[Jonathan Hillgren]

Hi,
When we're running the command "ardl lnIMnor lnBNPnor lnPPIne lnNokeur Vol, exog (FinD) aic lags(. . . . .) maxcombs(2500)" in stata we get an insignificant value for lnPPIne and also for Vol even though the model suggest we should include 2 lags for the volatility. If we keep the variables ans run the command "ardl lnIMnor lnBNPnor lnPPIne lnNokeur Vol, exog (FinD) aic ec1 lags(3 0 0 2 2)" the lnPPIne variable is still insignificant for both long and short run. Should we therefore remove lnPPIne from our model? For the Vol variable it's significant in the long run, but not in short run. What is your suggestion for this variable? Can we keep it even though it's insignificant when we run the first command since it looks significant in the long run?
This is what it looks like:

We would be really thankful for your reply!

[Sebastian Kripfganz]

Whether your variables are in logs or not does not matter for this question. It is more a matter of taste and most people seem to prefer the ec1 option.

[Jonathan Hillgren]

Thanks for your answer! Which one would you recommend when we are using log variables?

[Sebastian Kripfganz]

The long-run coefficients are the same in both specifications. Only the short-run coefficients of the contemporaneous changes of the exogenous regressors differ. In addition to the help file remarks section on "Long-run coefficients expressed in time t or t-1", this difference can also be seen on slide 9 of my presentation at the Stata Conference 2016 in Chicago.

[Jonathan Hillgren]

what is the difference between the two different methods here with ec1 and ec? With the help command we get ec = estimate with depvar in first differences and display output in error-correction form and ec1 = like option ec, but parameterizes long-runcoefficients as of time t-1. How would this affect our results? Regards Jonathan Hillgren


ardl lnIMsve lnBNPSve lnPPIse lnSekeur lnVol, exog (FinD) aic ec1 lags(3 0 0 0 2), ardl lnIMsve lnBNPSve lnPPIse lnSekeur lnVol, exog (FinD) aic ec lags(3 0 0 0 2)

[Sebastian Kripfganz]

The speed-of-adjustment coefficient (ADJ) is expected to fall into the range [-1, 0]. In your case, it is not statistically significantly different from -1. The interpretation would be that any deviation from the long-run relationship is fully corrected instantaneously.

[Cayley Gint]

Hi. What is the interpretation for my results? I am very confused by the negative sign!

[Marco Giansoldati]

Dear Sebastian,

My sincere apologies, as the first code is mistakenly reported. I am an idiot.

Here is the corrected version:

ardl mgsv rmp nc itv xgsv if ifscode==941, maxlags(5) aic maxcombs(2000000) fast
matrix list e(lags)
e(lags)[1,5]
    mgsv   rmp    nc   itv  xgsv
r1     1     4     2     5     4

and then

. ardl mgsv rmp nc itv xgsv if ifscode==941, ec1 lags(1 4 2 5 4) 

ARDL regression
Model: ec

Sample: 1996q2 - 2014q4 
Number of obs  = 75
Log likelihood = 180.45349
R-squared      = .87372196
Adj R-squared  = .82695232
Root MSE       = .02571366

------------------------------------------------------------------------------
      D.mgsv |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
ADJ          |
        mgsv |
         L1. |  -.6387662   .1048283    -6.09   0.000    -.8489344   -.4285981
-------------+----------------------------------------------------------------
LR           |
         rmp |
         L1. |  -.0667753   .2245187    -0.30   0.767    -.5169082    .3833576
             |
          nc |
         L1. |   .9271816   .1467499     6.32   0.000     .6329658    1.221397
             |
         itv |
         L1. |   .0454188   .0377112     1.20   0.234    -.0301876    .1210251
             |
        xgsv |
         L1. |   .4385941   .0484641     9.05   0.000     .3414295    .5357588
-------------+----------------------------------------------------------------
SR           |
         rmp |
         D1. |  -.5076078   .1285887    -3.95   0.000    -.7654127    -.249803
         LD. |  -.4923306   .1634993    -3.01   0.004    -.8201271   -.1645342
        L2D. |   .0718866   .1488338     0.48   0.631    -.2265073    .3702804
        L3D. |  -.2320498   .1198929    -1.94   0.058    -.4724206     .008321
             |
          nc |
         D1. |   .7332384   .1751755     4.19   0.000     .3820326    1.084444
         LD. |   .4090789   .1885467     2.17   0.034     .0310655    .7870923
             |
         itv |
         D1. |   .2362944   .0427336     5.53   0.000     .1506186    .3219701
         LD. |   .1047491   .0494219     2.12   0.039     .0056642     .203834
        L2D. |   .0489504   .0475332     1.03   0.308    -.0463479    .1442487
        L3D. |   .1018636   .0452727     2.25   0.029     .0110972      .19263
        L4D. |   .0789433   .0392244     2.01   0.049      .000303    .1575836
             |
        xgsv |
         D1. |   .4191204   .1076309     3.89   0.000     .2033335    .6349074
         LD. |   .2391912    .113977     2.10   0.041      .010681    .4677015
        L2D. |   .1915766   .1213281     1.58   0.120    -.0516716    .4348248
        L3D. |   -.192109   .1150332    -1.67   0.101    -.4227366    .0385186
             |
       _cons |   -1.17379   .3393757    -3.46   0.001    -1.854197   -.4933826
------------------------------------------------------------------------------

and the boud tests:

. estat btest

Pesaran/Shin/Smith (2001) ARDL Bounds Test
H0: no levels relationship             F =  8.370
                                       t = -6.093

Critical Values (0.1-0.01), F-statistic, Case 3

      | [I_0]   [I_1]  | [I_0]   [I_1]  | [I_0]   [I_1]  | [I_0]   [I_1] 
      |    L_1     L_1 |   L_05    L_05 |  L_025   L_025 |   L_01    L_01
------+----------------+----------------+----------------+---------------
  k_4 |   2.45    3.52 |   2.86    4.01 |   3.25    4.49 |   3.74    5.06
accept if F < critical value for I(0) regressors
reject if F > critical value for I(1) regressors

Critical Values (0.1-0.01), t-statistic, Case 3

      | [I_0]   [I_1]  | [I_0]   [I_1]  | [I_0]   [I_1]  | [I_0]   [I_1] 
      |    L_1     L_1 |   L_05    L_05 |  L_025   L_025 |   L_01    L_01
------+----------------+----------------+----------------+---------------
  k_4 |  -2.57   -3.66 |  -2.86   -3.99 |  -3.13   -4.26 |  -3.43   -4.60
accept if t > critical value for I(0) regressors
reject if t < critical value for I(1) regressors

k: # of non-deterministic regressors in long-run relationship
Critical values from Pesaran/Shin/Smith (2001)

The egranger tests is as follows:

. egranger mgsv rmp nc itv xgsv if ifscode==941
Replacing variable _egresid...

Engle-Granger test for cointegration                  N (1st step)  =       80
                                                      N (test)      =       79
------------------------------------------------------------------------------
                  Test         1% Critical       5% Critical      10% Critical
               Statistic           Value             Value             Value
------------------------------------------------------------------------------
 Z(t)             -4.280            -5.242            -4.595            -4.268

Critical values from MacKinnon (1990, 2010)

I do thank you very much for suggesting the use of the option lags() for egranger. I have to understand how to select the appropriate lag length to be used in the egranger command to check for the presence of serial correlation.

[Sebastian Kripfganz]

The observation that two different tests do not yield exactly the same results would not puzzle me. In your case, the results are also not too different from each other as both still reject the null hypothesis, say, at the 5% level.

Moreover, the (short-run) specifications differ between the ARDL bounds test and the Engle-Granger test. You might want to use the lags() option of egranger to make sure that there is no serial correlation left in the Engle-Granger residuals.

I am also puzzled how you obtained the lags(1 4 2 5 4) specification for your second ardl estimation. With maxlags(3) in your first specification, you should not obtain such high lag orders.

[Marco Giansoldati]

Dear Sebastian Kripfganz, dear Members

I am using the ARDL command to test for the presence of a long-run relationship between macroeconomic variables. I read the notes provided here: http://www.stata.com/meeting/chicago..._kripfganz.pdf and tried to follow the suggested steps.

I first selected the most appropriate lag length trough the AIC criterion, by making use of the following command:

ardl mgsv rmp iad if ifscode==946, maxlags(3) aic maxcombs(2000000) fast
matrix list e(lags)

and on the basis of its result I run the following ardl

. ardl mgsv rmp nc itv xgsv if ifscode==941, ec1 lags(1 4 2 5 4) 

ARDL regression
Model: ec

Sample: 1996q2 - 2014q4 
Number of obs  = 75
Log likelihood = 180.45349
R-squared      = .87372196
Adj R-squared  = .82695232
Root MSE       = .02571366

------------------------------------------------------------------------------
      D.mgsv |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
ADJ          |
        mgsv |
         L1. |  -.6387662   .1048283    -6.09   0.000    -.8489344   -.4285981
-------------+----------------------------------------------------------------
LR           |
         rmp |
         L1. |  -.0667753   .2245187    -0.30   0.767    -.5169082    .3833576
             |
          nc |
         L1. |   .9271816   .1467499     6.32   0.000     .6329658    1.221397
             |
         itv |
         L1. |   .0454188   .0377112     1.20   0.234    -.0301876    .1210251
             |
        xgsv |
         L1. |   .4385941   .0484641     9.05   0.000     .3414295    .5357588
-------------+----------------------------------------------------------------
SR           |
         rmp |
         D1. |  -.5076078   .1285887    -3.95   0.000    -.7654127    -.249803
         LD. |  -.4923306   .1634993    -3.01   0.004    -.8201271   -.1645342
        L2D. |   .0718866   .1488338     0.48   0.631    -.2265073    .3702804
        L3D. |  -.2320498   .1198929    -1.94   0.058    -.4724206     .008321
             |
          nc |
         D1. |   .7332384   .1751755     4.19   0.000     .3820326    1.084444
         LD. |   .4090789   .1885467     2.17   0.034     .0310655    .7870923
             |
         itv |
         D1. |   .2362944   .0427336     5.53   0.000     .1506186    .3219701
         LD. |   .1047491   .0494219     2.12   0.039     .0056642     .203834
        L2D. |   .0489504   .0475332     1.03   0.308    -.0463479    .1442487
        L3D. |   .1018636   .0452727     2.25   0.029     .0110972      .19263
        L4D. |   .0789433   .0392244     2.01   0.049      .000303    .1575836
             |
        xgsv |
         D1. |   .4191204   .1076309     3.89   0.000     .2033335    .6349074
         LD. |   .2391912    .113977     2.10   0.041      .010681    .4677015
        L2D. |   .1915766   .1213281     1.58   0.120    -.0516716    .4348248
        L3D. |   -.192109   .1150332    -1.67   0.101    -.4227366    .0385186
             |
       _cons |   -1.17379   .3393757    -3.46   0.001    -1.854197   -.4933826
------------------------------------------------------------------------------

I then conducted a bound test as follows:

. estat btest

Pesaran/Shin/Smith (2001) ARDL Bounds Test
H0: no levels relationship             F =  8.370
                                       t = -6.093

Critical Values (0.1-0.01), F-statistic, Case 3

      | [I_0]   [I_1]  | [I_0]   [I_1]  | [I_0]   [I_1]  | [I_0]   [I_1] 
      |    L_1     L_1 |   L_05    L_05 |  L_025   L_025 |   L_01    L_01
------+----------------+----------------+----------------+---------------
  k_4 |   2.45    3.52 |   2.86    4.01 |   3.25    4.49 |   3.74    5.06
accept if F < critical value for I(0) regressors
reject if F > critical value for I(1) regressors

Critical Values (0.1-0.01), t-statistic, Case 3

      | [I_0]   [I_1]  | [I_0]   [I_1]  | [I_0]   [I_1]  | [I_0]   [I_1] 
      |    L_1     L_1 |   L_05    L_05 |  L_025   L_025 |   L_01    L_01
------+----------------+----------------+----------------+---------------
  k_4 |  -2.57   -3.66 |  -2.86   -3.99 |  -3.13   -4.26 |  -3.43   -4.60
accept if t > critical value for I(0) regressors
reject if t < critical value for I(1) regressors

k: # of non-deterministic regressors in long-run relationship
Critical values from Pesaran/Shin/Smith (2001)

The results of the boun test confirm the presence of a long-run relationship, but I am puzzled by the result of the cointegration test performed as follows:

. egranger mgsv rmp nc itv xgsv if ifscode==941
Replacing variable _egresid...

Engle-Granger test for cointegration                  N (1st step)  =       80
                                                      N (test)      =       79
------------------------------------------------------------------------------
                  Test         1% Critical       5% Critical      10% Critical
               Statistic           Value             Value             Value
------------------------------------------------------------------------------
 Z(t)             -4.280            -5.242            -4.595            -4.268

Critical values from MacKinnon (1990, 2010)

which seems to point for the presence of an extremely weak cointegration (very close to the 10% bound)

I am aware that the ardl command tests for the presence of a long-run relationship between variables, whereas the egranger to test for the cointegration. Yet, I was surprises that the two procedures lead to very different results and I was wondering what could be the explanation.

I do apologise if the question is silly.

Many many thanks for your kind attention.

[Sebastian Kripfganz]

Try to restrict the maximum number of lags for lnBNPeuro to 2 with the maxlags() or lags() option, e.g.

ardl lnXsve lnBNPeuro lnPPIes lnEursek lnVol , exog(FinD) aic maxcombs(2500) maxlags(. 2 . . .)

[Jonathan Hillgren]

Hi again, I found that the regression didn´t work and decided to only test ln of the values like in this regression "ardl lnXsve lnBNPeuro lnPPIes lnEursek lnVol , exog (FinD) aic maxcombs(2500)" and recieved this message note: L3.lnBNPeuro omitted because of collinearity
Collinear variables detected.
I believe that this could be so because BNPeuro is a interpolated value, (quarterly values to monthly). Is there any way to deal with this problem? best regards and happy easter

[Jonathan Hillgren]

Sebastian Kripfganz thanks again, with the following regression ardl rXsve rBNPeuro rEursek rVol rPPIse, exog (FinD) aic maxcombs(2500)


I get these results

[Sebastian Kripfganz]

You can use the exog() option to attach a dummy variable to the regression.

[Jonathan Hillgren]

Sebastian Kripfganz It helped and thank you very much. I cant see any details in help ardl how to process a dummy variable in our regression, Do you know how to implement this effect?