  
• Useful Algrbra and Matrix Operations exp ln
  log  abs  sqrt  pi sin cos inv invpd(inverse)
  det(determinant)
• Example
• Least Squares by/x

4
GAUSS ProgrammingUseful GAUSS Functions

• System Functions use, load, output
• Data Generating Functionsones, zeros, eye,
  seqa, seqm, rndu, rndn
• Data Conversion Functionsreshape, selif, delif,
  vec, vech, xpnd, submat, diag, diagrv
• Basic Matrix Functions
• Matrix Descriptionrows, cols, maxc, minc,
  meanc, median, stdc
• Matrix Operationssumc,cumsumc,prodc,cumprodc,sor
  tc,sorthc,sortind
• Matrix Computationdet,inv,invpd,solpd,vcx,corrx,
  cond,rank,eig,eigh
• Probability and Statistical Functionspdfn,
  cdfn, cdftc, cdffc, cdfchic, dstat, ols
• Calculus Functionsgradp, hessp, intsimp,
  linsolve, eqsolve, sqpsolve

5
GAUSS ProgrammingControlling Execution Flow

• If Statementif then else elseif endif
• For Loopfor i (start,stop,step) ... endfor
• Do Loopdo while ... endodo until ... endo

6
GAUSS ProgrammingWrite Your Own Functions

• Single Line Functionfn fn_name(args)
  code_for_function
• Procedureproc (nrets) proc_name(arg_list)l
  ocal list of local variables... statements in
  the body of procedureretp(ret_list)endp

7
GAUSS ProgrammingExample 1

• Do you know the accuracy of your computer's
  numerical calculation? This example addresses
  this important problem. Suppose e is a known
  small positive number, and the 5x4 matrix X is
  defined as follows
• Verify that the eigenvalues of X'X are 4e2, e2,
  e2, and e2. How small of the value of e your
  computer will allow so that X'X can be inverted?
  (example.1)

oneones(1,4) e1.0 do until e lt 1.0e-20 xone(e.eye(4)) print "e " e reigrs(x'x) print r' invxinvpd(x'x) print invx ee/10 endo
8
GAUSS ProgrammingExample 2

• Write a single-line GAUSS function to convert a
  quarterly time series into the annual series by
  taking the average of every four data points. How
  you extend the single-line version of time series
  conversion function to a multi-line procedure so
  that it can handle the conversion of more than
  one time series? (example.2)

fn qtoa1(x) meanc(reshape(x,rows(x)/4,4)')
proc qtoa(x) local r,c,y,i r rows(x) c cols(x) y qtoa1(x.,1) i 2 do until i gt c y yqtoa1(x.,i) i i1 endo retp(y) endp
9
GPE2 for GAUSS

• GPE2 is a package of econometric procedures
  written in GAUSS. There are four main functions,
  driven by a set of global control variables
• ResetSet up global control (input and output)
  variables.
• EstimateEstimation of a linear or generalized
  linear model.
• ForecastForecasting based on a linear or
  generalized linear model.
• OptimizeEstimation of a nonlinear model.
• GpehelpOnline help of using GPE2.

10
GPE2 for GAUSSSelected Global Control Variables

• Input Control Variables_names, _begin, _end,
  _rstat, _rtest, _rplot, _rlist,_const, _restr,
  _vcov, _hacv, _weight, _ivar, _dlags, _pdl, _eq,
  _id, _ar, _ma, _arma, _garch, _acf, _acf2,
  _nlopt, _method, _iter, _tol, _step, _conv,
  _fbrgin, _fend, _fstat, _fplot, _splag, _spw,
  _spwd
• Output Control Variables__y, __x, __e, __b,
  __vb, __v, __rss, __r2, __f, __vf, __t, __a, __va

11
GPE2 for GAUSSA Typical Program Using GPE2

• /
• Comments on program title, purposes, and the
  usage of the program
• /
• use gpe2 _at_ using GPE package (version 2) _at_
• // this must be the first executable statement
• /
• Writing output to file or sending it to
  printer
• specify file name for output
• /
• // Loading data read data series from data
  files.
• /
• Generating or transforming data series
• create and generate variables with data
  scaling or transformation
• (e.g. y and x are generated here and will be
  used below)
• /
• call reset _at_ initialize global variables _at_
• /
• Set input control variables for model
  estimation
• (e.g. _names for variable names, see Appendix
  A)

12
GPE2 for GAUSSExamples

• More than 70 examples covering linear and
  nonlinear least squares, instrumental variables,
  system of simultaneous linear equations, time
  series analysis, panel data, limited dependent
  variables, maximum likelihood, generalized
  methods of moments, and
• The latest extensions include spatial lag model
  estimation, hypothesis testing, and robust
  inference.

13
Software Demonstration

• Installation
• GAUSS Light 10.0
• GPE2 for GAUSS 10.0
• Example Zellner and Revankar 1970U.S.
  Transportation Equipment Industry
• Cobb-Douglas Production Functionln(Q) a b
  ln(L) g ln(K) e
• Generalized Cobb-Douglas Production
  Functionln(Q) q Q a b ln(L) g ln(K) e

14
ExampleZellner and Revankar 1970

• Cobb-Douglas Production Function
• OLS Estimator
• Hypothesis Testing
• Constant Returns to Scale?
• Homoscedasticity?
• Generalized Production Function
• Output Effects?
• Instrumental Variables
• GAUSS/GPE2 Program and Data

15
References

• K.-P. Lin, Computational Econometrics GAUSS
  Programming for Econometricians and Financial
  Analysts, ETEXT Publishing, Los Angeles, 2001.
• C.-F. Chung, Learning Econometrics with GAUSS,
  Institute of Economics, Academia Sinica, 2000.
• A. Zellner and N. Revankar, "Generalized
  Production Functions," Review of Economic
  Studies, 1970, 241-250.