NARDL model for asymmetric impact of Brent price and NBP price on UK CPI Help

[Conor Savill]

hello I am trying to build an NARDL model in Stata modelling the asymmetric impact Brent oil price and NBP natural gas price has on UK CPI and have been running into problems. I am using data monthly from September 2007 - May 2024.
I have been adding a natural log to the variables and they are lnCPI, lnBrent and lnNBP, I then use the ADF and PP tests and have established that all variables are stationary at I(1) so I am able to preform the bounds test.

to decompose the variables i use the commands:
gen D_lnBrent = D.lnBrent
gen D_lnBrent_pos = cond(D_lnBrent > 0, D_lnBrent, 0)
gen D_lnBrent_neg = cond(D_lnBrent < 0, D_lnBrent, 0)

the first command is how I decomposed variables I did the same for the other two and the bottom two commands is how I decomposed lnBrent and lnNBP into positive and negative changes for asymmetric analysis

then I use this command to work out the error correction model:

ardl D_lnCPI D_lnBrent_pos D_lnBrent_neg D_lnNBP_pos D_lnNBP_neg, bic ec

and use the command: estat ectest
the ectest responds by rejecting H0 suggesting there is cointergration

My problem is most of the variables have a high p-value and are not significant I need help/ recommendations on how to improve this model I have tried playing around with the lags but Im still trying to find a variation that comes back with a better model
any help would be greatly appreciated

[George Ford]

is this a second difference model (including ec is a first-difference model, and you have ADRL(1,4,0,0,0)?

[Sebastian Kripfganz]

I second George's question: Are you sure you want to estimate an error correction model for the first-differenced variables, which would be a model explaining the second difference (the change in the Brent growth rate)? This might make sense if you initially established that ln_Brent is I(2) and therefore D.ln_Brent is I(1), which however is doubtful.

and use the command: estat ectest
the ectest responds by rejecting H0 suggesting there is cointergration

A rejection of the bounds test reported by estat ectest is not sufficient to conclude that their is a long-run (cointegrating) relationship. You also need to test for significance of the long-run coefficients. Here, all of them are statistically insignificant; hence, no long-run relationship. See also our paper on the ardl command:

• Kripfganz, S., and D. C. Schneider (2023). ardl: Estimating autoregressive distributed lag and equilibrium correction models. Stata Journal 23 (4), 983-1019.

[George Ford]

run this model:

ardl lnCPI lnBrent_pos lnBrent_neg lnNBP_pos lnNBP_neg, bic ec

though the vars may need to be modified.

need to get rid of the twice differencing somehow.

[Conor Savill]

I second George's question: Are you sure you want to estimate an error correction model for the first-differenced variables, which would be a model explaining the second difference (the change in the Brent growth rate)? This might make sense if you initially established that ln_Brent is I(2) and therefore D.ln_Brent is I(1), which however is doubtful.



A rejection of the bounds test reported by estat ectest is not sufficient to conclude that their is a long-run (cointegrating) relationship. You also need to test for significance of the long-run coefficients. Here, all of them are statistically insignificant; hence, no long-run relationship. See also our paper on the ardl command:

• Kripfganz, S., and D. C. Schneider (2023). ardl: Estimating autoregressive distributed lag and equilibrium correction models. Stata Journal 23 (4), 983-1019.

I established that all variables are stationary at I(1), I was told to difference the variables to calculate their positive and negative changes Is this messing up my results then
Thanks for the help

[Conor Savill]

run this model:

ardl lnCPI lnBrent_pos lnBrent_neg lnNBP_pos lnNBP_neg, bic ec

though the vars may need to be modified.

need to get rid of the twice differencing somehow.

I see I will try decompose the level variables instead of the first difference ones

[George Ford]

ardl automatically first differences when you ec.

"If option ec (or ec1) is used, ardl will run a regression corresponding to the first-difference equation"
"

[Conor Savill]

ardl automatically first differences when you ec.

"If option ec (or ec1) is used, ardl will run a regression corresponding to the first-difference equation"
"

I understand now thank you do you have any recommendations on how to split variables into positive and negative changes? unfortunately my Stata knowledge is very limited haha

[George Ford]

https://www.econstor.eu/bitstream/10419/74240/1/NDL2005-075.pdf

I suspect you'll have to estimate the EC term yourself then incorporate.