. capt prog drop _all



. * spurious regression: independent random walks
. prog irwd, rclass
  1.   version 11
  2.   drop _all
  3.   set obs $N
  4.   local drift 2
  5.   g double x = 0 in 1
  6.   g double y = 0 in 1
  7.   replace x = x[_n - 1] + $trcoef * `drift' + rnormal() /// 
>   in 2/l
  8.   replace y = y[_n - 1] + $trcoef * `drift' + rnormal() /// 
>   in 2/l
  9.   reg y x
 10.   return scalar b = _b[x]
 11.   return scalar se = _se[x]
 12.   return scalar t = _b[x]/_se[x]
 13.   return scalar r2 = abs(return(t)) > invttail($N - 2, 0.025)
 14. end



. 
. global N 100



. global nsim 10000



. set seed 1010101



. 
. // consider IRWs with no drift
. global trcoef 0



. simulate birwd=r(b) sirwd=r(se) tirwd=r(t) rejirwd=r(r2), ///
>  reps($nsim) nodots saving(irw0, replace): irwd



      command:  irwd
        birwd:  r(b)
        sirwd:  r(se)
        tirwd:  r(t)
      rejirwd:  r(r2)






. su



    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
       birwd |     10000    .0003267    .6336891  -3.682241   3.301136
       sirwd |     10000     .100645    .0649186   .0116683   .6898782
       tirwd |     10000   -.0225758    7.390102  -34.39042    35.8372
     rejirwd |     10000       .7572    .4287966          0          1



. l in 1/20



     +--------------------------------------------+
     |     birwd      sirwd       tirwd   rejirwd |
     |--------------------------------------------|
  1. |  .4797036   .0366694    13.08186         1 |
  2. | -.3215804    .126415   -2.543845         1 |
  3. |  .5518465   .0509739    10.82607         1 |
  4. | -.9704604   .0774199   -12.53502         1 |
  5. |  .9274789   .0991612    9.353246         1 |
     |--------------------------------------------|
  6. | -.7858061   .0432042   -18.18819         1 |
  7. | -.5938631   .0538909   -11.01972         1 |
  8. |  .6821204   .1127544    6.049611         1 |
  9. |  .5334677   .0528825     10.0878         1 |
 10. |  .0958101   .0618102    1.550069         0 |
     |--------------------------------------------|
 11. | -.3524039   .0844574   -4.172564         1 |
 12. |   .251032   .1512837    1.659346         0 |
 13. |  .8574678   .1752042    4.894105         1 |
 14. | -.3218689   .0791635   -4.065877         1 |
 15. |  .2293266   .0713637     3.21349         1 |
     |--------------------------------------------|
 16. | -.3609286   .1122861   -3.214365         1 |
 17. | -.5108765   .1038393   -4.919877         1 |
 18. | -.0265709   .0448767   -.5920879         0 |
 19. | -1.321453   .0955171   -13.83473         1 |
 20. | -1.061208   .0308577   -34.39042         1 |
     +--------------------------------------------+



. 
. // consider IRWs with drift
. global trcoef 1



. simulate birwd=r(b) sirwd=r(se) tirwd=r(t) rejirwd=r(r2), ///
>  reps($nsim) nodots saving(irw1, replace): irwd



      command:  irwd
        birwd:  r(b)
        sirwd:  r(se)
        tirwd:  r(t)
      rejirwd:  r(r2)






. su



    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
       birwd |     10000    1.001838    .0777357   .7386733   1.313212
       sirwd |     10000    .0061999    .0019246   .0020809    .018849
       tirwd |     10000    175.4512    49.80395   60.38373   473.0911
     rejirwd |     10000           1           0          1          1



. l in 1/20



     +------------------------------------------+
     |    birwd      sirwd      tirwd   rejirwd |
     |------------------------------------------|
  1. | 1.002217   .0063258   158.4322         1 |
  2. | 1.103606   .0050269   219.5395         1 |
  3. | 1.083013   .0069692    155.399         1 |
  4. | .9581092   .0051847   184.7967         1 |
  5. | 1.085191   .0053837   201.5711         1 |
     |------------------------------------------|
  6. | .9154854   .0059151   154.7701         1 |
  7. | 1.065713    .008413   126.6743         1 |
  8. | 1.042774     .00848   122.9693         1 |
  9. | 1.104847   .0062487   176.8136         1 |
 10. | .9713724   .0048474   200.3911         1 |
     |------------------------------------------|
 11. | .8808553   .0062393   141.1783         1 |
 12. |  1.08984   .0076755   141.9889         1 |
 13. | 1.003118   .0056677   176.9884         1 |
 14. | .9593877    .003884   247.0105         1 |
 15. | .9122529   .0037094   245.9296         1 |
     |------------------------------------------|
 16. | .9130253   .0113659   80.33036         1 |
 17. | .9648722   .0040714    236.988         1 |
 18. | .9089801   .0085264   106.6083         1 |
 19. | 1.079193   .0054492    198.045         1 |
 20. | .9045779   .0067149   134.7114         1 |
     +------------------------------------------+



.