[Sebastian Kripfganz]

Anirudh:

1. The speed-of-adjustment coefficient, \(\alpha\), is positive, as it should be to have convergence towards the long-run equilbrium. What is reported is \(- \alpha\). You cannot directly infer from the regression table that it is statistically significant because the usual p-values are not valid. You need to look at the results from the bounds test with estat ectest, precisely the bounds test for the t-statistic.
2. That is correct.
3. That is correct, too.

To have a cointegrating relationship, the sign of the speed-of-adjustment coefficient must be positive. That means, the reported sign in the output section ADJ must be negative.

[Anirudh Tagat]

Many thanks for this clarification, Sebastian.

[Alistair Alleyne]

Hi Everyone,

I am using STATA 13 and would like to know what is the command for performing the Bounds Test?

Regards

Alistair

[Sebastian Kripfganz]

If you have not done so already, you first need to install the ardl package as follows:

net install ardl, from(http://www.kripfganz.de/stata/)

or

ssc install ardl

Subsequently, you can estimate an ARDL model in the equilibrium correction form with option ec of the ardl command. The bounds test can be obtained afterwards by using the estat ectest postestimation command. Here is an example:

webuse lutkepohl2
ardl ln_inv ln_inc ln_consump, ec
estat ectest

Please see the following presentation for further information:

• Kripfganz, S. and D. C. Schneider (2018). ardl: Estimating autoregressive distributed lag and equilibrium correction models. Proceedings of the 2018 London Stata Conference.

[Sebastian Kripfganz]

I was kindly informed by one of the ardl users that there is a mismatch of the reported bounds test F-statistics between our Stata command and the Microfit program by Pesaran & Pesaran. I have tried to replicate the Stata results with Microfit 5.5. While the ARDL coefficient estimates coincide, I am unable to replicate the F-statistic reported by Microfit. I have double checked the F-statistic reported by our own postestimation command estat ectest and could verify by manual calculation that our F-statistic is correct. I thus want to issue a warning to everyone who uses Microfit that there is a potential problem with the bounds test F-statistic reported there.

[Emil Harberg]

Dear Sebastian Kripfganz,

I have a question regarding the ARDL module in Stata. Suppose I run an ARDL model using the "ec" option on a mix of I(1) and I(0) variables, where the estimated "Long-Run" coefficients are statistically insignificant. In this occasion, I presume that there is no cointegration among the variables, hence I would like to advance with an ARDL module excluding the "Error Correction Term".

How do I proceed? Should I run a new ARDL model using all the variables (i.e. transform non-stationary variables to become stationary) without the "ec" option, or should I only proceed with the estimated "Short-Run" coefficients provided in the first exercise?

Best regards,
Emil S. Harberg

[Sebastian Kripfganz]

All long-run coefficients being statistically insignificant is not sufficient for excluding the error correction term because the lagged dependent variable itself might still be relevant (indicated by a rejection of the null hypothesis from the t-statistic bounds test). If neither the F-test nor the t-test version of the bounds test reject the null hypothesis, then you can proceed with an ARDL model in first differences, excluding the EC term. You would need to transform the (nonstationary) variables into first differences first before running the ardl command without the ec option again.

There is nothing wrong with sticking to the EC model and interpreting only the short-run coefficients. The idea of reestimating the model without the EC term is just to obtain more efficient estimates (if the null hypothesis of the bounds test is indeed true).

[Joan Mannet]

Dear @Sebastian Kripfganz,

I have one question on the long run coefficients in the ardl cointegration approach. The sign that it´s reported on LR section it´s directly interpretable or i´ts neccesary to be multiplied it by minus 1.
Best regards,
Joan Mannet

[Sebastian Kripfganz]

The long-run coefficients can be direcly interpreted as the long-run level effects on the dependent variable; see slide 16 of my my presentation at last year's London Stata Conference.

[Joan Mannet]

Dear @Sebastian Kripfganz,thanks for your prompt response. Just to clarify, in your slide 13 of your presentation at last year's London Stata Conference, where you estimate the long-run relationship between the consumption, income and investment; we can assure that the income affects possitively in the long-term to the consumption?

Best regards,
Joan Mannet

[Sebastian Kripfganz]

That is correct. A 1% permanent increase in income raises consumption in the long-run by 1%.

[Jean Yang]

I have some problem.when I command "ardl Deficit GINI GDP,lags(1,0,0)ec btest" is sucessful. I change the variable position "ardl GINI Deficit GDP,lags(1,0,0)ec btest ", it appear error instruction"Maximum number of iterations exceeded r(498)". How can I do? Thanks

Jean

[Sebastian Kripfganz]

From the information you are giving us, it is not clear to me why this is happening. If you are happy with it, please feel free to send us your data set by e-mail such that we can further explore the issue.

Although this should not be related to the issue you are experiencing, please note that the btest option is outdated and superseded by the postestimation command estat ectest.

[Esti Widyastuti]

Dear Sebastian Kripfganz,

Thank you for creating updated ardl package! It helps me so much as I am new to Stata. Currently, I am incorporating structural break as dummy variable both in level (z1) and slope (z1_lworldprod z1_rea z1_lrac z1_lstock) shifts. I put below command.
ardl lworldprod rea lrac lstock z1_lworldprod z1_rea z1_lrac z1_lstock, exog(z1) aic maxcombs(1600000)
ARDL(3,0,1,4,4,0,1,4) regression

Sample: 1984m7 - 2018m12 Number of obs = 414
F( 25, 388) = 2392.05
Prob > F = 0.0000
R-squared = 0.9936
Adj R-squared = 0.9931
Log likelihood = 1329.0834 Root MSE = 0.0101

-------------------------------------------------------------------------------
lworldprod | Coef. Std. Err. t P>|t| [95% Conf. Interval]
--------------+----------------------------------------------------------------
lworldprod |
L1. | .8434059 .0492322 17.13 0.000 .7466107 .9402011
L2. | .0179606 .0648356 0.28 0.782 -.1095125 .1454336
L3. | .0795246 .0490225 1.62 0.106 -.0168583 .1759075
|
rea | -.0000349 .0000342 -1.02 0.309 -.0001022 .0000324
|
lrac |
--. | -.0283985 .0090052 -3.15 0.002 -.0461036 -.0106934
L1. | .0325137 .0092005 3.53 0.000 .0144247 .0506028
|
lstock |
--. | .1848714 .0628458 2.94 0.003 .0613105 .3084324
L1. | -.3122098 .0774477 -4.03 0.000 -.4644794 -.1599402
L2. | -.0927379 .0778389 -1.19 0.234 -.2457767 .060301
L3. | .0189898 .0790673 0.24 0.810 -.1364642 .1744438
L4. | .2644174 .0594542 4.45 0.000 .1475247 .38131
|
z1_lworldprod |
--. | .3001233 .0620832 4.83 0.000 .1780617 .4221849
L1. | -.2855497 .0894181 -3.19 0.002 -.4613543 -.1097451
L2. | -.0626762 .091144 -0.69 0.492 -.2418741 .1165217
L3. | .0237294 .0911547 0.26 0.795 -.1554896 .2029483
L4. | .148122 .061305 2.42 0.016 .0275904 .2686536
|
z1_rea | .0000442 .0000369 1.20 0.231 -.0000283 .0001167
|
z1_lrac |
--. | .0278079 .0127938 2.17 0.030 .0026541 .0529616
L1. | -.0332215 .0129242 -2.57 0.011 -.0586316 -.0078114
|
z1_lstock |
--. | -.397443 .0889488 -4.47 0.000 -.572325 -.222561
L1. | .427957 .128647 3.33 0.001 .1750245 .6808894
L2. | .0910252 .1313212 0.69 0.489 -.1671651 .3492154
L3. | -.0354836 .1313457 -0.27 0.787 -.293722 .2227547
L4. | -.2139277 .0883752 -2.42 0.016 -.3876819 -.0401735
|
z1 | -.3693239 .3294924 -1.12 0.263 -1.017138 .2784901
_cons | .1544295 .1345738 1.15 0.252 -.1101556 .4190145
-------------------------------------------------------------------------------

Then, for cointegration test, can I use the critical values that you created in postestimation command estat ectest with the presence of structural break?

ardl lworldprod rea lrac lstock z1_lworldprod z1_rea z1_lrac z1_lstock, exog(z1) aic maxcombs(1600000) ec1

ARDL(3,0,1,4,4,0,1,4) regression

Sample: 1984m7 - 2018m12 Number of obs = 414
R-squared = 0.2068
Adj R-squared = 0.1557
Log likelihood = 1329.0834 Root MSE = 0.0101

-------------------------------------------------------------------------------
D.lworldprod | Coef. Std. Err. t P>|t| [95% Conf. Interval]
--------------+----------------------------------------------------------------
ADJ |
lworldprod |
L1. | -.0591089 .0187848 -3.15 0.002 -.0960417 -.0221761
--------------+----------------------------------------------------------------
LR |
rea |
L1. | -.0005899 .0005327 -1.11 0.269 -.0016372 .0004574
|
lrac |
L1. | .0696216 .0569549 1.22 0.222 -.0423573 .1816005
|
lstock |
L1. | 1.071428 .2730239 3.92 0.000 .5346361 1.608219
|
z1_lworldprod |
L1. | 2.093572 .6446344 3.25 0.001 .8261588 3.360986
|
z1_rea |
L1. | .0007484 .0005808 1.29 0.198 -.0003935 .0018902
|
z1_lrac |
L1. | -.0915875 .0694734 -1.32 0.188 -.2281789 .045004
|
z1_lstock |
L1. | -2.163331 .6971521 -3.10 0.002 -3.533999 -.7926623
--------------+----------------------------------------------------------------
SR |
lworldprod |
LD. | -.0974852 .0498722 -1.95 0.051 -.1955388 .0005684
L2D. | -.0795246 .0490225 -1.62 0.106 -.1759075 .0168583
|
rea |
D1. | -.0000349 .0000342 -1.02 0.309 -.0001022 .0000324
|
lrac |
D1. | -.0283985 .0090052 -3.15 0.002 -.0461036 -.0106934
|
lstock |
D1. | .1848714 .0628458 2.94 0.003 .0613105 .3084324
LD. | -.1906693 .0609148 -3.13 0.002 -.3104337 -.0709048
L2D. | -.2834071 .0598333 -4.74 0.000 -.4010452 -.1657691
L3D. | -.2644174 .0594542 -4.45 0.000 -.38131 -.1475247
|
z1_lworldprod |
D1. | .3001233 .0620832 4.83 0.000 .1780617 .4221849
LD. | -.1091752 .0626578 -1.74 0.082 -.2323666 .0140162
L2D. | -.1718514 .0624797 -2.75 0.006 -.2946925 -.0490102
L3D. | -.148122 .061305 -2.42 0.016 -.2686536 -.0275904
|
z1_rea |
D1. | .0000442 .0000369 1.20 0.231 -.0000283 .0001167
|
z1_lrac |
D1. | .0278079 .0127938 2.17 0.030 .0026541 .0529616
|
z1_lstock |
D1. | -.397443 .0889488 -4.47 0.000 -.572325 -.222561
LD. | .1583861 .0903033 1.75 0.080 -.0191589 .3359311
L2D. | .2494113 .0900341 2.77 0.006 .0723955 .426427
L3D. | .2139277 .0883752 2.42 0.016 .0401735 .3876819
|
z1 | -.3693239 .3294924 -1.12 0.263 -1.017138 .2784901
_cons | .1544295 .1345738 1.15 0.252 -.1101556 .4190145
-------------------------------------------------------------------------------

. estat ectest

Pesaran, Shin, and Smith (2001) bounds test

H0: no level relationship F = 2.175
Case 3 t = -3.147

Finite sample (7 variables, 414 observations, 17 short-run coefficients)

Kripfganz and Schneider (2018) critical values and approximate p-values

| 10% | 5% | 1% | p-value
| I(0) I(1) | I(0) I(1) | I(0) I(1) | I(0) I(1)
---+------------------+------------------+------------------+-----------------
F | 2.012 3.146 | 2.309 3.514 | 2.936 4.275 | 0.069 0.432
t | -2.543 -4.217 | -2.845 -4.557 | -3.430 -5.190 | 0.023 0.436

do not reject H0 if
both F and t are closer to zero than critical values for I(0) variables
(if p-values > desired level for I(0) variables)
reject H0 if
both F and t are more extreme than critical values for I(1) variables
(if p-values < desired level for I(1) variables)

Looking forward to your advice.

Thank you and Best Regards,
Esti

[Sebastian Kripfganz]

Unfortunately, the bounds test critical values are not valid when there is a structural break. I would recommend that you do a sample split and perform the bounds test separately for the two samples before and after the break.