[Sebastian Kripfganz]

I could not replicate the problem with an artificial data set of the same dimensions. There seems to be an idiosyncratic problem with your data set. Would it be possible to share your data set with us (or any subset of the data set that can be used to replicate the problem)?

[Franz Langmann]

Hi Sebastian,

Sorry, but I have one additional question. I have an ARDL with 11 endogenous variables and 3 exogenous variables with a sample size of around 4000 daily observations. I predefined the optimal number of lags already. I estimate the model as follows

tsset ORDER, daily
ardl Y X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11, trendvar(ORDER) exog(X12 X13 X14) ec lags(2,3,3,0,0,0,0,0,0,0,0,0)

When running the model without *ec*, everything works smoothly. However, when applying error correction parametrization, I receive the following error:

Maximum number of iterations exceeded

As I found out, this error arises from the *nlcom* command, which you use for the ec model.

Is it possible to increase the number of iterations? What else can I do to make the command running?

Thanks for your help!

[Sebastian Kripfganz]

After the newey command, you can obtain the long-run coefficients with the corresponding delta-method standard errors by using the nlcom postestimation command. The respective formulae differ depending on whether you have used the level representation or the EC representation of ardl:

. webuse lutkepohl2

. ardl ln_inv ln_inc ln_consump, regstore(ardl)
. estimates restore ardl
. local cmdline `"`e(cmdline)'"'
. gettoken cmd cmdline : cmdline
. newey `cmdline' lag(1)
. nlcom (_b[ln_inc] / (1 - _b[L.ln_inv])) ((_b[ln_consump] + _b[L.ln_consump] + _b[L2.ln_consump]) / (1 - _b[L.ln_inv]))

. ardl ln_inv ln_inc ln_consump, ec regstore(ardl_ec)
. estimates restore ardl_ec
. local cmdline `"`e(cmdline)'"'
. gettoken cmd cmdline : cmdline
. newey `cmdline' lag(1)
. nlcom (_b[ln_inc] / (- _b[L.ln_inv])) (_b[ln_consump] / (- _b[L.ln_inv]))

[Franz Langmann]

Hi Sebastian,

Regarding the application of Newey-West, I tried your code:

webuse lutkepohl2
ardl ln_inv ln_inc ln_consump, regstore(ardl)
estimates restore ardl
local cmdline `"`e(cmdline)'"'
gettoken cmd cmdline : cmdline
newey `cmdline' lag(1)

However, I recognized that when I apply this on the ec regression:

ardl ln_inv ln_inc ln_consump, ec regstore(ardl_ec)
estimates restore ardl_ec
local cmdline `"`e(cmdline)'"'
gettoken cmd cmdline : cmdline
newey `cmdline' lag(1)

...then also the coefficients (and not just the standard errors) of the long-run effects change after the application of the Newey-West errors. Do you know how to derive the NW errors also for the long-run coefficients?

Thanks for your help!

[Sebastian Kripfganz]

I received a request as a private message that I want to answer publicly because I believe others might benefit from the answers as well:¹

I read the original paper by Pesaran and Shin (1997, http://citeseerx.ist.psu.edu/viewdoc...=rep1&type=pdf) and compared it to the information about the ARDL Stata package. There are some important questions remaining and I would be very grateful if you could help me with these issues.

(1) In Eq. (1.1) in the PS (1997) paper, the authors define the ARDL with levels of y_t and y_t-i, however, the contemperanous effects of the explantory variables (x_t) and the first differences of the contemperanous and the lagged explanatories (last term with delta x). Where can I see this equation from PS (1997) in the Stata package? For me the Eq. (1.1) seems to be a mix of ARDL model and its error correction representation. However, y_t is not in differences, therefore it is not a fully error-correction representation? How does this fit to the Stata package?

(2) Do you usually estimate Eq. (1.1) in one step or do you first estimate the ARDL with lagged explanatories to identify long-run effects and then afterwards in the second stage estimate the error-correction model to derive the short-run effects? So is it just one equation to be estimated or two steps?

(3) When estimating the long-run and short-run effects, how to you derive the standard errors/t-statistics? Is it a specific method like delta method?

(4) I read other empirical papers applying Newey-West standard errors in ARDL models. Is this appropriate? Is it possible to do Newey-West in the Stata ARDL package?

1. Your observation is correct that equation (1.1) in PS (1997) is something in between the ARDL and EC representation. You cannot obtain this representation directly with our ardl command. The coefficients \(\phi_i\) of the lagged dependent variables and the coefficient \(\beta\) of the contemporaneous x-regressor are those that are reported in the standard levels output of ardl. The coefficients \(\beta_i^\ast\) of the contemporaneous and lagged differences of the x-regressors are those from the EC output of ardl with the option ec. Because there is a 1:1 mapping between the coefficients of these two output representations, you could separately collect the coefficients from these two representations and report them as if you had estimated equation (1.1) directly.
2. It is just one equation with all the coefficients estimated jointly.
3. Indeed, the standard errors are obtained with the usual delta method.
4. That might indeed be appropriate but it is not directly possible with the ardl command. But there is a workaround, illustrated with the following example:

. webuse lutkepohl2
. ardl ln_inv ln_inc ln_consump, regstore(ardl)
. estimates restore ardl
. local cmdline `"`e(cmdline)'"'
. gettoken cmd cmdline : cmdline
. newey `cmdline' lag(1)

--
¹ In general, please post your questions publicly here on Statalist. First, your questions might be of general interest. Second, it is much easier to respond to the questions here in the forum than by e-mail due to the possibility of easily posting code and estimation output.

[Dimas Bagas Herlambang]

I see, thank you Sebastian!

[Sebastian Kripfganz]

You cannot compute the F-statistic directly from the error-correction output. Please see slides 9 and 10 of my presentation at the 2016 Stata Conference in Chicago.

You can recover it from the ARDL representation (ardl without the ec1 option), e.g.

. webuse lutkepohl2
(Quarterly SA West German macro data, Bil DM, from Lutkepohl 1993 Table E.1)

. ardl ln_inv ln_inc, lags(2) ec1

ARDL regression
Model: ec

Sample: 1960q3 - 1982q4
Number of obs  = 90
Log likelihood = 158.62362
R-squared      = .13799034
Adj R-squared  = .08668024
Root MSE       = .04298403

------------------------------------------------------------------------------
    D.ln_inv |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
ADJ          |
      ln_inv |
         L1. |  -.1515065   .0624739    -2.43   0.017    -.2757427   -.0272702
-------------+----------------------------------------------------------------
LR           |
      ln_inc |
         L1. |   .8237427   .0599558    13.74   0.000      .704514    .9429713
-------------+----------------------------------------------------------------
SR           |
      ln_inv |
         LD. |  -.1362943   .1078979    -1.26   0.210     -.350861    .0782725
             |
      ln_inc |
         D1. |    .565835    .402307     1.41   0.163    -.2341965    1.365867
         LD. |    .655617   .3925048     1.67   0.099     -.124922    1.436156
             |
       _cons |   .0302675   .0666281     0.45   0.651    -.1022298    .1627648
------------------------------------------------------------------------------

. estat btest

Pesaran/Shin/Smith (2001) ARDL Bounds Test
H0: no levels relationship             F =  3.083
                                       t = -2.425
[some output omitted]

. ardl ln_inv ln_inc, lags(2)

ARDL regression
Model: level

Sample: 1960q3 - 1982q4
Number of obs  = 90
Log likelihood = 158.62362
R-squared      = .99160203
Adj R-squared  = .99110215
Root MSE       = .04298403

------------------------------------------------------------------------------
      ln_inv |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      ln_inv |
         L1. |   .7121993   .1083168     6.58   0.000     .4967993    .9275992
         L2. |   .1362943   .1078979     1.26   0.210    -.0782725     .350861
             |
      ln_inc |
         --. |    .565835    .402307     1.41   0.163    -.2341965    1.365867
         L1. |   .2145843   .5745405     0.37   0.710    -.9279526    1.357121
         L2. |   -.655617   .3925048    -1.67   0.099    -1.436156     .124922
             |
       _cons |   .0302675   .0666281     0.45   0.651    -.1022298    .1627648
------------------------------------------------------------------------------

. test (1 - L1.ln_inv - L2.ln_inv = 0) (ln_inc + L1.ln_inc + L2.ln_inc = 0)

 ( 1)  - L.ln_inv - L2.ln_inv = -1
 ( 2)  ln_inc + L.ln_inc + L2.ln_inc = 0

       F(  2,    84) =    3.08
            Prob > F =    0.0510

The p-value of the test command is of course invalid.

[Dimas Bagas Herlambang]

Sebastian,

I want to ask about F-test for PSS. I run ardl in ec1 mode, and got this result:

. ardl lr mrpos mrneg lnlipos lnlineg, ec1 fast lags(. . . . .) maxlags(6 6 6 6 6) maxcombs(15000)

ARDL regression
Model: ec

Sample:  2000m7 -  2017m2
Number of obs  = 200
Log likelihood = 122.64809
R-squared      = .51863377
Adj R-squared  = .50108396
Root MSE       = .13375199

------------------------------------------------------------------------------
        D.lr |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
ADJ          |
          lr |
         L1. |  -.0506548   .0122413    -4.14   0.000    -.0747994   -.0265101
-------------+----------------------------------------------------------------
LR           |
       mrpos |
         L1. |   .3373259   .0836383     4.03   0.000     .1723581    .5022938
             |
       mrneg |
         L1. |   .3748366   .0895931     4.18   0.000     .1981234    .5515498
             |
     lnlipos |
         L1. |  -1.291288   .3078728    -4.19   0.000    -1.898535   -.6840407
             |
     lnlineg |
         L1. |  -1.295418   .3102576    -4.18   0.000    -1.907368   -.6834666
-------------+----------------------------------------------------------------
SR           |
          lr |
         LD. |   .4615063   .0709036     6.51   0.000     .3216562    .6013564
        L2D. |   .2238202   .0698491     3.20   0.002     .0860501    .3615902
             |
       mrpos |
         D1. |   .0170872   .0054116     3.16   0.002     .0064134    .0277609
             |
       mrneg |
         D1. |   .0189873   .0061479     3.09   0.002     .0068613    .0311133
             |
     lnlipos |
         D1. |  -.0654099   .0237949    -2.75   0.007    -.1123428   -.0184769
             |
     lnlineg |
         D1. |  -.0656191   .0240508    -2.73   0.007    -.1130568   -.0181813
             |
       _cons |    1.37524   .4237449     3.25   0.001     .5394466    2.211033
------------------------------------------------------------------------------

after that, I try using estat btest and test to compare the PSS F-stat, and the results are:

. estat btest

Pesaran/Shin/Smith (2001) ARDL Bounds Test
H0: no levels relationship             F =  3.620
                                       t = -4.138


. test L1.lr = L1.mrpos = L1.mrneg = L1.lnlipos = L1.lnlineg = 0

 ( 1)  [ADJ]L.lr - [LR]L.mrpos = 0
 ( 2)  [ADJ]L.lr - [LR]L.mrneg = 0
 ( 3)  [ADJ]L.lr - [LR]L.lnlipos = 0
 ( 4)  [ADJ]L.lr - [LR]L.lnlineg = 0
 ( 5)  [ADJ]L.lr = 0

       F(  5,   192) =   30.74
            Prob > F =    0.0000

Does it meant to be different? and which one represent the true F-stat according to PSS?

Thank you

[Daniel Schneider]

The previous post depends heavily on a Word attachment which is discouraged in Section "12.5 Posting attachments: please don't..." in the Statalist FAQ. Since it would be difficult to follow the discussion, I have responded to the inquiry in a private email.

[Vernon Mila]

Some questions (please see attachment for full question with images of outputs included)>>

1. Here is the data we’re looking to run ARDL on – LunitedStates is the dependent variable and LUnitedStatesPS is independent variable
   1. Given below plot would we run the following specs for ARDL?
      1. ardl LUnitedStates LUnitedStatesPS, lags(3 1) ec [constant] trendvar(LUnitedStates)
   2. When I run above I get below error –
      1. Trend variable must be collinear with the time variable.
      2. I maybe mis-specifying above – how may I correctly specify this model
2. How do I tell the ardl to explicitly include contemeraneous terms in the independent variables (X’s) or is this always a default (i.e. LAG 0)?
   1. For eg. ardl LUnitedStates LUnitedStatesPS, lags(3 1), automatically includes lag 0
   2. When I am modeeling ec form, ardl LUnitedStates LUnitedStatesPS, lags(3 1) ec, only has the contemperanous difference in the “short run” equation due to inclusion of only Lag(1)
   3. See outputs below – should I worry if PART (b) is not including the contemperaneous term?

[NIP NIP]

Thanks!

[Sebastian Kripfganz]

It is not really possible to give a general answer to this question. Please also see my comments #269 and #273 above.

[Zuhura Anne]

Thank you so much for the responses. The trend and dummy variables have been so helpful. I have parameter stability and all other diagnostic tests are satisfied. However, normality is not upheld when I use this syntax:

mvtest normality variable

Is this something to worry about or since most of the properties have been satisfied, then I can continue using the model?

[Sebastian Kripfganz]

Dear both,
If the breaks are known due to some identifiable events, you can model them with dummy variables that shift the intercept for some time period. By interacting these dummies with the regressors, you can model breaks in the short-run coefficients. Similarly, you can interact the dummy variables with the trend variable to allow for different trends in different periods. It really depends on the type of break. Another possibility could be to split the time series if you have enough observations. I could already be sufficient to remove a few observations at the beginning or end (for example, use only observations prior to the financial crisis) and see if this gives you parameter stability.

A temporary break could be a shift that lasts for a couple of time points only (some crisis period) but afterwards the time series' behave in the same way as before this period.

I am not an expert on structural breaks / parameter stability and cannot provide more specific help on how to identify them or how to deal with them.

[Anne Wanyonyi]

If you have structural breaks, you might want to directly model them

Kindly what do you mean by this?
How can I distinguish between a permanent and temporary break in the series?