[Marco Giansoldati]

Dear sebastian,

I am extremely thankful for your detailed answer.

I will try to implement it and I will kee you timely posted.

Many many thanks.

Marco

[Marco Giansoldati]

Dear Sebastian,

I followed your indications and got good results with no serial correlation in the ardl exploiting the aic lag selection, for two of the three countries I am looking at.

Yet, for one of the countries there is something tricky. I noticed a significant speed of adjustment which lies between 0 and -1. In addition most of the coefficients in the long-run are significant. Here are the results.

. ardl mgsv rmp nc itv xgsv LVix if ifscode==941, ec1 lags(1 3 0 4 0 3) regstore(ardl2)

ARDL regression
Model: ec

Sample: 1996q1 - 2015q4 
Number of obs  = 80
Log likelihood = 174.74148
R-squared      = .79215454
Adj R-squared  = .73936839
Root MSE       = .03069176

------------------------------------------------------------------------------
      D.mgsv |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
ADJ          |
        mgsv |
         L1. |  -.4433418   .0896522    -4.95   0.000    -.6224974   -.2641863
-------------+----------------------------------------------------------------
LR           |
         rmp |
         L1. |  -1.052398   .4343518    -2.42   0.018    -1.920381   -.1844149
             |
          nc |
         L1. |     1.3357   .2414046     5.53   0.000     .8532912    1.818108
             |
         itv |
         L1. |  -.1411704   .1032663    -1.37   0.176    -.3475317    .0651909
             |
        xgsv |
         L1. |   .9868565   .2768151     3.57   0.001     .4336856    1.540027
             |
        LVix |
         L1. |   .0316129   .0463461     0.68   0.498    -.0610025    .1242283
-------------+----------------------------------------------------------------
SR           |
         rmp |
         D1. |  -.6759413   .2137826    -3.16   0.002    -1.103152   -.2487309
         LD. |   .1832689   .1789283     1.02   0.310    -.1742908    .5408286
        L2D. |    .418125   .1975192     2.12   0.038     .0234144    .8128357
             |
          nc |
         D1. |   .5921716   .1287776     4.60   0.000     .3348301    .8495131
             |
         itv |
         D1. |   .2427257   .0502375     4.83   0.000     .1423341    .3431173
         LD. |   .1387496   .0494968     2.80   0.007     .0398381    .2376612
        L2D. |    .069666    .049202     1.42   0.162    -.0286565    .1679884
        L3D. |   .0835589   .0447848     1.87   0.067    -.0059364    .1730542
             |
        xgsv |
         D1. |   .4375148   .0837006     5.23   0.000     .2702524    .6047771
             |
        LVix |
         D1. |    .001864   .0181743     0.10   0.919    -.0344544    .0381824
         LD. |  -.0593211   .0213976    -2.77   0.007    -.1020808   -.0165614
        L2D. |  -.0541236   .0190216    -2.85   0.006    -.0921353   -.0161119
             |
       _cons |  -1.954917   .3880763    -5.04   0.000    -2.730425   -1.179408
------------------------------------------------------------------------------

. 
end of do-file

Yet, there is an issue with the result of the -egranger- command. It indicates the absence of cointegration, even if I increase the lags to four or more. This is reported here below.

. egranger mgsv rmp nc itv xgsv if ifscode==941
Replacing variable _egresid...

Engle-Granger test for cointegration                  N (1st step)  =       84
                                                      N (test)      =       83
------------------------------------------------------------------------------
                  Test         1% Critical       5% Critical      10% Critical
               Statistic           Value             Value             Value
------------------------------------------------------------------------------
 Z(t)             -3.890            -5.228            -4.586            -4.262

Critical values from MacKinnon (1990, 2010)

or here:

. egranger mgsv rmp nc itv xgsv if ifscode==941, regress
Replacing variable _egresid...

Engle-Granger test for cointegration                  N (1st step)  =       84
                                                      N (test)      =       83
------------------------------------------------------------------------------
                  Test         1% Critical       5% Critical      10% Critical
               Statistic           Value             Value             Value
------------------------------------------------------------------------------
 Z(t)             -3.890            -5.228            -4.586            -4.262

Critical values from MacKinnon (1990, 2010)
------------------------------------------------------------------------------
Engle-Granger 1st-step regression
------------------------------------------------------------------------------
        mgsv |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         rmp |  -.4261249   .1679457    -2.54   0.013    -.7604125   -.0918372
          nc |   .7540739   .1180109     6.39   0.000     .5191791    .9889686
         itv |   .1368718   .0415571     3.29   0.001     .0541545    .2195891
        xgsv |   .6422247   .1119674     5.74   0.000     .4193591    .8650903
       _cons |  -1.993745   .4072917    -4.90   0.000    -2.804439   -1.183051
------------------------------------------------------------------------------
Engle-Granger test regression
------------------------------------------------------------------------------
  D._egresid |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    _egresid |
         L1. |  -.3157309   .0811657    -3.89   0.000    -.4771953   -.1542664
------------------------------------------------------------------------------

. 
end of do-file

I was wondering if a speed-of-adjustment coefficient different from zero may imply that there is cointegrating relationship among the dependent variable and the independent variables. Maybe I am wrong but I was puzzled by the results of the -egranger- command. Do you have any suggestions in this respect?

Many thanks

Marco

[Sebastian Kripfganz]

The speed-of-adjustment coefficient being different from zero is a necessary but not sufficient condition for a cointegrating relationship. There is nothing that guarantees that the Engle-Granger test and the Pesaran-Shin-Smith test will always yield the same conclusion.

[Marco Giansoldati]

Dear sebastian,

Thank you very much for your kind reply.

Is it thus correct to infer that if the Engle-Granger test does not show cointegration, but the Pesaran-Shin-Smith indicates the presence of long-term association, the series present a weak form of long-term relationship? I hope this does not seem too bizarre.

Thanks

[Sebastian Kripfganz]

Not sure what you mean by "weak form". I would say, there is conflicting evidence and a clear conclusion cannot be drawn.

[Marco Giansoldati]

Thank you very much sebastian.

[NIP NIP]

Why "regress" output and "ardl" output are not exactly the same?
I used the ardl specification, for instance, (2,0,2) and I ran normal least square regression with the excatly the same lags for the dependent and independent variables, but the results are not exactly the same.

[Sebastian Kripfganz]

Why "regress" output and "ardl" output are not exactly the same?
I used the ardl specification, for instance, (2,0,2) and I ran normal least square regression with the excatly the same lags for the dependent and independent variables, but the results are not exactly the same.

Above question crossposted here: Question regarding ARDL adon.

The ardl command silently estimates many models with different lag combinations and picks the one with the smallest value of the AIC. To ensure comparability of the models, all of them are estimated based on the sample. This sample is determined by the largest lag order which is 4 by default.

The regress command estimates the model as specified, in your case with a maximum of 2 lags. It thus uses 2 more observations. Because the samples do not coincide, the estimation results consequently differ from ardl.

You can obtain identical results by restricting the sample in the following way (based on the help file example):

. webuse lutkepohl2
. ardl ln_inv ln_inc ln_consump
. regress L(0/1).ln_inv ln_inc L(0/2).ln_consump if e(sample)

[Mahana Noorma]

Dear Sebastian,
Dear all,

I have a theoretical question regarding the bounds testing approach developed by Pesaran et al. (2001). It is related to the determination of the optimal lag length when the bounds test indicates that there is no long-run relationship between the variables.

According to Giles’s blog (2013: http://davegiles.blogspot.ch/2013/06...nds-tests.html), we start the bounds testing procedure with the following equation
Δy_t = β₀ + Σ β_iΔy_t-i + Σγ_jΔx_1t-j + Σδ_kΔx_2t-k + θ₀y_t-1 + θ₁x_1t-1 + θ₂ x_2t-1 + e_t (Unconstrained ECM)
Source: http://davegiles.blogspot.ch/2013/06...nds-tests.html

The appropriate lag structure of this equation is determined by means of one information criteria such as AIC or BIC. If this model is stable and that there is no serial autocorrelation of the errors, the bounds test can be performed. If the latter indicates that there is a long-run relationship between the variables, the final equation would be:

Δy_t = β₀ + Σ β_iΔy_t-i + Σγ_jΔx_1t-j + Σδ_kΔx_2t-k + φz_t-1 + e_t (equ : fin1)
where z_t is the error correction term.

On the other hand, if the bounds test indicates that there is no long-run relationship between the variables, the final equation would be:
Δy_t = β₀ + Σ β_iΔy_t-i + Σγ_jΔx_1t-j + Σδ_kΔx_2t-k + e_t (equ : fin2)

My question is the following: if the bounds tests indicates that there is no long-run relationship between the variables, would the optimal lag structure be the same as the one determined at the beginning of the bounds testing procedure or is it necessary to determine it once again directly from the equation (fin2)?

I kindly thank you for your help and your commitment.

Best regards

[Sebastian Kripfganz]

Your description of the procedure is very accurate. In principle, there is no need to adjust the lag structure when you remove the error correction term from the model (assuming that the result of the bounds test is correct). In practice, however, it can happen that for a given sample the AIC or BIC indicate a different lag order for the ARDL model in first differences (equ:fin2). It is an interesting question and spontaneously I do not have a clear opinion on whether I would reestimate the model with a different lag order.

In any case, to be comparable, you should reduce the maximum lag order that you are using in the model selection by one when you compute the AIC / BIC for the first-differenced ARDL model compared to the ARDL model in levels. Say, maxlag(4) for the ARDL model in levels would correspond to maxlag(3) for the ARDL model in first differences.

[Mahana Noorma]

Dear Sebastian,

Thank you very much for your quick reply and for your pieces of advice.

Kind regards

[Zuhura Anne]

Which syntax can I use in order to carry out parameter stability tests as a postestimation for ARDL?

Or how do I test for a structural break with unknown date?

[Anne Wanyonyi]

Hello,
Is it okay to continue with estimation when there is non-normality or my results will be biased?

Or how can I correct for non-normality?

[Sebastian Kripfganz]

Which syntax can I use in order to carry out parameter stability tests as a postestimation for ARDL?

Or how do I test for a structural break with unknown date?

Stata 15 has the new postestimation command sbcusum. It works after regress but does not work directly after ardl, but you can recover the underlying regress estimation results:

webuse lutkepohl2
ardl ln_inv ln_inc ln_consump, regstore(ardl)
estimates restore ardl
estat sbcusum

Hello,
Is it okay to continue with estimation when there is non-normality or my results will be biased?

Or how can I correct for non-normality?

For the estimation of the coefficients, non-normality of the errors usually is not much of a problem. You cannot use the t-distribution or F-distribution for finite-sample hypothesis tests in this case. If your sample size is large enough, hypothesis tests (for short-run coefficients) that have standard asymptotics can still be used. In contrast, the Pesaran et al. (2001) bounds test procedure for the existence of a long-run level relationship, implemented in estat btest after ardl, has non-standard asymptotics. Its critical values rely on the assumption of i.i.d. normally distributed errors.

There is no general approach to deal with non-normality. Sometimes, a log-transformation of some or all of your variables can help, in particular if you expect these variables to fluctuate around a balanced growth path.

[Zuhura Anne]

Thank you Sebastian for the response. Unfortunately, I am using stata 14 and I do not have access to stata 15. Which test can I use in this case? What was being used initially before the recent release of stata 15?

With stata 14, I get the error message

subcommand estat sbcusum is unrecognized