[Georg Neuschaeffer]

Thank you very much Sebastian. This is a great help!

[valérie orozco]

In my message on the 23rd of Nov, I pasted results obtained from some colleagues with Microfit (F-statistic of 11.8907 and same upper and lower bounds). I told you (message on the 24th of november) that I succeed in obtaining same coefficients (both with the ardl command of Stata and with Microfit) than those of my colleagues except the F statistic (I obtained 6.9345 with Microfit and 6.395 with Stata).

I 've just discovered how my colleagues obtained a different F test (but same coefficients). They force the lnY variable to not appear in lagged form. So we can say it is a k=0 model (Microfit output indicates ARDL(2) instead of ARDL(2,0) I obtained). The estimated coefficients are exactly the same. I don't understand how it can be possible to have exactly the same coefficients, with some X coefficients (and so for me it is not a k=0 case) and not the same F test.

In fact, in their case it seems for me that the F test only tests L.lnY=0 whereas in my ARDL(2,0) estimation I test (L.lnY=0 and L.lnX=0). As in the LR term we have the lnX coefficients (the ECM term can be written L.lnY- b L.lnX) I don't understand how it can be possible to consider a k=0 case...I even don't know what it means. Do you have some ideas?

Here the results of my colleagues (with Microfit) :

Autoregressive Distributed Lag Estimates
            ARDL(2) selected based on Akaike Information Criterion
*******************************************************************************
 Dependent variable is LTFP
 50 observations used for estimation from 1963 to 2012
*******************************************************************************
 Regressor              Coefficient       Standard Error         T-Ratio[Prob]
 LNY(-1)                   .26434             .13493             1.9592[.056]
 LNY(-2)                   .31955             .12454             2.5658[.014]
 C                         1.8713             .53340             3.5082[.001]
 LNX                      .067817            .020605             3.2913[.002]
*******************************************************************************
 R-Squared                     .98785   R-Bar-Squared                   .98706
 S.E. of Regression           .026446   F-Stat.    F(3,46)      1246.4[.000]
 Mean of Dependent Variable    5.1312   S.D. of Dependent Variable      .23244
 Residual Sum of Squares      .032173   Equation Log-likelihood       112.7696
 Akaike Info. Criterion      108.7696   Schwarz Bayesian Criterion    104.9456
 DW-statistic                  2.0606
*******************************************************************************
         Error Correction Representation for the Selected ARDL Model
            ARDL(2) selected based on Akaike Information Criterion
*******************************************************************************
 Dependent variable is dLTFP
 50 observations used for estimation from 1963 to 2012
*******************************************************************************
 Regressor              Coefficient       Standard Error         T-Ratio[Prob]
 dLNY1                    -.31955             .12454            -2.5658[.014]
 dLNX                  .067817            .020605             3.2913[.002]
 ecm(-1)                   -.41611             .12067            -3.4483[.001]
*******************************************************************************
 List of additional temporary variables created:
 dLTFP = LTFP-LTFP(-1)
 dLTFP1 = LTFP(-1)-LTFP(-2)
 dLKFRS25 = LKFRS25-LKFRS25(-1)
 ecm = LTFP   -4.4971*INPT   -.16298*LKFRS25
*******************************************************************************
 R-Squared                     .39903   R-Bar-Squared                   .35984
 S.E. of Regression           .026446   F-Stat.    F(3,46)     10.1810[.000]
 Mean of Dependent Variable   .014236   S.D. of Dependent Variable     .033054
 Residual Sum of Squares      .032173   Equation Log-likelihood       112.7696
 Akaike Info. Criterion      108.7696   Schwarz Bayesian Criterion    104.9456
 DW-statistic                  2.0606
Estimated Long Run Coefficients using the ARDL Approach
            ARDL(2) selected based on Akaike Information Criterion
*******************************************************************************
 Dependent variable is LTFP
 50 observations used for estimation from 1963 to 2012
*******************************************************************************
 Regressor              Coefficient       Standard Error         T-Ratio[Prob]
 C                       4.4971            .036804           122.1924[.000]
 LNX                     .16298           .0068402            23.8264[.000]
*******************************************************************************

Testing for existence of a level relationship among the variables in the ARDL model
*******************************************************************************
 F-statistic  95% Lower Bound  95% Upper Bound  90% Lower Bound  90% Upper Bound
   11.8907         12.6082         12.6082         10.3543         10.3543

 W-statistic  95% Lower Bound  95% Upper Bound  90% Lower Bound  90% Upper Bound
   11.8907         12.6082         12.6082         10.3543         10.3543
*******************************************************************************

[Nazib Lee]

Hi sebastian,

Can I apply this ardl command in panel data ardl? or I can simply use xtdpdqml to estimate ardl in stata?
as far as I know, ols estimator cannot obtain consisten estimate on dynamic panel data

[Sebastian Kripfganz]

Dear Valérie,
Thanks for following up on this issue. It took me some time to understand what you mean but I think I got it. Essentially, the variable LNX is treated as an exogenous regressor. In principle, the ardl command has the option exog() that can be used for this purpose. However, the ardl command would then no longer report a long-run coefficient for this regressor as it is essentially left out from the long-run relationship. This is just a matter of how the results are presented and does not affect the estimation or testing.

However, I just realized that the current version of our ardl package does not accept the situation, where there is no regressor other than the lagged dependent variable included in the long-run relationship. In other words, the situation of k=0 is currently not supported. We may have to put this on our to-do list for potential improvements.

Thank you very much again for raising this issue.

[Sebastian Kripfganz]

Dear Nazib,
This ardl command is not suitable for panel data but only for a single time series.

My other command, xtdpdqml, implements a specific quasi-maximum likelihood (QML) estimator for dynamic panel data models with a short time horizon. You are right that in this context the OLS estimator is biased and inconsistent (under fixed T). Currently, xtdpdqml only allows for a single lag of the dependent variable and it does not automatically select the optimal number of lags for the other regressors. Please see the following topic for more information:
XTDPDQML: new Stata command for quasi-maximum likelihood estimation of linear dynamic panel models

The QML estimator underlying the xtdpdqml command is only one possible approach to tackle the bias of the OLS estimator. Others include bias-corrected estimators (see for example the user-written command xtlsdvc), GMM estimators (see for example the user-written command xtabond2), or full-information maximum likelihood / structural equation modelling (see for example the user-written command xtdpdml [note the missing q in the command name compared to my command]). This list is not exhaustive.

When the time dimension is large (and tends to infinity), OLS estimation can be consistent. In such a situation, mean-group or pooled mean-group estimation (see for example the user-written command xtpmg) might be appropriate. This depends very much on your particular context but should not be further discussed in this topic here. If you have any follow-up query about these other estimators, please post it in existing Statalist topics dealing with these commands or start a new topic. Other people might be more able to advise on them. As a first step, I suggest that you make yourself familiar with the literature in particular in your area of research to find out which estimators are used by others in similar situations and what are the pros and cons of these estimators.

[Disclaimer: I am not associated with any of these commands other than ardl and xtdpdqml. Please employ a Stata, Statalist, or google search to find out more about them.]

[Muhammad Bah]

Following your advice Sebastian, i used the minlag function to coax out coefficients for my variable. However, i noticed that my LR estimates are reported as a lag for my variables. Can it be used to interpret long run estimates?

[Sebastian Kripfganz]

Yes, it can. Please see the remarks section "Long-run coefficients expressed in time t or t-1" in the ardl help file.

[Muhammad Bah]

Thanks Sebastian, appreciate your help

[Georg Neuschaeffer]

Hey all,

regarding the 5 cases presented by Pesaran et al. (2001) I have difficulties to to select the right one. When no constant or time trend is included it is clear, but I could not find a reliable source which case (restricted intercept and/or time trend) should be preferred. I checked the sources given in the ARDL command, but they only help partially. Does anybody have a "rule of thumb" or a source in which it is explained how to distinguish between the restricted and the unrestricted cases with regard to the interpretation of the results? I could not find any empirical paper yet in which this issue is further discussed.

I am thankful for any help.

[iftikhar yasin]

Sir Sebastian Kripfganz,

I've an issue in running ARDL in STATA , please help me.

As soon as I use " ec " option in ARDL in STATA SE , I receive an error

"Maximum number of iterations exceeded" r(498).

Please help me what to do now ????

I've 9 variables and about 35 observations, and using STATA SE.

Regards

[Sebastian Kripfganz]

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.

[Jingyang liu]

@ Sebastian,
Hi, I am using ARDL to do forecast vis Stata. I confront some problems. Could you please help me tackle it? Thanks in advance.

Here is my command code

ardl lrcredit lrgdp lt_re net_bank_ro if qtr>tq(2001Q1), ec aic maxlag(2,2,2,2) regstore(ardl_res)
estimates store reg_res
estimates restore ardl_res
forecast creat creditardl, replace
forecast estimates creditardl
forecast solve, prefix(ars_) begin(tq(2002Q2)) static


. forecast estimates creditardl
estimation result creditardl not found
Could not restore estimation result creditardl. Use estimates dir to list results stored in memory. If the
estimation results are saved on disk, use forecast estimates using along with the name of a file containing
saved estimation results.

when I change the estimates to reg_res

. forecast estimates reg_res
option names() required
Because the dependent variable specified with ardl included time-series operators, you must specify an
alternative name in the names() option of forecast estimates. ardl reports 1 dependent variable, so you must
specify 1 name in names().

It's my first time to use ARDL and forecast, maybe it is a stupid question, but I am looking forward to your reply.

JY

[Sebastian Kripfganz]

It seems to me that you are specifying the wrong name with forecast estimates. It should be the name that you have specified with the regstore() option of ardl:

forecast estimates ardl_res

[James Rossi]

I'm trying to examine the effects of various industries (by two digit NAICS classification with a few aggregations measured by GDP) and personal income on several different socioeconomic indicators (e.g. voter turn-out, crime rates, volunteerism, charitable giving, patents, etc.). I have state-level observations for the contiguous U.S. states (N=48) with different time lengths depending on the independent variable (generally T between 8 to 14). Obviously, I plan on running a separate model for each independent variable.

So as a rough estimate of my model, think something like this:
Y_i,t = B Agr_i,t + B Manuf_i,t+ ... + B Inc_i,t + ... B Agr_i,t-p + B Manuf_i,t-p + ... + B Inc_i,t-p +Y_i,t-p + e_i,t
Where i is the i^th observation (i.e. state), t is the t^th year, and p is the maximum lag length. Some specifications may also include dummy variables to account for seasonal trends (e.g. campaign spending would require one).

Can I estimate this model using ARDL? Do I need to include time and/or state dummies (or, more importantly, should I or should I not)? Do I need to address any potential collinearity issues in the explanatory variables before running ARDL?

As a sidenote, am I better using the QML version of the ARDL estimator?

I want to use the outputs of these regressions to help justify the linking of certain industries and the household sector to the production of different forms of capital (e.g. human, social, cultural, political, etc.) in a dynamic social accounting matrix.

[Sebastian Kripfganz]

No, you cannot estimate this model with the ardl command. ardl is for a single time series while you want to estimate a panel model. See my comment #80 above, in particular in the context that your time dimension is small.

If you would like to use my QML estimator for dynamic panel models, keep in mind that it only allows for one lag of the dependent variable (instead of p), but given your small time dimension you need to be restrictive regarding the choice of p in any case.

In general, it is advisable to include time effects and state effects (fixed or random effects). Note that you cannot include both time dummies and other dummy variables for seasonal trends together (if they affect all states jointly) because of perfect collinearity.