[Sebastian Kripfganz]

You need to restore the underlying regress estimation results first before you can use these standard postestimation commands. Please see slides 27 to 29 of my presentation at last year's London Stata Conference:
Kripfganz, S. and D.C. Schneider (2018). ardl: Estimating autoregressive distributed lag and equilibrium correction models. Proceedings of the 2018 London Stata Conference

Further discussion of the new version of the ARDL command in the following Statalist topic:
ARDL: updated Stata command for the estimation of autoregressive distributed lag and error correction models

[Anil Raj]

After running the estat ectest when I try to run estat hettetst/imtest/durbinalt stat14 shows the error "estat hettest not valid". Please help.

[Sebastian Kripfganz]

Marcelo Dias-Paes-Ferreira:
We just compared the output from our ardl Stata command to the EViews (version 9.5) table "ARDL Long Run Form and Bounds Test" (subtable "Levels Equation"). The coefficients and standard errors exactly coincide. Not sure, where you have seen different standard errors in EViews.

Pesaran and Shin (1998) compare the conventional Delta-method standard errors (which are implemented in our ardl package) with standard errors obtained from an asymptotic formula (valid only under the assumption that the long-run forcing variables are I(1)). They conclude:

Therefore, the standard error for the estimator of the long run parameter, µ, obtained using the Δ-method is asymptotically the same as that given by [the asymptotic formula], which was derived assuming that x_t is I(1). One important advantage of the variance estimator obtained by the Δ-method over the asymptotic formula [..] lies in the fact that it is asymptotically valid irrespective of whether x_t is I(1) or I(0), while the latter estimator is valid only if x_t is I(1).
The two variance estimators clearly differ in …finite samples.

Given that the bounds test does not require all variables to be I(1) and the asymptotic equivalence of the two methods if this was the case, we currently do not plan to implement alternative standard errors.

Reference:
Pesaran, M. H. and Y. Shin (1998). An autoregressive distributed-lag modelling approach to cointegration analysis. In S. Strom (Ed.), Econometrics and Economic Theory in the 20th Century. The Ragnar Frisch Centennial Symposium, Chapter 11, pp. 371-413. Cambridge: Cambridge University Press.


Anil Raj:
The BIC tends to select more parsimonious models than the AIC. If your sample size is rather small, you might prefer the BIC to avoid the estimation of too many parameters. Otherwise, in particular if you want to carry out the bounds test, you might prefer the AIC because the chance to have remaining serial error correlation is reduced in models with richer dynamics (i.e. higher lag orders). There is a vast literature on model selection criteria that you can easily find online if you need more background information.

[Anil Raj]

Kindly help me with the ardl command to find maximum lags to be used. My depvar is bank benchmark rate and independent variables are monetary policy rate(repo),cost of funds and non performing loans (log of gnpa) with 36 observations.

I ran the following command in stata
ardl bnchmrk repo lgnpa cof, aic
ardl bnchmrk repo lgnpa cof, bic

aic mentions ARDL(1,1,0,0) regression and bic mentions ARDL(1,0,0,0) regression.

I am confused about the selection . Please help

Also please help me with the vecrank command in stata which i used to find co-integrating vector as mentioned in an earlier post here. How to interpret the output?

//* vecrank bnchmrk repo lgnpa cof

Johansen tests for cointegration
Trend: constant Number of obs = 34
Sample: 3 - 36 Lags = 2
-------------------------------------------------------------------------------
5%
maximum trace critical
rank parms LL eigenvalue statistic value
0 20 76.161843 . 57.4386 47.21
1 27 89.835272 0.55261 30.0917 29.68
2 32 97.807025 0.37433 14.1482* 15.41
3 35 104.19286 0.31315 1.3765 3.76
4 36 104.88112 0.03968
*//

Does this mean that there is 2 cointegrating vectors? So can I use the ARDL model here?

Thanks in advance.

[Marcelo Dias-Paes-Ferreira]

Hello Sebastian

Great work you guys have done on ardl command. It seems that ardl uses the regular delta method to calculate standart errors for LR equation. E-views presents diferent se for long run equation, which they claim is a delta method proposed by Pesaran and Shin (1998). Do you know how to get the Pesaran and Shin (1998) standart errors in stata?

Thanks in advance.

[Sebastian Kripfganz]

Sure, we are happy about every reference to our work.

[Valeria Kos]

Thank you very much for your promt reply, Professor Kripfganz.

Also, I would like to quote your and Mr. Schneider's presentation at STATA Conference in 2018 in the bibliography section of my Master thesis at Bocconi University since it was instrumental for my research. I want to verify if it is okay with you?

[Sebastian Kripfganz]

The null hypothesis of the bounds test is that there exists no level relationship. This does not imply that the variables are stationary. In contrast, since neither the test based on the F-statistic nor the one based on the t-statistic reject the null hypothesis, this result would be in line with a nonstationary dependent variable that is not cointegrated with any of the (nonstationary) independent variables.

You can still interpret the short-run effects from the estimated error-correction representation of the model. Given that there is no long-run level relationship, you can also reestimate a more parsimonious (more efficient) ARDL model (without the ec option) where all variables are transformed into first differences (before they enter the model).

Further discussion of the new version of the ARDL command in the following Statalist topic:
ARDL: updated Stata command for the estimation of autoregressive distributed lag and error correction models

[Valeria Kos]

Dear all,

I haven't dealt with the ARDL model before so I would like to seek your advice. I have run the bounds test and the null hypothesis is accepted. I suppose it means that all the variables are stationary (but I feel a bit conflicted about it since augmented Dickey-Fuller test results showed integration of order one for two variables and stationarity for another one). What are my next steps? There is no long-run relationship, can I use ARDL estimated to test short-run effects?

Thank you in advance.

Here are the testing results

H0: no level relationship F = 4.250
Case 5 t = -2.077

Finite sample (2 variables, 39 observations, 3 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 | 4.381 5.454 | 5.274 6.494 | 7.370 8.919 | 0.111 0.218
t | -3.121 -3.669 | -3.470 -4.052 | -4.185 -4.830 | 0.474 0.645

[NIP NIP]

TY! Sebastian.

1 noconstant
2 constant restricted
3 constant
4 constant trendvar(trendvarname) restricted
5 constant trendvar(trendvarname)

I used the 4th case since I need an intercept and a linear trend. I created my own trend variable, Trend2.

By fixed regressor I meant exogenous variable.

I used this the following command:

ardl Y X1 X2, exog( D1 D2 ) lags(4,0,0) constant trendvar( Trend2 ) restricted ec

If this is incorrect in any way, please, say it! :D

[Mike Zyphur]

Thank you, Sebastian, it works splendidly!

[Sebastian Kripfganz]

Here is an algorithm that should work:

webuse lutkepohl2
ardl ln_consump ln_inc ln_inv, ec

loc varname "ln_inv"

local lag = el(e(lags), 1, colnumb(e(lags), "`varname'"))
local --lag        // the number of lags in the EC form is one less than the number of lags in levels

if `lag' >= 0 {
    loc lagsum "D.`varname'"
    loc laglist "D.`varname'"
    forv l = 1/`lag' {
        loc lagsum "`lagsum' + L`l'D.`varname'"
        loc laglist "`laglist' L`l'D.`varname'"
    }
    lincom `lagsum'
    test `laglist'
}

ardl stores the number of lags in the level representation of the model in the matrix e(lags). The relevant lag order can be extracted from that matrix. The above code can be easily adjusted to work with the ec1 instead of the ec option by removing the if `lag' >= 0 condition.

[Mike Zyphur]

Hi Sebastian,
Thank you for your ARDL command! It's very helpful and incredibly well done. I was wondering if you would mind giving me your thoughts on something?

Is there a simple way to sum the short-run lagged effects on a single predictor x when it has many lags? I ask because I'm running many ARDL models in a single .do file. The problem created here is two-fold. On the one hand using lag selection via BIC or AIC will make each ARDL model's lags unique, and therefore no single 'lincom' or 'test' command will work to sum all of the lagged short-run effects for a single predictor. On the other hand the reported output is not the same (using ec1) as the underlying regression model that would be used to construct the sum of the short-run effects using lincom. Of course, the second problem can be solved algebraically, but not the first. In combination, these issues make it very difficult to compute the sum of lagged short-run effects.

Is there a simple solution to this issue that you know of? I've read through all of the ARDL documentation as well as all 22 pages of this thread, but I've not found this question asked or answered previously, which kind of surprised me. Shouldn't it be common to conduct an overall test of the short-run effect of a predictor's short-run effects when it has many lags included in the model?

Thanks again!!
Mike

[Sebastian Kripfganz]

If you want to include a time trend, you should always specify the trend() option rather than directly specifying the trend variable as a regressor. Without seeing your Stata command line, I do not know what you mean by "fixed regressor". If there is a trend in your model, the only relevant cases are 4 or 5. Without the trend() option, the postestimation command for the bounds test does not know that there is a trend in the model and it would show you the wrong critical values and in the restricted case even compute the wrong F-statistic.

In many cases, it is advisable to use the restricted option, which results in case 2 without a trend or case 4 with a trend. For example, if there is a trend in the model but you do not restrict it, then your data-generating process would follow a quadratic time trend under the null hypothesis but a linear trend under the alternative hypothesis. Either of the two processes would usually not be in line with the observed data. With a restricted time trend, however, the deterministic trend component remains linear both under the null and under the alternative hypothesis.

Please ensure that you have the latest version of our ardl command. For details, please see the following new Statalist topic and please ask any further questions about this new command version in this new topic (to avoid any confusion with some outdated comments above): ARDL: updated Stata command for the estimation of autoregressive distributed lag and error correction models

[NIP NIP]

Hello all!

In the ARDL methology, there is 5 cases.
Could you please help me with some guidelines about when a case should selected over the others?

I'm trying to estimate a ARDL model as follows:

Y = Intercept + b1*Trend + b2*X1 + b3*X2

I selected case II (restricted intercepts; no trends) and then I added the "Trend" variable as a fixed regressor. Is this ok? Will bounds test and long run estimators be ok?

Thanks & Regards!