. 
. * Define global macros for sample size and number of simulations
. global numobs 150             // sample size N



. global numsims "1000"         // number of simulations 



. 
. * Program for finite-sample properties of OLS
. program chi2data, rclass
  1.     version 11  
  2.     drop _all
  3.     set obs $numobs
  4.     generate double x = rchi2(1)   
  5.     generate y = 1 + 2*x + rchi2(1)-1     // demeaned chi^2 error 
  6.     regress y x
  7.     return scalar b2 =_b[x]
  8.     return scalar se2 = _se[x]
  9.     return scalar t2 = (_b[x]-2)/_se[x]
 10.     return scalar r2 = abs(return(t2))>invttail($numobs-2,.025)
 11.     return scalar p2 = 2*ttail($numobs-2,abs(return(t2)))
 12. end



. 
. set seed 10101



. * Simulation for finite-sample properties of OLS
. simulate b2f=r(b2) se2f=r(se2) t2f=r(t2) ///
> reject2f=r(r2) p2f=r(p2), reps($numsims) ///
> saving(chi2datares, replace) nolegend nodots: chi2data






. 
. summarize b2f se2f reject2f



    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
         b2f |      1000    2.000506      .08427   1.719513    2.40565
        se2f |      1000    .0839776    .0172588   .0415919    .145264
    reject2f |      1000        .046    .2095899          0          1



. * Summarize results
. mean b2f se2f reject2f



Mean estimation                     Number of obs    =    1000



--------------------------------------------------------------
             |       Mean   Std. Err.     [95% Conf. Interval]
-------------+------------------------------------------------
         b2f |   2.000506   .0026649      1.995277    2.005735
        se2f |   .0839776   .0005458      .0829066    .0850486
    reject2f |       .046   .0066278       .032994     .059006
--------------------------------------------------------------



. 
. // histogram t2f
. histogram p2f
(bin=29, start=.0000108, width=.0344747)



. graph export mus04p2test.pdf, replace
(file /Users/baum/Documents/Courses 2009-2010/EC771 S2010/mus04p2test.pdf written in PDF format)



. 
. * t-statistic distribution
. kdensity t2f,  n(1000) gen(t2_x t2_d) nograph



. generate double t2_d2 = tden(148, t2_x)



. graph twoway (line t2_d t2_x) (line t2_d2 t2_x)



. 
. graph export mus04ttest.pdf, replace
(file /Users/baum/Documents/Courses 2009-2010/EC771 S2010/mus04ttest.pdf written in PDF format)