[Lilian Rolim]

1. I would like some help concerning the interpretation of the ECM and LR coefficients.

1.a. If the bounds test shows that there is a long run relation, but all the LR coefficients are not significant, should I conclude that there is no long run relation?
1.b. If the bounds test shows that there is a long run relation, but the ADJ coefficient is not significant, should I conclude that there is no long run relation?

2. How can I conclude that there is only one cointegrating relation among the variables? Johansen's test?

Thank you.

[Johanna Melinder]

Thank you very much for your quick reply Sebastian!

Just to make sure, is this approach suitable also with the ec- option? And then with the "structural break-variables" in the as part of the ec-term, if the coef. of the interaction term is significant, can that be interpreted as a structural break in the long-run relationship?

Thank you once again!

Best,
Johanna

[Sebastian Kripfganz]

Johanna:
The ec option just displays the estimates in a different way. The underlying estimation is still the same. I do not have a conclusive answer whether you can interpret a significant interaction term in the long-run relationship as statistical evidence for a structural break. That would require some deeper analysis of the econometric theory. The problem is that we would have to ascertain first if there exists a long-run relationship at all. But as mentioned before, the usual critical values for the bounds test may not be valid anymore.

[Sebastian Kripfganz]

Lilian:
1.a. If all LR coefficients are statistically insignificant, then there exists no long-run relationship between the dependent variable and these independent variables. If the bounds test still indicates a rejection of the null hypothesis, this would then imply that the dependent variable is an I(1) variable that is not cointegrated with the other variables.
1.b. You cannot interpret the p-value of the t-statistic for the ADJ coefficient in the usual way. Instead, you have to look at the bounds test for the t-statistic that is also reported by estat btest. If the bounds test rejects the null hypothesis for the F-test but does not reject the null hypothesis for the t-test, then you can would indeed not have evidence for the existence of a long-run relationship. Please also compare with Slide 10 of my presentation at the Stata Conference in Chicago last year.

2. The Johansen test can be helpful in that regard. You cannot directly test for it within the ARDL framework.

[Jonathan Hillgren]

Hello the following function work and gives us the laggs for each variable "ardl rXsve rBNPeuro rEursek rVol, aic" but when we add one more independent variable it says
"ardl rXsve rBNPeuro rEursek rVol rPPIes, aic"
# of lag permutations (2500) exceeds setting of 'maxcombs' (500)
Is there any way to fix this problem?


rXsve is first difference of export
rBNPeuro is first difference of GDP
rEursek is the first difference of the exchange rate
rVol is the first difference of volatility
rPPIes is the first difference of PPI between Euro countries and Sweden

[Sebastian Kripfganz]

You need to use the maxcombs() option top allow for a larger number of lag permutations, e.g.

ardl rXsve rBNPeuro rEursek rVol rPPIes, aic maxcombs(2500)

Please see help ardl for details.

[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?

[Sebastian Kripfganz]

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

[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

[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

[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 . . .)

[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]

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,

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.

[Cayley Gint]

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