GAUSS Programming for Econometricians

1. GAUSS Programming for Econometricians Introduction to GAUSS Using GPE2/GAUSS

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

3. GAUSS Basic • Basic Operations on Matrices + -  ^   .*   ./   %   !   *   / .<   .<=   .==   .>=   .>   ./=     <   <=   ==   >=   >   /= .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)

4. Useful GAUSS Functions • System Functions: use, load, output • Data Generating Functions:ones, zeros, eye, seqa, seqm, rndu, rndn • Data Conversion Functions:reshape, selif, delif, vec, vech, xpnd, submat, diag, diagrv • Basic Matrix Functions: • Matrix Description:rows, cols, maxc, minc, meanc, median, stdc • Matrix Operations:sumc,cumsumc,prodc,cumprodc,sortc,sorthc,sortind • Matrix Computation:det,inv,invpd,solpd,vcx,corrx,cond,rank,eig,eigh • Probability and Statistical Functions:pdfn, cdfn, cdftc, cdffc, cdfchic, dstat, ols • Calculus Functions:gradp, hessp, intsimp, linsolve, eqsolve, sqpsolve

5. 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.

6. GPE2 for GAUSS • Selected 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 • Output Control Variables__y, __x, __e, __b, __vb, __v, __rss, __r2, __f, __vf, __t, __a, __va

7. A Typical Program Using GPE2 /* ** Comments on program title, purposes, and the usage of the program */ use gpe2; @ using GPE package (version 2) @ // 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; @ initialize global variables @ /* ** Set input control variables for model estimation ** (e.g. _names for variable names, see Appendix A) */ call estimate(y,x); @ do model estimation @ // variables y, x are generated earlier /* ** Retrieve output control variables for model evaluation and analysis */ /* ** Set more input control variables if needed, for model prediction ** (e.g. _b for estimated parameters) */ call forecast(y,x); @ do model prediction @ end; @ important: don’t forget this @

8. Where is the Data? • GAUSS Dataset • Datasets (or matrices) • Text Data • Type your own data • Import from Notebook, … • Spreadsheet • Excel

9. Stata Dataset sp500.dta • Interactive mode • Use GPE2; • Load dataset • Data Analysis • Generate variables • Regression and Graph • Call GPE functions: Reset, Estimate,… • Help for GAUSS and GPE2 • Gpehelp

10. /* ** Load GAUSS dataset ** Data management and analysis using GPE2 */ use gpe2; datfile="c:\\course09\\ec570\\data\\sp500.dat"; // "\" is a special character in GAUSS alldata=loadd(datfile); names=getname(datfile); high=alldata[.,4]; low=alldata[.,5]; closed=alldata[.,6]; // can not use "close" volumed=alldata[.,7]; // can not use "volume" change=alldata[.,8]; volatility=high-low; call reset; _names={"returns","risk","volume"}; _rplot=2; _begin=2; call estimate(change,volatility); call estimate(change,volatility~ln(volumed)); end;

11. Text Data gasoline.txt • Batch Mode: write your program • Use GPE2; • Load text (or spreadsheet) data • Generate variables • Call GPE functions: Reset, Estimate,…

12. /* ** Example 1.1: U.S. Gasoline Market ** Regression without using GPE2 */ load txtdata[52,11]=c:\course09\ec570\data\gasoline.txt; year=txtdata[.,1]; // year, 1953-2004 gasexp=txtdata[.,2]; // total U.S. gasoline expenditure popu=txtdata[.,3]; // U.S. population gasp=txtdata[.,4]; // price index for gasoline income=txtdata[.,5]; // per capita disposable income pnc=txtdata[.,6]; // price index for new cars puc=txtdata[.,7]; // price index for used cars ppt=txtdata[.,8]; // price index for public transportation pd=txtdata[.,9]; // price index for consumer duraqbles pn=txtdata[.,10]; // price index for consumer nondurables ps=txtdata[.,11]; // price index for consumer services call dstat(0,txtdata); g=ln(gasexp./(popu.*gasp)); pg=ln(gasp); y=ln(income); n=rows(g); one=ones(n,1); xvar=pg~y~one; yvar=g; b=invpd(xvar'*xvar)*xvar'*yvar; // b=yvar/xvar; e=yvar-xvar*b; print b; M=eye(n)-xvar*invpd(xvar'*xvar)*xvar'; print e~(M*e)~(M*xvar); end;

13. /* ** Example 1.2: U.S. Gasoline Market ** Checking Frisch-Waugh Theorem using GPE2 */ use gpe2; load txtdata[52,11]=c:\course09\ec570\data\gasoline.txt; /* ** … skip data definition, same as Example 1.1 … ** */ g=ln(gasexp./(popu.*gasp)); // log-per-capita gas consumption y=ln(income); // log-per-capita income pg=ln(gasp); // log price of gas call reset; call estimate(g,year); gstar=__e; call estimate(y,year); // partial regression ystar=__e; call estimate(pg,year); pgstar=__e; _names={"G","Y","PG","year"}; call estimate(gstar,ystar~pgstar); call estimate(g,ystar~pgstar~year); call estimate(g,y~pg~year); // full regression end;

14. /* ** Example 1.3: U. S. Gasoline Market ** Checking R-square and effects of adding variables */ use gpe2; load txtdata[52,11]=c:\course09\ec570\data\gasoline.txt; /* ** … skip data definition, same as Example 1.1 … ** */ g=ln(gasexp./(popu.*gasp)); // log-per-capita gas consumption y=ln(income); // log-per-capita income pg=ln(gasp); // log price of gas pnew=ln(pnc); // log price of new cars pused=ln(puc); // log price of used cars call reset; _names={"g","y","pg"}; call estimate(g,y~pg); call estimate(g,y~pg~year); call estimate(g,y~pg~pnew); call estimate(g,y~pg~pused); _names={"g","y","pg","year","pnew","pused"}; call estimate(g,y~pg~year~pnew~pused); end;