ARDL ECM Interpretation

[Munkhtuul Gantumur]

Hi, I have been a little confused about interpreting my results from "ardl" command and "ardl, ec" command.

Could anyone please help me with answering these questions?

1. Prior to the bound test, I am running the command "ardl [indep.var] [dep.vars]" and I am getting coefficients for the variables under different lags. I was wondering whether these coefficients are the ones I am getting from the regression equation on Slide 5 from your presentation file (here)? If so, could you please tell me if it is correct to just interpret them as I would interpret normal regression results?


2. If the above is correct, are the long-run and short-run coefficients I get from "ardl, ec" command is the coefficients from the regression equation in slide 12? What is the difference between the coefficients from Question 1 and coefficients from ARDL with EC?

3. How do I explain it if the lagged terms of the same variables have different signs? For example, for variable x, lag 1 is positive and lag 2 is negative etc.

4. I am running my error correction with the command "ardl, ec1" because I am losing two of my coefficients in the short run when I use ec. Could you please help me with how I should interpret my short-run results with ec1 with the adjustment term? I have seen a different post on a similar question, but I am still a little bit confused.

I would highly appreciate it if anyone could answer my questions.

Kind Regards,
Munkhtuul

[Justin Niakamal]

1. Prior to the bound test, I am running the command "ardl [indep.var] [dep.vars]" and I am getting coefficients for the variables under different lags. I was wondering whether these coefficients are the ones I am getting from the regression equation on Slide 5 from your presentation file (here)? If so, could you please tell me if it is correct to just interpret them as I would interpret normal regression results?

Yes. Just a clarifying point, you have it backwards here. It’s ardl dep.var [indep.vars].

2. If the above is correct, are the long-run and short-run coefficients I get from "ardl, ec" command is the coefficients from the regression equation in slide 12? What is the difference between the coefficients from Question 1 and coefficients from ARDL with EC?

These are alternate reparameterizations in EC form. There are two forms (option ec and ec1). See slides 13-14 for example output(s).

3. How do I explain it if the lagged terms of the same variables have different signs? For example, for variable x, lag 1 is positive and lag 2 is negative etc.

It’s difficult to interpret the individual coefficients. I’ve seen authors use a bit of algebra to make sense of lagged variables with different signs. The focus is typically the error-correction term.

4. I am running my error correction with the command "ardl, ec1" because I am losing two of my coefficients in the short run when I use ec. Could you please help me with how I should interpret my short-run results with ec1 with the adjustment term? I have seen a different post on a similar question, but I am still a little bit confused.

The error-correction term implies that about X.X% of any movements into disequilibrium are corrected within one period.

[Munkhtuul Gantumur]

Hello, thank you very much for your help Justin Niakamal, I have just two more questions. Your prompt reply would be greatly appreciated.

In my paper, I am trying to include both short-run impacts and long-run impacts of the regressors on the dependent variable. I get the long-run coefficients from "ardl ec" and interpreting them as I would interpret results from a normal regression. However, I am a little confused about how to report my results in the short run.

1. When interpreting my results on the short-run relationship, should I rely on results in the "ardl" command or "ardl ec" command? I can see that the quantity for the highest lag is the same but have a different sign, positive on "ardl" and negative on "ardl ec".

2. Also since you said it is difficult to interpret individual lagged coefficients on the same variable, how I should make my conclusion on the overall effect of variable X on Y in the short run?
For example, on variable X, the appropriate lag number is 4 and the results on the "ardl ec" shows results for LD, L2D, L3D. Is it correct to just rely on the coefficient of the highest lag, L3D?

[Justin Niakamal]

Regarding #1, take a look at page 16 of Sebastian Kripfganz's presentation (link below). As for #2, I can't really give any advice without seeing the actual output. I'm sorry but I don't understand what you mean by relying on the coefficient of the highest lag.

http://repec.org/usug2018/uk18_Kripfganz.pdf

[Doreen Dai]

Justin Niakamal

Many thanks, Justin. Your answer does help a lot for new learners like me. I am exploring how to explain the short-term impacts, although our primary focus often lies on the error correction term and long-term effects. In the following, I attached an example examining the influence of tweets on Bitcoin returns on the daily frequency. Interpreting their lagged coefficients presents a challenge. I try to explain the short-term impact by examining the trend from t-2 to t, where coefficients transition from positive to negative. However, I am unsure if this approach is the most effective.

I have observed that some studies report short-term coefficients without detailing their calculation methods and omitting time subscripts. One possible explanation might be the aggregation of these coefficients in ARDL-ECM models to study their cumulative effect, but there is no clear documentation in the existing literature to support this technique.

If possible, could you kindly offer any suggestions? Many thanks.


ARDL(2,3,3,2,2,4) regression

Sample: 5 thru 861 Number of obs = 857
R-squared = 0.3714
Adj R-squared = 0.3556
Log likelihood = 1604.4523 Root MSE = 0.0377

------------------------------------------------------------------------------------------
D.lnprice_BTC | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------------------+----------------------------------------------------------------
ADJ |
lnprice_BTC |
L1. | -.0381123 .0117203 -3.25 0.001 -.0611169 -.0151076
-------------------------+----------------------------------------------------------------
LR |
lntweets | .2038901 .0869165 2.35 0.019 .0332896 .3744907
lnCPT | .4465655 .127368 3.51 0.000 .1965663 .6965646
lnCNUS | -3.046907 2.297881 -1.33 0.185 -7.557208 1.463395
lnNasdaq | 1.122732 .4804514 2.34 0.020 .1796972 2.065766
volatility_OHLC_percen~e | -.3853551 .197171 -1.95 0.051 -.7723641 .0016539
-------------------------+----------------------------------------------------------------
SR |
lnprice_BTC |
LD. | -.15722 .0314823 -4.99 0.000 -.2190137 -.0954263
|
lntweets |
D1. | -.0002491 .0072514 -0.03 0.973 -.0144822 .0139841
LD. | .0158885 .0072153 2.20 0.028 .0017263 .0300508
L2D. | .015567 .0069769 2.23 0.026 .0018726 .0292614
|

[Justin Niakamal]

I highly recommend Sebastian Kripfganz 's Stata Journal article on ardl (he and Daniel Schneider authored the command). It has a detailed example that conveniently uses Bitcoin.