[Tino Tinsky]

In the ardl package are there the critical values implemented that have been calculated by Banerjee et al. (1996), as the usual critical values do not apply.

[Sebastian Kripfganz]

In the ardl package are there the critical values implemented that have been calculated by Banerjee et al. (1996), as the usual critical values do not apply.

Which paper by Banerjee et al. (1996) are you refering to? This reference is not precise enough to identify the exact piece of work.

The relevant critical values in the context of the bounds testing procedure implemented in the ardl package are the asymptotic critical values by Pesaran et al. (2001) and the finite-sample critical values by Narayan (2005):

• Pesaran, M. H., Y. Shin, and R. Smith (2001). Bounds testing approaches to the analysis of level relationships. Journal of Applied Econometrics 16(3): 289–326.
• Narayan, P. K (2005). The saving and investment nexus for China: evidence from cointegration tests. Applied Economics 37(17): 1979–1990

[charles martens]

Dear Sebastian Kripfganz,

regarding the use of the ardl package I have the following two questions:

1) When co-integration is established, estimating an error correction model (using ardl depvar indepvar, ec) provides the following insight:

Consider a regression model with two independent variables X_1 and X_2. By using "ardl depvar indepvar1 indepvar2, ec
", an error correction term is generated, namely: [ Y_t - theta_1 * X_{1t} - theta_2 * X_{2t} ].This term is stationary and usable in regression analysis.

Consequently, in the output table of "ardl depvar indepvar1 indepvar2, ec", the "LR" estimates are the corresponding coefficients for the theta's in the aforementioned error correction term.
The "ADJ" estimate is alpha in the following regression equation: delta*Y_t = alpha_t*[Y_t - theta_1 * X_{1t} - theta_2 * X_{2t}].

Are these two last statements right? (The theta's corresponding to the LR estimates and the ADJ estimate being the estimate for alpha).

2) When the found F-statistic (using estat btest / ardl, noctable btest) falls within the bounds of the critical values, it is necessary to check the co-integration rank. If the rank is equal to 1, we can continue using the error correction specification by using "ardl depvar indepvar, ec". Is this right as well? Or should we not use the error correction specification when the found F-statistic falls within the bounds?

Thanks in advance

[Sebastian Kripfganz]

The statements in your first question are correct. The long-run estimates (LR) are the coefficients theta, and the speed-of-adjustment coefficient (ADJ) is the coefficient alpha (without subscript t). (As an aside, it should be Y_{t-1} instead of Y_t in the error-correction term.)

The answer to your second question is a bit more tricky. There should be at most one cointegrating relationship that involves Y_t; but that does not exclude the possibility that the cointegration rank exceeds one if there is an additional cointegrating relationship just between X_{1t} and X_{2t} that does not involve Y_t.

If the F-statistic falls in between the two bounds, the result is generally inconclusive. You could proceed by testing the order of integration for each variable. If all variables are individually I(1), then the upper bound is the relevant one and you would not reject the null hypothesis of no long-run relationship. If all variables are individually I(0), then the lower bound becomes relevant and you would reject the same null hypothesis. It is getting tricky, if some of the variables are I(0) and others are I(1). In principal, you would need to simulate the respective critical value for your specific case. Alternatively, you might want to be conservative and not reject the null hypothesis.

Depending on your conclusion, you would continue using the error-correction specification if you do reject the null hypothesis while it would be more efficient to estimate a model purely in first differences if you cannot reject it.

[charles martens]

The statements in your first question are correct. The long-run estimates (LR) are the coefficients theta, and the speed-of-adjustment coefficient (ADJ) is the coefficient alpha (without subscript t). (As an aside, it should be Y_{t-1} instead of Y_t in the error-correction term.)

The answer to your second question is a bit more tricky. There should be at most one cointegrating relationship that involves Y_t; but that does not exclude the possibility that the cointegration rank exceeds one if there is an additional cointegrating relationship just between X_{1t} and X_{2t} that does not involve Y_t.

If the F-statistic falls in between the two bounds, the result is generally inconclusive. You could proceed by testing the order of integration for each variable. If all variables are individually I(1), then the upper bound is the relevant one and you would not reject the null hypothesis of no long-run relationship. If all variables are individually I(0), then the lower bound becomes relevant and you would reject the same null hypothesis. It is getting tricky, if some of the variables are I(0) and others are I(1). In principal, you would need to simulate the respective critical value for your specific case. Alternatively, you might want to be conservative and not reject the null hypothesis.

Depending on your conclusion, you would continue using the error-correction specification if you do reject the null hypothesis while it would be more efficient to estimate a model purely in first differences if you cannot reject it.

Thank you so much for your quick reply. It makes better sense now!
I will probably not reject the null hypothesis when the F-statistic falls between bounds, just to be sure. Thanks again.

[Abu Kom]

Hello everyone,

I have followed several comments on this forum and I have really benefited from the discussions. I have used ARDL to carry out estimations for my thesis, but I am unclear as to what step-by-step Stata codes (commands) I need to work through to get the error correction term. I tried the ardl help on Stata, but I could not still do it. Does anyone want to help me with this? Thanks.

[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!

[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]

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]

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]

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.

[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?

[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

[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

[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.