Notice: On March 31, it was announced that Statalist is moving from an email list to a forum. The old list will shut down on April 23, and its replacement, statalist.org is already up and running.

# Re: Re: Re: st: RE: dfuller: why do I get different results?

 From Yuval Arbel To statalist@hsphsun2.harvard.edu Subject Re: Re: Re: st: RE: dfuller: why do I get different results? Date Sat, 19 Nov 2011 18:36:12 +0200

```Here are the same outcomes with a constant.

The problem is that the maximum length of each panel will be 114
periods. So I might have many panels with less than 100 periods - so I
still need the -xtunitroot- commands. Am I correct?

What you said about the sample size required to make the dfuller valid
is interesting. I wonder how did econometricians work in the past when
they had small macro series of GDPs (take Milton Friedman for example
- theory of the consumption function)?

name:  <unnamed>
log:  D:\kingston\public_housing\dfuller_20111118.smcl
log type:  smcl
opened on:  19 Nov 2011, 18:21:49

. dfuller reduct_per if appt==2851, regress

Dickey-Fuller test for unit root                   Number of obs   =        27

---------- Interpolated Dickey-Fuller ---------
Test         1% Critical       5% Critical      10% Critical
Statistic           Value             Value             Value
------------------------------------------------------------------------------
Z(t)             -0.891            -3.736            -2.994            -2.628
------------------------------------------------------------------------------
MacKinnon approximate p-value for Z(t) = 0.7910

------------------------------------------------------------------------------
D.reduct_per |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
reduct_per |
L1. |  -.0666667   .0748331    -0.89   0.381    -.2207884    .0874551
|
_cons |          6   6.136774     0.98   0.338    -6.638923    18.63892
------------------------------------------------------------------------------

. dfuller reduct_per if appt==2862, regress

Dickey-Fuller test for unit root                   Number of obs   =        37

---------- Interpolated Dickey-Fuller ---------
Test         1% Critical       5% Critical      10% Critical
Statistic           Value             Value             Value
------------------------------------------------------------------------------
Z(t)             -6.784            -3.668            -2.966            -2.616
------------------------------------------------------------------------------
MacKinnon approximate p-value for Z(t) = 0.0000

------------------------------------------------------------------------------
D.reduct_per |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
reduct_per |
L1. |  -.6557562   .0966619    -6.78   0.000    -.8519902   -.4595222
|
_cons |    4.71219   1.944633     2.42   0.021     .7643737    8.660005
------------------------------------------------------------------------------

. dfuller reduct_per if appt==2906, regress

Dickey-Fuller test for unit root                   Number of obs   =        94

---------- Interpolated Dickey-Fuller ---------
Test         1% Critical       5% Critical      10% Critical
Statistic           Value             Value             Value
------------------------------------------------------------------------------
Z(t)             -1.313            -3.518            -2.895            -2.582
------------------------------------------------------------------------------
MacKinnon approximate p-value for Z(t) = 0.6233

------------------------------------------------------------------------------
D.reduct_per |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
reduct_per |
L1. |  -.0437803   .0333491    -1.31   0.193    -.1100146    .0224539
|
_cons |   1.406441   1.244567     1.13   0.261    -1.065375    3.878258
------------------------------------------------------------------------------

. dfuller reduct_per if appt==2907, regress

Dickey-Fuller test for unit root                   Number of obs   =       103

---------- Interpolated Dickey-Fuller ---------
Test         1% Critical       5% Critical      10% Critical
Statistic           Value             Value             Value
------------------------------------------------------------------------------
Z(t)             -2.647            -3.509            -2.890            -2.580
------------------------------------------------------------------------------
MacKinnon approximate p-value for Z(t) = 0.0836

------------------------------------------------------------------------------
D.reduct_per |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
reduct_per |
L1. |  -.0798791   .0301724    -2.65   0.009    -.1397331   -.0200251
|
_cons |    .877063   .6982839     1.26   0.212    -.5081445    2.262271
------------------------------------------------------------------------------

. dfuller reduct_per if appt==2908, regress

Dickey-Fuller test for unit root                   Number of obs   =        99

---------- Interpolated Dickey-Fuller ---------
Test         1% Critical       5% Critical      10% Critical
Statistic           Value             Value             Value
------------------------------------------------------------------------------
Z(t)             -0.603            -3.511            -2.891            -2.580
------------------------------------------------------------------------------
MacKinnon approximate p-value for Z(t) = 0.8703

------------------------------------------------------------------------------
D.reduct_per |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
reduct_per |
L1. |  -.0143708   .0238291    -0.60   0.548    -.0616649    .0329233
|
_cons |   .9428312   1.059461     0.89   0.376    -1.159906    3.045569
------------------------------------------------------------------------------

. dfuller reduct_per if appt==2907, regress

Dickey-Fuller test for unit root                   Number of obs   =       103

---------- Interpolated Dickey-Fuller ---------
Test         1% Critical       5% Critical      10% Critical
Statistic           Value             Value             Value
------------------------------------------------------------------------------
Z(t)             -2.647            -3.509            -2.890            -2.580
------------------------------------------------------------------------------
MacKinnon approximate p-value for Z(t) = 0.0836

------------------------------------------------------------------------------
D.reduct_per |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
reduct_per |
L1. |  -.0798791   .0301724    -2.65   0.009    -.1397331   -.0200251
|
_cons |    .877063   .6982839     1.26   0.212    -.5081445    2.262271
------------------------------------------------------------------------------

. dfuller reduct_per if appt==2908, regress

Dickey-Fuller test for unit root                   Number of obs   =        99

---------- Interpolated Dickey-Fuller ---------
Test         1% Critical       5% Critical      10% Critical
Statistic           Value             Value             Value
------------------------------------------------------------------------------
Z(t)             -0.603            -3.511            -2.891            -2.580
------------------------------------------------------------------------------
MacKinnon approximate p-value for Z(t) = 0.8703

------------------------------------------------------------------------------
D.reduct_per |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
reduct_per |
L1. |  -.0143708   .0238291    -0.60   0.548    -.0616649    .0329233
|
_cons |   .9428312   1.059461     0.89   0.376    -1.159906    3.045569
------------------------------------------------------------------------------

. dfuller reduct_per if appt==2912, regress

Dickey-Fuller test for unit root                   Number of obs   =        85

---------- Interpolated Dickey-Fuller ---------
Test         1% Critical       5% Critical      10% Critical
Statistic           Value             Value             Value
------------------------------------------------------------------------------
Z(t)             -2.030            -3.531            -2.902            -2.586
------------------------------------------------------------------------------
MacKinnon approximate p-value for Z(t) = 0.2736

------------------------------------------------------------------------------
D.reduct_per |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
reduct_per |
L1. |  -.0826385   .0407099    -2.03   0.046    -.1636088   -.0016683
|
_cons |   1.403384   1.497567     0.94   0.351    -1.575217    4.381985
------------------------------------------------------------------------------

. dfuller reduct_per if appt==2915, regress

Dickey-Fuller test for unit root                   Number of obs   =        87

---------- Interpolated Dickey-Fuller ---------
Test         1% Critical       5% Critical      10% Critical
Statistic           Value             Value             Value
------------------------------------------------------------------------------
Z(t)             -1.276            -3.528            -2.900            -2.585
------------------------------------------------------------------------------
MacKinnon approximate p-value for Z(t) = 0.6403

------------------------------------------------------------------------------
D.reduct_per |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
reduct_per |
L1. |  -.0375646   .0294495    -1.28   0.206    -.0961181    .0209888
|
_cons |   .8777472   1.084656     0.81   0.421     -1.27884    3.034335
------------------------------------------------------------------------------

. dfuller reduct_per if appt==3035, regress

Dickey-Fuller test for unit root                   Number of obs   =        47

---------- Interpolated Dickey-Fuller ---------
Test         1% Critical       5% Critical      10% Critical
Statistic           Value             Value             Value
------------------------------------------------------------------------------
Z(t)             -2.921            -3.600            -2.938            -2.604
------------------------------------------------------------------------------
MacKinnon approximate p-value for Z(t) = 0.0430

------------------------------------------------------------------------------
D.reduct_per |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
reduct_per |
L1. |   -.280148   .0959161    -2.92   0.005    -.4733329    -.086963
|
_cons |   1.635018   1.943664     0.84   0.405    -2.279723     5.54976
------------------------------------------------------------------------------

. dfuller reduct_per if appt==3051, regress

Dickey-Fuller test for unit root                   Number of obs   =        39

---------- Interpolated Dickey-Fuller ---------
Test         1% Critical       5% Critical      10% Critical
Statistic           Value             Value             Value
------------------------------------------------------------------------------
Z(t)             -2.863            -3.655            -2.961            -2.613
------------------------------------------------------------------------------
MacKinnon approximate p-value for Z(t) = 0.0499

------------------------------------------------------------------------------
D.reduct_per |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
reduct_per |
L1. |  -.2573525    .089898    -2.86   0.007    -.4395032   -.0752017
|
_cons |    5.53697   2.505182     2.21   0.033      .460989    10.61295
------------------------------------------------------------------------------

. dfuller reduct_per if appt==3057, regress

Dickey-Fuller test for unit root                   Number of obs   =        26

---------- Interpolated Dickey-Fuller ---------
Test         1% Critical       5% Critical      10% Critical
Statistic           Value             Value             Value
------------------------------------------------------------------------------
Z(t)             -0.784            -3.743            -2.997            -2.629
------------------------------------------------------------------------------
MacKinnon approximate p-value for Z(t) = 0.8238

------------------------------------------------------------------------------
D.reduct_per |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
reduct_per |
L1. |  -.0677992   .0864757    -0.78   0.441    -.2462763    .1106779
|
_cons |   4.904603   5.209682     0.94   0.356    -5.847653    15.65686
------------------------------------------------------------------------------

. log close
name:  <unnamed>
log:  D:\kingston\public_housing\dfuller_20111118.smcl
log type:  smcl
closed on:  19 Nov 2011, 18:25:56
------------------------------------------------------------------------------

On Sat, Nov 19, 2011 at 5:42 PM, Christopher Baum <kit.baum@bc.edu> wrote:
> <>
>
> I still need the formal statistical test - for a research paper a
> general plot will not be sufficient.
>
> BTW: I just ran manually the first 10 panels. It is not a
> representative sample, but as you can see below indeed, in most of
> them the unit-root hypothesis was not rejected at the 1% significance
> level:
>
> Unit root tests have notoriously low power with < 100 observations -- that's why we have panel unit root tests.
> Three rejections at 5% out of 10 samples suggests that "most" might be I(1), but then a df test with no constant nor trend is a queer bird indeed. The process you are modeling has to make sense under both null and alternative hypotheses for the test to be valid. A bit of algebra shows that a DF regression without a constant implies that the mean of Y is the mean of epsilon == 0 under the alternative hypothesis of stationarity. If your data in levels do not have a mean of zero, this model is incapable of reproducing the data with any choice of ]beta < 0, and so the test is flawed.
>
> Kit
>
> Kit Baum   |   Boston College Economics & DIW Berlin   |   http://ideas.repec.org/e/pba1.html
>                             An Introduction to Stata Programming  |   http://www.stata-press.com/books/isp.html
>  An Introduction to Modern Econometrics Using Stata  |   http://www.stata-press.com/books/imeus.html
>
>
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/
>

--
Dr. Yuval Arbel