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

 From Yuval Arbel To statalist@hsphsun2.harvard.edu Subject Re: Re: st: RE: dfuller: why do I get different results? Date Sat, 19 Nov 2011 17:26:18 +0200

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:

. dfuller reduct_per if appt==2851, noconstant 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)              0.912            -2.657            -1.950            -1.601

------------------------------------------------------------------------------
D.reduct_per |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
reduct_per |
L1. |   .0061958   .0067958     0.91   0.370    -.0077733    .0201648
------------------------------------------------------------------------------

. dfuller reduct_per if appt==2862, noconstant 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)             -6.026            -2.641            -1.950            -1.605

------------------------------------------------------------------------------
D.reduct_per |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
reduct_per |
L1. |  -.5409015   .0897625    -6.03   0.000    -.7229484   -.3588546
------------------------------------------------------------------------------

. dfuller reduct_per if appt==2906, noconstant 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)             -0.771            -2.602            -1.950            -1.610

------------------------------------------------------------------------------
D.reduct_per |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
reduct_per |
L1. |  -.0199276   .0258578    -0.77   0.443    -.0712761     .031421
------------------------------------------------------------------------------

. dfuller reduct_per if appt==2907, noconstant 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)             -2.412            -2.600            -1.950            -1.610

------------------------------------------------------------------------------
D.reduct_per |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
reduct_per |
L1. |  -.0549333   .0227781    -2.41   0.018    -.1001135    -.009753
------------------------------------------------------------------------------

. dfuller reduct_per if appt==2908, noconstant 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)             -0.158            -2.600            -1.950            -1.610

------------------------------------------------------------------------------
D.reduct_per |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
reduct_per |
L1. |  -.0031937   .0202288    -0.16   0.875    -.0433372    .0369498
------------------------------------------------------------------------------

. dfuller reduct_per if appt==2912, noconstant 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)             -1.807            -2.606            -1.950            -1.610

------------------------------------------------------------------------------
D.reduct_per |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
reduct_per |
L1. |  -.0628124   .0347553    -1.81   0.074    -.1319273    .0063024
------------------------------------------------------------------------------

. dfuller reduct_per if appt==2915, noconstant 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)             -0.988            -2.605            -1.950            -1.610

------------------------------------------------------------------------------
D.reduct_per |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
reduct_per |
L1. |  -.0224454   .0227184    -0.99   0.326    -.0676081    .0227174
------------------------------------------------------------------------------

. dfuller reduct_per if appt==3035, noconstant 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)             -2.808            -2.625            -1.950            -1.609

------------------------------------------------------------------------------
D.reduct_per |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
reduct_per |
L1. |   -.253886   .0904045    -2.81   0.007    -.4358607   -.0719113
------------------------------------------------------------------------------

. dfuller reduct_per if appt==3051, noconstant 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)             -1.795            -2.638            -1.950            -1.606

------------------------------------------------------------------------------
D.reduct_per |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
reduct_per |
L1. |  -.0865433   .0482161    -1.79   0.081    -.1841516     .011065
------------------------------------------------------------------------------

. dfuller reduct_per if appt==3057, noconstant 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)             -0.208            -2.658            -1.950            -1.600

------------------------------------------------------------------------------
D.reduct_per |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
reduct_per |
L1. |  -.0133552   .0641473    -0.21   0.837    -.1454689    .1187586
------------------------------------------------------------------------------

.

On Sat, Nov 19, 2011 at 5:12 PM, Nick Cox <njcoxstata@gmail.com> wrote:
> If it is sufficient to demonstrate gross or general non-stationarity,
> why not just plot all the data versus time?
>
> On Sat, Nov 19, 2011 at 3:00 PM, Yuval Arbel <yuval.arbel@gmail.com> wrote:
>> Would it be a good idea to run lag(2) and a drift on the full sample?
>>
>> On Sat, Nov 19, 2011 at 4:22 PM, Christopher Baum <kit.baum@bc.edu> wrote:
>>> <>
>>> On Nov 19, 2011, at 2:33 AM, Yuval wrote:
>>>
>>>> Fisher-type unit-root test for reduct_per
>>>> Based on augmented Dickey-Fuller tests
>>>> - -----------------------------------------
>>>> Ho: All panels contain unit roots           Number of panels       =   9547
>>>> Ha: At least one panel is stationary        Avg. number of periods =  53.19
>>>>
>>>> AR parameter: Panel-specific                Asymptotics: T -> Infinity
>>>> Panel means:  Included
>>>> Time trend:   Not included
>>>> Drift term:   Not included                  ADF regressions: 1 lag
>>>> - ------------------------------------------------------------------------------
>>>>                                  Statistic      p-value
>>>> - ------------------------------------------------------------------------------
>>>> Inverse chi-squared(19060)P      8814.2739       1.0000
>>>> Inverse normal            Z        60.7097       1.0000
>>>> Inverse logit t(46659)    L*       55.5908       1.0000
>>>> Modified inv. chi-squared Pm      -52.4767       1.0000
>>>> - ------------------------------------------------------------------------------
>>>> P statistic requires number of panels to be finite.
>>>> Other statistics are suitable for finite or infinite number of panels.
>>>> - ------------------------------------------------------------------------------
>>>>
>>>> .
>>>> I'm happy with the results, because they show that tenants could not
>>>> anticipate a long-run mean reduction rates.
>>>
>>> I would not draw great comfort from these findings. The huge number of panels in the test, based on T->\infty rather than N->\infty, leads to a p-value of 1.0 for all forms of the test statistic. All that means is that the data cannot possibly reject the null that ALL panels have unit roots. That could well result from a sample in which 9,500 panels did and 47 panels didn't, but the test does not have the power to reject.
>>>
>>> I would run the test -- with a drift term, and probably more than one lag in the DF -- for a relatively small number of panels, perhaps chosen at random. If you look at the example in the xtunitroot fisher help file, a rejection arises when the Z-stat or L*-stat takes on negative values (just as with the standard D-F regression). It might well be if you looked at, say, 150 panels you would find that the test has some power. I am always suspicious of p-values of 1.0000.
>>>
>
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--
Dr. Yuval Arbel