Interpretation of ARDL in Stata

[Ujjwal]

Hi, I was trying to use ARDL estimation in Stata with the command,

ardl index lara, lags(2) ec exog(adr) btest

where I defined two endogenous and one variable exogenous. The model shows a long run cointegration as bound test F statistics is higher than the critical value. My first question is how I can get the error correction rate through Stata? My second question is, what the short run coefficients mean? Can we interpret these coefficients like simple OLS coefficients? My third question is, should we also interpret the coefficient of exogenous variable in the same way as OLS?

[Sebastian Kripfganz]

Some comments and answers:

1) You are saying that you "defined two endogenous" variables. That is not quite true. The variable index is your dependent variable. The variable lara is assumed to be a (weakly) exogenous variable as is the variable adr specified with the exog() option. The exog() option has the effect that adr enters the short-run relationship contemporaneously without further lags and is excluded from the long-run relationship. In fact, the following two specifications yield exactly the same ARDL representation with identical coefficients:

ardl index lara, lags(2) exog(adr)
ardl index lara adr, lags(2 2 0)

Yet, if you compare the error-correction representations, adr appears in the first case only in the short-run relationship and in the second case only in the long-run relationship:

ardl index lara, lags(2) exog(adr) ec
ardl index lara adr, lags(2 2 0) ec

As you can see, this does not affect the other coefficients. It is merely an "accounting" issue of where to put the variable in the error-correction output because those coefficients are functions of the underlying ARDL estimates which are the same for both specifications.

2) The "error correction rate", also named speed-of-adjustment coefficient, is given by the first coefficient in the ec output labelled ADJ.

3) The interpretation of the short-run coefficients is as in any other linear model. They are ceteris-paribus effects and inference can be based on the usual OLS standard errors and test statistics.

4) Regarding your last question, see my point 1). The variables specified in exog() enter only the short-run relationship and those coefficients have the usual interpretation, see point 3).

5) Please also see the following Statalist topic on ARDL estimation: ARDL in Stata

[Ujjwal]

Thanks Sebastian

[Ngozi ADELEYE]

Some comments and answers:

1) You are saying that you "defined two endogenous" variables. That is not quite true. The variable index is your dependent variable. The variable lara is assumed to be a (weakly) exogenous variable as is the variable adr specified with the exog() option. The exog() option has the effect that adr enters the short-run relationship contemporaneously without further lags and is excluded from the long-run relationship. In fact, the following two specifications yield exactly the same ARDL representation with identical coefficients:

ardl index lara, lags(2) exog(adr)
ardl index lara adr, lags(2 2 0)

Yet, if you compare the error-correction representations, adr appears in the first case only in the short-run relationship and in the second case only in the long-run relationship:

ardl index lara, lags(2) exog(adr) ec
ardl index lara adr, lags(2 2 0) ec

As you can see, this does not affect the other coefficients. It is merely an "accounting" issue of where to put the variable in the error-correction output because those coefficients are functions of the underlying ARDL estimates which are the same for both specifications.

2) The "error correction rate", also named speed-of-adjustment coefficient, is given by the first coefficient in the ec output labelled ADJ.

3) The interpretation of the short-run coefficients is as in any other linear model. They are ceteris-paribus effects and inference can be based on the usual OLS standard errors and test statistics.

4) Regarding your last question, see my point 1). The variables specified in exog() enter only the short-run relationship and those coefficients have the usual interpretation, see point 3).

5) Please also see the following Statalist topic on ARDL estimation: ARDL in Stata

Hi Sebastian,
Thanks for being an amazing online tutor. I've followed your responses on queries relating to ARDL application and interpretation, downloaded your Kripfangz & Schneider (2016) and I must say that you have simplified learning at best...I am not there yet, but I am definitely getting better and gaining more confidence on the ARDL model

However, I have an issue: I use Stata 13 and I have 4 variables listed thus: lndcps I(1) , rir I(0), lnfsd I(1) and gdppcgr I(0)....and I used this code:

ardl lndcps rir, exog(lnfsd gdppcgr) maxlags(2) aic

....which does not indicate the different levels of order of integration of the variable. Then I tried to specify each variable given their respective order of integration as thus:

ardl d.dcps rir, exog(d.lnfsd gdppcgr) maxlags(2) aic

...and I got this error message:

factor variables and time-series operators not allowed
r(101);

Is Stata saying that there is no need to indicate the order of integration? and is the first specification okay? Kindly advice....thank you!

[Sebastian Kripfganz]

I am happy to hear that you find the ardl command useful.

The ardl command (currently) does not allow time-series operators such as "d." This has more a technical than an econometric reason.

That said, there is indeed no need to specify any order of integration, i.e. to take differences of I(1) variables. Whether your first specification is okay or not depends mainly on your underlying economic theory that you want to analyze and is hard to answer in general.

[Cayley Gint]

Some comments and answers:

1) You are saying that you "defined two endogenous" variables. That is not quite true. The variable index is your dependent variable. The variable lara is assumed to be a (weakly) exogenous variable as is the variable adr specified with the exog() option. The exog() option has the effect that adr enters the short-run relationship contemporaneously without further lags and is excluded from the long-run relationship. In fact, the following two specifications yield exactly the same ARDL representation with identical coefficients:

ardl index lara, lags(2) exog(adr)
ardl index lara adr, lags(2 2 0)

Yet, if you compare the error-correction representations, adr appears in the first case only in the short-run relationship and in the second case only in the long-run relationship:

ardl index lara, lags(2) exog(adr) ec
ardl index lara adr, lags(2 2 0) ec

As you can see, this does not affect the other coefficients. It is merely an "accounting" issue of where to put the variable in the error-correction output because those coefficients are functions of the underlying ARDL estimates which are the same for both specifications.

2) The "error correction rate", also named speed-of-adjustment coefficient, is given by the first coefficient in the ec output labelled ADJ.

3) The interpretation of the short-run coefficients is as in any other linear model. They are ceteris-paribus effects and inference can be based on the usual OLS standard errors and test statistics.

4) Regarding your last question, see my point 1). The variables specified in exog() enter only the short-run relationship and those coefficients have the usual interpretation, see point 3).

5) Please also see the following Statalist topic on ARDL estimation: ARDL in Stata

Hi Sebastian. I have been reading about ARDL but I am confused with what the ADJ gives and the range it should be in? Also, how would I interpret the actual relationship between my variables? As GDP increase by 1% and then I don't know where to look for the actual result?