[Sebastian Kripfganz]

Yes, you can.

[Mustapha Immurana]

I am most grateful

[Mustapha Immurana]

Yes, you can.

Dear Sebastian,

''You can always run the ARDL model in levels no matter whether your variables are I(0), I(1), or a mixture of both. The ec and ec1 options are just reparameterizations of the ARDL model, another way of displaying the results, but the underlying estimation is the same as without these options.''

Please is the above statement the reason why you said even when the ardl is run with the ec1 or ec option and there is no co-integration we can still maintain the sr and lr results? If not please kindly provide me with the reasons.

Thanks so much for your time.

[Sebastian Kripfganz]

Yes, with the qualification that there are no long-run effects if your variables are I(1) but without co-integration.

[Mustapha Immurana]

Please what then will be the solution if there is no co-integration and the vars are mixed and not strictly I(1)?

[Sebastian Kripfganz]

If the speed-of-adjustment coefficient is not equal to zero (based on the t-test with asymptotic critical value bounds by Pesaran et al. (2001), see estat btest after ardl) and the corresponding long-run coefficients of the I(1) regressors are zero (otherwise this would be a contradiction to the claim that there is no cointegration), then the dependent variable is I(0) and there can be long-run effects from other I(0) variables.

[Mustapha Immurana]

Dear Sebastian,

The situations below are what I am encountering so please kindly check and see what can be done.

1. Please see the results below where lnsubisdies was stationary at both the levels and after first difference with all other remaining variables being stationary only after first difference and please make suggestions accordingly since the estat btest did not show the existence of co-integration.


ardl lngdp lnrevenueexpenditure lnsubsidies lnloansandadvances dummy, lags(. . . . 0) ec1 regstore(reg3av)

ARDL regression
Model: ec

Sample: 1975 - 2015
Number of obs = 41
Log likelihood = 93.995963
R-squared = .32610714
Adj R-squared = .20718487
Root MSE = .02683852

------------------------------------------------------------------------------
D.lngdp | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ADJ |
lngdp |
L1. | -.1355375 .0552442 -2.45 0.019 -.2478072 -.0232678
-------------+----------------------------------------------------------------
LR |
lnrevenuee~e |
L1. | .9376934 .1748956 5.36 0.000 .5822628 1.293124
|
lnsubsidies |
L1. | -.0063636 .1545198 -0.04 0.967 -.3203856 .3076584
|
lnloansand~s |
L1. | -.055389 .1027476 -0.54 0.593 -.2641972 .1534192
|
dummy |
L1. | .0850619 .1626433 0.52 0.604 -.245469 .4155927
-------------+----------------------------------------------------------------
SR |
lngdp |
LD. | .4202878 .1416326 2.97 0.005 .1324558 .7081198
|
lnrevenuee~e |
D1. | .1270926 .0651898 1.95 0.060 -.005389 .2595742
|
lnsubsidies |
D1. | -.0008625 .021089 -0.04 0.968 -.0437206 .0419956
|
lnloansand~s |
D1. | -.0075073 .0147952 -0.51 0.615 -.0375748 .0225602
|
dummy |
D1. | .0115291 .0221685 0.52 0.606 -.0335228 .0565809
|
_cons | .4470966 .1504409 2.97 0.005 .141364 .7528292
------------------------------------------------------------------------------

. estat btest

Pesaran/Shin/Smith (2001) ARDL Bounds Test
H0: no levels relationship F = 1.525
t = -2.453

Critical Values (0.1-0.01), F-statistic, Case 3

| [I_0] [I_1] | [I_0] [I_1] | [I_0] [I_1] | [I_0] [I_1]
| L_1 L_1 | L_05 L_05 | L_025 L_025 | L_01 L_01
------+----------------+----------------+----------------+---------------
k_4 | 2.45 3.52 | 2.86 4.01 | 3.25 4.49 | 3.74 5.06
accept if F < critical value for I(0) regressors
reject if F > critical value for I(1) regressors

Critical Values (0.1-0.01), t-statistic, Case 3

| [I_0] [I_1] | [I_0] [I_1] | [I_0] [I_1] | [I_0] [I_1]
| L_1 L_1 | L_05 L_05 | L_025 L_025 | L_01 L_01
------+----------------+----------------+----------------+---------------
k_4 | -2.57 -3.66 | -2.86 -3.99 | -3.13 -4.26 | -3.43 -4.60
accept if t > critical value for I(0) regressors
reject if t < critical value for I(1) regressors

k: # of non-deterministic regressors in long-run relationship
Critical values from Pesaran/Shin/Smith (2001)

2. Also Please see theexamples below where lnGDP (dep. var) and lngrofiscdfct were stationary at both the levels and after first difference with all other remaining variables being stationary only after first difference and please make suggestions accordingly since the estat btest did not show the existence of co-integration.


. ardl lnGDP lngrofiscdfct lngroprmrdfct lnrvnudfct dummy, lags(2 . . 3 0) ec1 regstore(obj5a)

ARDL regression
Model: ec

Sample: 1983 - 2015
Number of obs = 33
Log likelihood = 167.04464
R-squared = .78999092
Adj R-squared = .66398548
Root MSE = .00196845

------------------------------------------------------------------------------
D.lnGDP | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ADJ |
lnGDP |
L1. | -.0398259 .0302614 -1.32 0.203 -.1029501 .0232983
-------------+----------------------------------------------------------------
LR |
lngrofiscd~t |
L1. | .0719433 .0594311 1.21 0.240 -.0520279 .1959144
|
lngroprmrd~t |
L1. | -.0149252 .0127062 -1.17 0.254 -.0414299 .0115796
|
lnrvnudfct |
L1. | -.0093973 .050849 -0.18 0.855 -.1154664 .0966719
|
dummy |
L1. | .0367571 .0566491 0.65 0.524 -.0814109 .154925
-------------+----------------------------------------------------------------
SR |
lnGDP |
LD. | .4503183 .1627292 2.77 0.012 .1108711 .7897655
|
lngrofiscd~t |
D1. | .0167166 .0070456 2.37 0.028 .0020199 .0314134
LD. | .0062744 .003314 1.89 0.073 -.0006384 .0131872
L2D. | .0100202 .0028935 3.46 0.002 .0039845 .0160559
|
lngroprmrd~t |
D1. | -.0005944 .0006257 -0.95 0.353 -.0018995 .0007107
|
lnrvnudfct |
D1. | -.009855 .0038587 -2.55 0.019 -.0179041 -.001806
LD. | -.0028182 .0017471 -1.61 0.122 -.0064625 .0008261
L2D. | -.0044568 .001266 -3.52 0.002 -.0070977 -.0018159
|
dummy |
D1. | .0014639 .0016406 0.89 0.383 -.0019584 .0048862
|
_cons | .0777555 .0438411 1.77 0.091 -.0136955 .1692065
------------------------------------------------------------------------------

. estat btest

Pesaran/Shin/Smith (2001) ARDL Bounds Test
H0: no levels relationship F = 3.323
t = -1.316

Critical Values (0.1-0.01), F-statistic, Case 3

| [I_0] [I_1] | [I_0] [I_1] | [I_0] [I_1] | [I_0] [I_1]
| L_1 L_1 | L_05 L_05 | L_025 L_025 | L_01 L_01
------+----------------+----------------+----------------+---------------
k_4 | 2.45 3.52 | 2.86 4.01 | 3.25 4.49 | 3.74 5.06
accept if F < critical value for I(0) regressors
reject if F > critical value for I(1) regressors

Critical Values (0.1-0.01), t-statistic, Case 3

| [I_0] [I_1] | [I_0] [I_1] | [I_0] [I_1] | [I_0] [I_1]
| L_1 L_1 | L_05 L_05 | L_025 L_025 | L_01 L_01
------+----------------+----------------+----------------+---------------
k_4 | -2.57 -3.66 | -2.86 -3.99 | -3.13 -4.26 | -3.43 -4.60
accept if t > critical value for I(0) regressors
reject if t < critical value for I(1) regressors

k: # of non-deterministic regressors in long-run relationship
Critical values from Pesaran/Shin/Smith (2001)

3. In this third example lngdp (depvar) and lnntprmr_dfct were stationary at both the levels and after first difference with all other remaining variables being stationary only after first difference but there was no co-integration. Please what do you suggest?

. ardl lnGDP lnntfiscdfct lnntprmr_dfct lnrvnudfct dummy, lags(2 4 4 2 0) ec1 regstore(obj5b)

ARDL regression
Model: ec

Sample: 1982 - 2015
Number of obs = 34
Log likelihood = 170.40245
R-squared = .79608787
Adj R-squared = .60417057
Root MSE = .00227858

------------------------------------------------------------------------------
D.lnGDP | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ADJ |
lnGDP |
L1. | -.3778128 .1431732 -2.64 0.017 -.6798817 -.0757438
-------------+----------------------------------------------------------------
LR |
lnntfiscdfct |
L1. | .145113 .004913 29.54 0.000 .1347476 .1554784
|
lnntprmr_d~t |
L1. | -.0534484 .0058057 -9.21 0.000 -.0656973 -.0411994
|
lnrvnudfct |
L1. | -.0143404 .0044234 -3.24 0.005 -.0236729 -.0050079
|
dummy |
L1. | -.0004593 .0055216 -0.08 0.935 -.0121089 .0111904
-------------+----------------------------------------------------------------
SR |
lnGDP |
LD. | .785179 .1902565 4.13 0.001 .3837729 1.186585
|
lnntfiscdfct |
D1. | .0088769 .0085029 1.04 0.311 -.0090627 .0268165
LD. | -.0366148 .0130208 -2.81 0.012 -.0640863 -.0091432
L2D. | -.0082798 .0092129 -0.90 0.381 -.0277173 .0111578
L3D. | -.003322 .006488 -0.51 0.615 -.0170105 .0103664
|
lnntprmr_d~t |
D1. | -.0047031 .0028639 -1.64 0.119 -.0107454 .0013392
LD. | .0140574 .0050259 2.80 0.012 .0034536 .0246612
L2D. | .0051476 .0039065 1.32 0.205 -.0030944 .0133896
L3D. | .0024171 .0030758 0.79 0.443 -.0040723 .0089065
|
lnrvnudfct |
D1. | -.0002549 .0022499 -0.11 0.911 -.0050019 .004492
LD. | .0060727 .002081 2.92 0.010 .001682 .0104633
|
dummy |
D1. | -.0001735 .0021155 -0.08 0.936 -.0046369 .0042899
|
_cons | .6215836 .23034 2.70 0.015 .1356087 1.107559
------------------------------------------------------------------------------

. estat btest

Pesaran/Shin/Smith (2001) ARDL Bounds Test
H0: no levels relationship F = 2.086
t = -2.639

Critical Values (0.1-0.01), F-statistic, Case 3

| [I_0] [I_1] | [I_0] [I_1] | [I_0] [I_1] | [I_0] [I_1]
| L_1 L_1 | L_05 L_05 | L_025 L_025 | L_01 L_01
------+----------------+----------------+----------------+---------------
k_4 | 2.45 3.52 | 2.86 4.01 | 3.25 4.49 | 3.74 5.06
accept if F < critical value for I(0) regressors
reject if F > critical value for I(1) regressors

Critical Values (0.1-0.01), t-statistic, Case 3

| [I_0] [I_1] | [I_0] [I_1] | [I_0] [I_1] | [I_0] [I_1]
| L_1 L_1 | L_05 L_05 | L_025 L_025 | L_01 L_01
------+----------------+----------------+----------------+---------------
k_4 | -2.57 -3.66 | -2.86 -3.99 | -3.13 -4.26 | -3.43 -4.60
accept if t > critical value for I(0) regressors
reject if t < critical value for I(1) regressors

k: # of non-deterministic regressors in long-run relationship
Critical values from Pesaran/Shin/Smith (2001)

[Sebastian Kripfganz]

In all three cases, essentially you cannot reject the null hypothesis of no long-run relationship with the bounds testing procedure. There is nothing wrong with these regressions (provided that your choice of the lag orders is not too conservative). Maybe you want to add a time trend to you regression - see the option trendvar() of ardl - since macroeconomic variables often exhibit a trending behavior.

[Mustapha Immurana]

Dear Sebastian,

Thanks so much.

Please my issue has to do with if I am asked why did I still maintain the results since there was no cointegration, how do I defend that?.

[Sebastian Kripfganz]

The best defense is that the estimates are still consistent even if there is no cointegration. In addition, there is of course always the (small) chance that the bounds test incorrectly did not reject the null hypothesis even though it is not true. The ARDL / EC estimates are also robust to the latter situation.

[Mustapha Immurana]

Thanks so much

[Simon Suleiman]

Hello everyone, When I run ARDL model the error << r(9) "# of lag permutations (2500) exceeds setting of 'maxcombs' (500)>> appeared. What should I do ?

[Sebastian Kripfganz]

This error message tells you that you are trying to estimate a large number of models (more than 500) because you are allowing for large orders and probably have a relatively large number of exogenous variables. The error message is implemented as a device to encourage you to think again whether you really want to estimate such large models.

You can increase the allowed number of lag combinations by setting a higher number # with the option maxcombs(#). Depending on the size of your model, the estimations might take a long time. I would recommend in this case to combine this option with the options fast and dots.

Alternatively, you can reduce the actual number of lag combinations by pre-specifying fixed lag numbers for some variables with the lags(numlist) option or by restricting the maximum number of allowed lags for some (or all) variables with the maxlags(numlist) option.

For details about all of these options, please see the ardl help file.

[Simon Suleiman]

Thank you very much. I would like also to know whether it is possible to run nonlinear ARDL by using stata ?

[Abdul Rauf]

sebastian I tried this link net from "http://www.kripfganz.de/stata/" in my STATA-14 but i could not run it. what should i do???