[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]

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]

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.

[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.

[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

[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.

[Sebastian Kripfganz]

Currently, the ardl module does not accept interaction terms with the factor-variables notation. However, you can generate your interaction terms first as new variables and then run the ardl command more or less as usual, e.g.

gen x1_dummy = x1 * dummy
ardl y x1 x2 x1_dummy, exog(dummy)

Note that I have specified the break-point dummy with the exog() option because I suppose that you do now want this dummy to be lagged.

In addition, you maybe want to further restrict the number of lags for the interaction term to be the same as for the x1 variable itself. There is no option to directly achieve this restriction, but you can proceed in two steps and use the lags() option at the second step:

ardl y x1 x2 x1_dummy, exog(dummy) lags(. 3 . 3)

assuming in this example that the optimal lag order for x1 obtained in the first step was 3.

Last but not least, you should be aware that the critical values of the Pesaran et al. (2001) bounds test (estat btest) are no longer valid when you have such structural breaks.

Finally, if you want to use any standard postestimation commands usually available after the regress command, you can store the underlying regress estimation results from ardl with the regstore() option, e.g.

ardl y x1 x2 x1_dummy, exog(dummy) regstore(ardl_results)
estimates restore ardl_results
// followed by any regress postestimation command of your choice

[Johanna Melinder]

Dear Sebastian,
Dear all,

I am using your program for my Master thesis and it has helped me a lot. So first of all, a big thank you!

I would like to test for structural break(s) in my model at a known period in time, with a particular interest on if the coefficients for some variables have changed. Using a normal OLS regression I would have included interaction terms for the variables of interest. (eg Y = c+ x1+x2 + D + D*x1 where D=1 after the break point). But since I have a mixture of I(0) and I(1) variables where the I(1) variables seems to be cointegrated I want to use ardl.

My question is therefore: can I use a similar approach in the ardl frame work? What would the model look like then?
If not, are you aware of any other approach I can use to test for a structural break in my model?

Thank you very much in advance!

Best,
Johanna

[Sebastian Kripfganz]

The lag classification that the author uses in that linked NRB paper is not conventional. He counts the number of lags in the error-correction representation of the model, while the usual way would be to count the lags in the levels representation. This is what ardl stores in the matrix e(lags). Compare with the ardl output when you do not use the ec or ec1 option. Please also see the remarks sections in the ardl help file on "Terminology" and "Long-run coefficients expressed in time t or t-1", as well as slides 8, 9, and 14 to 17 in my Stata Conference presentation:
http://www.stata.com/meeting/chicago..._kripfganz.pdf

[bui quang hien]

Dear Mr.Kripfganz,
-------------+----------------------------------------------------------------
SR |
golds |
D1. | .1662788 .0740476 2.25 0.027 .0196315 .3129261
|
reer |
D1. | -.4335587 .1802798 -2.40 0.018 -.7905934 -.076524
|
interest|
D1. | .0078001 .0026632 2.93 0.004 .0025257 .0130744
LD. | -.0067299 .0024835 -2.71 0.008 -.0116484 -.0018115
|
_cons | -19.7153 12.30821 -1.60 0.112 -44.09106 4.660461
------------------------------------------------------------------------------

. matrix list e(lags)

e(lags)[1,8]
lrm2s golds oil stock reer interest ex cpi
r1 1 1 0 0 1 2 0 0

May I ask why some coefficient were hidden in ADRL (1, 1, 0, 0, 1, 2, 0, 0)? Ex: oil, stock, ex, cpi
I try to compare with https://www.nrb.org.np/ecorev/pdffiles/vol25-1_art2.pdf. The result give all coefficient of all variables.

The constant term can either be included in the short-run part or in the long-run relationship but not in both at the same time.

[Sebastian Kripfganz]

The constant term can either be included in the short-run part or in the long-run relationship but not in both at the same time.

[bui quang hien]

Dear Mr.Schneider,
I can executed long-run including coefficient parameter. However, when use option "restricted.", coefficient of SR term is hidden. Did you know why it occurred?

Thank you!

[Daniel Schneider]

Hi Bui,

I am not sure whether I understood your question fully, but here are a couple of statements that may be helpful:

• The long-run relationship will be the same for options ec and ec1. Most short-run coefficients will be unaffected too.
• In order to pull the constant into the long-run relationship, use option restricted.
• I have double-checked the calculation of the constant in the long-run relationship and could not find any mistake.

Please also see the help file for ardl. In particular, sections "Deterministic components", "Long-run coefficients expressed in time t or t-1", and "The error-correction term" should help you. If anything remains unclear, please let me know.

[bui quang hien]

Dear All,

Currently, I am investigating ardl using http://www.stata.com/meeting/chicago..._kripfganz.pdf
(slide 9)

*CASE1
. webuse lutkepohl2
. ardl ln_inv ln_inc ln_consump , maxlag(8) maxcomb(1500) ec dots fast
------------------------------------------------------------------------------
D.ln_inv | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ADJ |
ln_inv |
L1. | -.1882187 .063747 -2.95 0.004 -.3152092 -.0612281
-------------+----------------------------------------------------------------
LR |
ln_inc | -1.381501 1.827062 -0.76 0.452 -5.021196 2.258194
ln_consump | 2.272314 1.875768 1.21 0.230 -1.464407 6.009035
-------------+----------------------------------------------------------------
SR |
ln_inv |
LD. | -.1358362 .1031304 -1.32 0.192 -.3412826 .0696101
L2D. | -.0336715 .1069373 -0.31 0.754 -.2467014 .1793585
L3D. | .2087659 .1018203 2.05 0.044 .0059294 .4116025
L4D. | .4012027 .097397 4.12 0.000 .207178 .5952275
|
ln_consump |
D1. | 1.36573 .4398616 3.10 0.003 .4894806 2.241979
|
_cons | -.0030844 .0657358 -0.05 0.963 -.1340368 .127868
------------------------------------------------------------------------------

So, LR and SR formula will be rewrite as below.
How to calculate constant parameter for LR?
Does LR and SR formula rewrite correct?
*LR:
ln_inv = -1.381501 ln_inc + 2.272314 ln_consump + constant

*SR:
D.ln_inv = -.1882187 ECT(t-1) -.1358362 D.ln_inv (t -1) -.0336715 D.ln_inv (t -2) + .2087659 D.ln_inv (t -3)+ .4012027 D.ln_inv (t -3)
+ 1.36573 D.ln_consump (t) -.0030844

*CASE2:
. ardl ln_inv ln_inc ln_consump , maxlag(8) maxcomb(1500) ec1 dots fast
------------------------------------------------------------------------------
D.ln_inv | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ADJ |
ln_inv |
L1. | -.1882187 .063747 -2.95 0.004 -.3152092 -.0612281
-------------+----------------------------------------------------------------
LR |
ln_inc |
L1. | -1.381501 1.827062 -0.76 0.452 -5.021196 2.258194
|
ln_consump |
L1. | 2.272314 1.875768 1.21 0.230 -1.464407 6.009035
-------------+----------------------------------------------------------------
SR |
ln_inv |
LD. | -.1358362 .1031304 -1.32 0.192 -.3412826 .0696101
L2D. | -.0336715 .1069373 -0.31 0.754 -.2467014 .1793585
L3D. | .2087659 .1018203 2.05 0.044 .0059294 .4116025
L4D. | .4012027 .097397 4.12 0.000 .207178 .5952275
|
ln_inc |
D1. | -.2600243 .3042968 -0.85 0.396 -.8662145 .346166
|
ln_consump |
D1. | 1.793422 .5861078 3.06 0.003 .6258353 2.961008
|
_cons | -.0030844 .0657358 -0.05 0.963 -.1340368 .127868
------------------------------------------------------------------------------
How to calculate constant parameter for LR?
Does LR formula rewrite same as CASE1 ? I still confused "ln_inc L1."
*LR:
ln_inv = -1.381501 ln_inc + 2.272314 ln_consump + constant
-------------+----------------------------------------------------------------
LR |
ln_inc |
L1. | -1.381501 1.827062 -0.76 0.452 -5.021196 2.258194
|
ln_consump |
L1. | 2.272314 1.875768 1.21 0.230 -1.464407 6.009035
-------------+----------------------------------------------------------------

Thank you very much!

[Mahana Noorma]

Dear Sebastian,

Thank you so much for your reply.

Kind regards