[Mustapha Immurana]

Please what then will be the solution if there is no co-integration and the vars are mixed and not strictly I(1)?

[Sebastian Kripfganz]

Yes, with the qualification that there are no long-run effects if your variables are I(1) but without co-integration.

[Mustapha Immurana]

Yes, you can.

Dear Sebastian,

''You can always run the ARDL model in levels no matter whether your variables are I(0), I(1), or a mixture of both. The ec and ec1 options are just reparameterizations of the ARDL model, another way of displaying the results, but the underlying estimation is the same as without these options.''

Please is the above statement the reason why you said even when the ardl is run with the ec1 or ec option and there is no co-integration we can still maintain the sr and lr results? If not please kindly provide me with the reasons.

Thanks so much for your time.

[Mustapha Immurana]

I am most grateful

[Sebastian Kripfganz]

Yes, you can.

[Mustapha Immurana]

1./2. You can always run the ARDL model in levels no matter whether your variables are I(0), I(1), or a mixture of both. The ec and ec1 options are just reparameterizations of the ARDL model, another way of displaying the results, but the underlying estimation is the same as without these options.

3. If there is only 1 lag of the dependent variable in the ARDL specification of the model, then there will not be any additional short-run term (lagged differences of the dependent variable). The one lag of the dependent variable determines the speed-of-adjustment coefficient in the error-correction representation.

Dear Sebastian,
Thanks so much

So please does response1./2. mean if I use the ec1 option and the short run and long run results are displayed BUT the estat btest command showed no cointegration I can still maintain the results?

[Sebastian Kripfganz]

1./2. You can always run the ARDL model in levels no matter whether your variables are I(0), I(1), or a mixture of both. The ec and ec1 options are just reparameterizations of the ARDL model, another way of displaying the results, but the underlying estimation is the same as without these options.

3. If there is only 1 lag of the dependent variable in the ARDL specification of the model, then there will not be any additional short-run term (lagged differences of the dependent variable). The one lag of the dependent variable determines the speed-of-adjustment coefficient in the error-correction representation.

[Mustapha Immurana]

Mustapha:

1. Worry about what? You can still consistently estimate the ARDL model but estimation purely in first differences would be more efficient.

2. If you want your dummy to appear in the long-run relationship, you could alternatively use the following specification:

ardl lngdp lnalindirect lnaldirect dummy, lags(. . . 0) ec1

which forces the dummy to enter the ARDL model with zero lags while the lag order for all other variables is still chosen optimally.


Usman:

This can happen for example if you do not have full administrator rights on a company PC. I have sent you a private message here on Statalist.

Dear Sebastian,

Thanks so much for the knowledge you have been sharing.

Could you Please kindly help with the following questions.

You have explained that if all vars are I(1) and there is no cointegration, then it is better to use first differences of the vars and run the ardl directly without the ec or ec1.

1. So please what I want to be sure about is whether vars are all I(1) or Mixed I(0) and I(1) , provided there is no cointegration, the ardl should be directly run WITHOUT the ec or ec1 options but lags options can be stated?

2. Based on your response above, can I say that If vars are mixed I(0) and I(1) and there is no cointegration, running the ardl drectly using the vars in LEVEL forms and WITHOUT the ec or ec1 options is appropriate?

3. Please what could be the reason for such a result below where the lag or first difference of the dependent var was not seen in the Short run estimates?

. ardl lndvlp lntexpnd lntrev dumy, lags(. . . 0) ec1 regstore(reg1)

ARDL regression
Model: ec

Sample: 1977 - 2015
Number of obs = 39
Log likelihood = 72.370326
R-squared = .48755266
Adj R-squared = .42726473
Root MSE = .04051888

------------------------------------------------------------------------------
D.lndvlp | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ADJ |
lndvlp |
L1. | -.2975397 .0727746 -4.09 0.000 -.4454355 -.149644
-------------+----------------------------------------------------------------
LR |
lntexpnd |
L1. | .2827662 .2020133 1.40 0.171 -.1277741 .6933065
|
lntrev |
L1. | .7414265 .2378828 3.12 0.004 .2579904 1.224863
|
dumy |
L1. | -.1744303 .0955046 -1.83 0.077 -.3685191 .0196585
-------------+----------------------------------------------------------------
SR |
lntexpnd |
D1. | .0841342 .0674223 1.25 0.221 -.0528845 .2211529
|
lntrev |
D1. | .2206038 .0818039 2.70 0.011 .0543582 .3868494
|
dumy |
D1. | -.0519 .0282168 -1.84 0.075 -.1092434 .0054435
|
_cons | -.1322512 .1203211 -1.10 0.279 -.3767731 .1122708
------------------------------------------------------------------------------

[Mahana Noorma]

Again, thank you very much for your precious help
Kind regards

[Sebastian Kripfganz]

Mustapha:

1. Worry about what? You can still consistently estimate the ARDL model but estimation purely in first differences would be more efficient.

2. If you want your dummy to appear in the long-run relationship, you could alternatively use the following specification:

ardl lngdp lnalindirect lnaldirect dummy, lags(. . . 0) ec1

which forces the dummy to enter the ARDL model with zero lags while the lag order for all other variables is still chosen optimally.


Usman:

This can happen for example if you do not have full administrator rights on a company PC. I have sent you a private message here on Statalist.

[Usman Bashir]

I just released a user-written command by myself and Daniel Schneider that accomplishes this task.

The command ardl fits a linear regression model of depvar on indepvars with lagged depvar and indepvars as additional regressors. Information criteria can be used to find the optimal lag lengths. Estimation output is delivered either in levels form or in error-correction form. As an option, results from the Pesaran/Shin/Smith (2001) bounds testing procedure for the existence of a levels relationship can be displayed.

You can find and install the ardl package by typing the following line in the Stata command window:
net from "http://www.kripfganz.de/stata/"

Please see the Stata help file for additonal information about the command. Comments, suggestions, and bug reports are highly welcome.

Dear Sebastian i am currently using STATA 14 and i am unable to download your program this is the error when i run "net install ardl, from(http://www.kripfganz.de/stata/)"

net install ardl, from(http://www.kripfganz.de/stata/)
connection timed out -- see help r(2) for troubleshooting
http://www.kripfganz.de/stata/ either
1) is not a valid URL, or
2) could not be contacted, or
3) is not a Stata download site (has no stata.toc file).
r(2);

.
your help would be appreciated

[Mustapha Immurana]

Mahana:

It really depends on what you are interested in. The first coefficient of your x-variable gives you the contemporaneous short-run effect of a change in that variable on the change in y. The second coefficient gives you the one period lagged effect, and so on. Of course, if the respective coefficient is statistically insignificant, than you would conclude that the corresponding effect is zero.

Adding all the coefficients would yield a cumulative effect. You can compute it with the lincom command. For this exercise, the significance of individual coefficients is not crucial but the significance of the sum of all coefficients.

Since you estimated the model in first differences without an error-correction term, you are imposing that there exists no long-run effect of the level of x on the level of y.


Mustapha:

1. No, if all variables are individually I(1) you can still have a cointegrating / long-run relationship among them.

2. The ardl options ec or ec1 both produce estimates for an error-correction model including the long-run terms. If you want to estimate an ardl model purely in first differences, you should use the time-series first-difference operator D. to generate first-differenced variables and then run the ardl command with these differenced variables and without the option ec or ec1. (Unfortunately, ardl does not allow time-series operators right now. You would have to generate new variables in a first step.) But note that such a first-differenced model would be misspecified if there is in fact a long-run relationship.

3. I do not really understand this point. Can you show an example with the command line as you have typed it and the corresponding Stata output?

4. You should specify the dummy variables with the exog() option of the ardl command. Then there will be no problem using the ec or ec1 option.

Dear Sebastian,

Thanks so much.

1. Please I need clarity concerning response 1 above. Thus if all variables are individually I(1) and we do not have a cointegrating / long-run relationship is there the need to be worried?

2. In using the ardl command in stata and applying the exog option, the variables stated in the parenthesis do not appear in the long run results, so please how do you explain this especially when that exog var assuming is a dummy, is the main variable of interest as shown in the results below:

. ardl lngdp lnalindirect lnaldirect, exog(dummy) ec1 regstore(obj2)

ARDL regression
Model: ec

Sample: 1975 - 2015
Number of obs = 41
Log likelihood = 99.629501
R-squared = .48803084
Adj R-squared = .37943132
Root MSE = .02374474

------------------------------------------------------------------------------
D.lngdp | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ADJ |
lngdp |
L1. | -.2676916 .0792778 -3.38 0.002 -.4289835 -.1063996
-------------+----------------------------------------------------------------
LR |
lnalindirect |
L1. | .69882 .0862262 8.10 0.000 .5233916 .8742484
|
lnaldirect |
L1. | .2651334 .0800871 3.31 0.002 .1021949 .4280719
-------------+----------------------------------------------------------------
SR |
lngdp |
LD. | .3157183 .1478288 2.14 0.040 .0149583 .6164782
|
lnalindirect |
D1. | .2418461 .094818 2.55 0.016 .0489374 .4347549
LD. | -.2319939 .0905123 -2.56 0.015 -.4161426 -.0478453
|
lnaldirect |
D1. | .070974 .0356959 1.99 0.055 -.00165 .1435979
|
dummy | -.0172295 .0214643 -0.80 0.428 -.0608989 .0264399
_cons | -.3642064 .1204868 -3.02 0.005 -.6093387 -.1190741
------------------------------------------------------------------------------

[Sebastian Kripfganz]

If the speed-of-adjustment coefficient ϕ and the long-run coefficient ρ are nonzero, then there exists a long-run relationship in the levels between x and y. Otherwise there does not exist such a relationship. The long-run coefficient tells you how large the effect of a change in x on y in the long-run equilibrium is, and the speed-of-adjustment coefficient tells you how fast the convergence back to this equilibrium is.

[Mahana Noorma]

Sebastian,

Thank you so much for your quick reply and your explanations.

I just have one additional question regarding your last comment. What would the presence of an error correction term would imply?

The model would be:
Δy_t = β₀ + Σ β_iΔy_t-i + Σγ_jΔx_1t-j + ϕz_t-1+ e_t

where z_t-1=y_t-1-c-ρx_1t-1 and is the error correction term.

Thank you very much for your help.

Kind regards

[Sebastian Kripfganz]

Mahana:

It really depends on what you are interested in. The first coefficient of your x-variable gives you the contemporaneous short-run effect of a change in that variable on the change in y. The second coefficient gives you the one period lagged effect, and so on. Of course, if the respective coefficient is statistically insignificant, than you would conclude that the corresponding effect is zero.

Adding all the coefficients would yield a cumulative effect. You can compute it with the lincom command. For this exercise, the significance of individual coefficients is not crucial but the significance of the sum of all coefficients.

Since you estimated the model in first differences without an error-correction term, you are imposing that there exists no long-run effect of the level of x on the level of y.


Mustapha:

1. No, if all variables are individually I(1) you can still have a cointegrating / long-run relationship among them.

2. The ardl options ec or ec1 both produce estimates for an error-correction model including the long-run terms. If you want to estimate an ardl model purely in first differences, you should use the time-series first-difference operator D. to generate first-differenced variables and then run the ardl command with these differenced variables and without the option ec or ec1. (Unfortunately, ardl does not allow time-series operators right now. You would have to generate new variables in a first step.) But note that such a first-differenced model would be misspecified if there is in fact a long-run relationship.

3. I do not really understand this point. Can you show an example with the command line as you have typed it and the corresponding Stata output?

4. You should specify the dummy variables with the exog() option of the ardl command. Then there will be no problem using the ec or ec1 option.