[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.

[Mustapha Immurana]

If your variables are I(1) and you have more than one co-integrating relationship among them, the single-equation ARDL model would be misspecified as it can accommodate only one co-integrating relationship. In that case you would prefer to estimate a vector error-correction model (VECM).

If your variables are I(1) and you have exactly one co-integrating relationship, you can rewrite the ARDL model analytically in error-correction representation with first-differences of depvar on the left-hand side, the co-integrating relationship of the level variables as well as additional lags of first-differenced depvar and indepvars on the right-hand side. All those components are then I(0) which shows that you can safely estimate this ARDL model in levels.

If your variables are I(1) but you do not have any co-integrating relationship among them, estimation is still fine because there exist values for the population parameters such that the error term can be I(0) due to the inclusion of lags of the dependent variable (the sum of the coefficients for the lags of depvar would equal unity in the underlying data generating process such that the level term drops out in the error-correction representation of the model; similarly for indepvars that are I(1)). However, in this case it would be more efficient to estimate an ARDL model directly in first differences.

If all of your variables are I(0) then you obviously do not have any problem with the ARDL model.

The point that I want to make is the following: Testing for non-stationarity and co-integration of your variables is still useful as it guides you towards the optimal model choice (VECM, ARDL in levels, ARDL in first differences).

Dear Sebastian,

1. Please based on the above, can I confidently say that if all vars are I(1), establishing long-run relationship or cointegration among variables does not matter anymore?

2. Also from what you have said above, does it mean using ARDL directly in first differences imply applying the ec1?

3. Further, I would want to know the reason behind getting a result that shows only the constant term and not other vars in a short run ARDL model using stata when ec is used and not ec1.

4. Last and not the least, please is it appropriate to use the ec1 even when some explanatory variables are dummies?

[Mahana Noorma]

Dear all,

I have a question regarding the interpretation of the coefficients in an ARDL model.

I estimated the following ARDL model

Δy_t = β₀ + Σ β_iΔy_t-i + Σγ_jΔx_1t-j + e_t

 
 regress d.y  c  l(1/2).d.y  l(0/2).d.x1

I would like to interpret the impact of x₁ on y. As several lags of the variable x₁ is included in the econometric specification, I do not know how to interpret the impact of x₁ on y. Should I consider the sum of the coefficients of the different lagges values of x₁ or should I interpret each of them separately? What if the coefficients are not all statistically significant?

I kindly thank you for your help.

Kind regards

[Viktorija Mano]

Thanks, I will try to rescale it. In terms of collinearity that didn't show a high correlation.

[Sebastian Kripfganz]

I am affraid that I cannot say much more other than guessing that there might be a collinearity problem between FDI and FDI^2. It might help to rescale the variable FDI, i.e. dividing it by 1.000 or one million, depending on its unit of measurement, before squaring it.

[Viktorija Mano]

Difficult to say. My answer would be that 22 observations is probably too small to meaningfully fit such a model. There is not much hope to obtain precise estimates of a third-order polynomial (and corresponding standard errors for the long-run coefficients) in your FDI variable.

Hi Sebastian,

Thanks for your response, I agree that the data is limited, but I am puzzled why does the specific variable (FDI^2) shows me r498 error. I have ran a number of combinations of a similar model investigating GDP and even thoug including 5-6 variables it never showed me this error.

This is a PhD research that I am doing and I am aware that the data is limited, but one of my examiners wanted me to include polynomial.

Thanks again.

[Sebastian Kripfganz]

Difficult to say. My answer would be that 22 observations is probably too small to meaningfully fit such a model. There is not much hope to obtain precise estimates of a third-order polynomial (and corresponding standard errors for the long-run coefficients) in your FDI variable.

[Viktorija Mano]

Dear Iftikhar,

The error message seems to be related to the iterate() option of the nlcom command which is used by ardl to compute the error-correction coefficients and standard errors. With 9 variables and possibly a couple of lags for each, your number of parameters is very large (too large?) relative to your sample size of 35 observations. You might have to reduce the number of variables and/or the number of lags, for example with the maxlags() option of ardl.

Also, I would expect that already the OLS results (ardl without the ec option) are not very meaningful given your large number of coefficients.

Dear Sebastian,


I've a similar issue in running ARDL in Stata , please help me.

When I run the following model with 22 obseervations and lag 1:

lnGDP = a + b1FDI + b2 FDI^2 + b3 FDI^3 + b4INF

I get an error "Maximum number of iterations exceeded" r(498).

However if I run the same number of variables :

lnGDP = a + b1FDI + b2 Dummy1 + b3 FDI^3 + b4INF

It does not show me this error.

I have tried including only lnGDP = a + b1FDI + b2 FDI^2 + b3 FDI^3 and again I get the same error. I have realised that the FDI^2 is the problem, because however I construct the model if it includes this variables it gives me error, with out it runs the model. Any ideas?

Thanks

[Daniel Schneider]

Hi Gus,

thank you for your interest in the -ardl- package. The reason for the error is that critical values for the bounds test are only tabulated up to 10 regressors, so you cannot do bounds testing with eleven regressors. -ardl- errors out when it tries to calculate e(F_critval) and e(t_critval). It should not do this, however, but instead let you estimate the model and inform you about the critical values problem. We will implement this in the next version of the command. Thanks a lot for bringing this issue to our attention.

Unfortunately I do not see a fully satisfying workaround at the moment. It may be ok for you to estimate the model without the -ec- or -ec1- options. You can then calculate the long-run coefficients yourself, but this is a little tedious. Alternatively, if you are willing to take one independent variable out of the long-run relationship, you can relegate it (including lags) to the -exog()- option. Note that optimal lag selection without the -ec- or -ec1- options is still possible with k>10. For optimal lag selection with eleven indepvars, -maxlag(1)- will be reasonably fast, -maxlag(2)- will take a long time, and -maxlag(3)- is infeasible; with any -maxlag()- specification, be sure to use options -maxcombs()-, -fast- and -dots-.

Greetings,
Daniel

[Gus Lane]

Hi Sebastian,

Thanks for your dedication to replying to the posts in this thread. I have found it incredibly useful for my studies thus far.

I'm using your ardl package (will be sure to cite it as requested) for my thesis.

I am trying to use it for a model specification with 1 dependent variable and 11 independent variables, yet am getting a "conformability error r(503)" when implementing the EC representation (ec1). Wondering whether this is because there is max number of variables allowed?

If so, are you aware of any way around this, other than reducing the number of indep vars?

[Sebastian Kripfganz]

Charles:
A temporary unit increase in \(x_t\) immediately increases \(y_t\) by 0.2. Now shift the whole equation one period forward and you will see that \(y_{t+1}\) reacts to \(x_t\) with a negative coefficient. That is, you first observe an increase and then a decrease in the next period and the two effects exactly offset each other.

Even though in this simple case it would not be necessary, in general it is best to rewrite the model in error-correction form to facilitate the interpretation:
\[
\Delta y_t = - [y_{t-1} - (0.2 - 0.2) x_{t-1}] + 0.2 \Delta x_t
\]
We see that the long-run effect of \(x\) on \(y\) is zero because the two coefficients cancel each other. The short-run effect is the coefficient of the change in \(x_t\) on the change in \(y_t\), which is 0.2 with a positive sign in this simple case. It only corresponds to the coefficient of \(x_t\) in your initial model because the two coefficients are identical.

[charles martens]

1) Additive dummy variables can be attached to the equation with the option exog(varlist). See the empirical part of my presentation at the Stata conference for an example.

2) I have never heard about the association of specific lags with outliers. That does not seem to make sense to me. There is nothing wrong with different lags having different signs. Intuitively, this would mean that your dependent variable overshoots initially to a shock in that explanatory variable and subsequently experiences a correction in the opposite direction. I do not have any reference for this interpretation at hand; sorry.

Thanks for your answer.

Consider the following example: \hat{Y}_t = 0.2\hat{X}_t - 0.2\hat{X}_t-1
Would that mean, that a positive shock in X, initially results in an increase of Y, after which the effect is reversed/neutralized? Or is it the other way around? I am having trouble comprehending the direction in which to read the effects. I.e., a positive shock in X initially resulting in a .2 decrease in Y, after which it is neutralized by an increaseof .2. - would this be the wrong interpretation?
If I follow your intuition, is it correct to say that the coefficient corresponding to \hat{X}_t is the short-run coefficient?

[Sebastian Kripfganz]

1) Additive dummy variables can be attached to the equation with the option exog(varlist). See the empirical part of my presentation at the Stata conference for an example.

2) I have never heard about the association of specific lags with outliers. That does not seem to make sense to me. There is nothing wrong with different lags having different signs. Intuitively, this would mean that your dependent variable overshoots initially to a shock in that explanatory variable and subsequently experiences a correction in the opposite direction. I do not have any reference for this interpretation at hand; sorry.

[charles martens]

For those who are interested, the slides for the presentation about the ardl package that I have delivered last week at the Stata Conference are available on the conference proceedings website: www.stata.com/meeting/chicago16/slides/chicago16_kripfganz.pdf

For the time being, if you find the package useful for your own work, we would appreciate it if you acknowledge our programming effort by citing the ardl package as follows:

• Kripfganz, S. and D. C. Schneider (2016). ardl: Stata module to estimate autoregressive distributed lag models. Presented July 29, 2016, at the Stata Conference, Chicago.

Happy estimations!

Hey Sebastian, I will cite you in my master's thesis for what it's worth, haha.

If you have time, I have two more questions: 1) earlier this thread I read that we cannot use the ardl commands with a dummy variable in the model. For one of my countries, I have detected a break using the CUSUM tests. In order to deal with the break, I could impose a dummy variable. But as we cannot use dummies in ARDL models, is there any other way to deal with this break?

2) In two of my countries, different lags give me different (significant) signs for variables. I.e. my variable EX (exchange rate) gives a positive and significant effect of about -.130 at \Delta EX_t, but a negative and significant effect of about .120 at \Delta EX_{t-1}. On some sites, I have read that you should interpret the "closest" lag, as lags farther away correspond with outliers. But in literature, I cannot find any papers backing this. Do you know how to interpret different signs of different lags, and if you do, do you happen to have a reference?


Thanks so much again in advance!
Charles

[Sebastian Kripfganz]

For those who are interested, the slides for the presentation about the ardl package that I have delivered last week at the Stata Conference are available on the conference proceedings website: www.stata.com/meeting/chicago16/slides/chicago16_kripfganz.pdf

For the time being, if you find the package useful for your own work, we would appreciate it if you acknowledge our programming effort by citing the ardl package as follows:

• Kripfganz, S. and D. C. Schneider (2016). ardl: Stata module to estimate autoregressive distributed lag models. Presented July 29, 2016, at the Stata Conference, Chicago.

Happy estimations!