Selecting the optimal order of lags in ARDL model

[Frank Giaquinto]

Hi everyone,

I'm working with panel of 105 countries and with T=49. My objective is to implement a CS-ARDL model, as cross-sectional correlation is a concern in my analysis.

To address this, I set the number of cross-sectional averages for the dependent and independent variables to 4, based on the floor of of T^1/3.

To select the optimal number of lags for the autoregressive and distributed lag parts, I would appreciate your guidance on the best strategy.

My variables are: 1) Growth rate of GDP per capita, 2) log ( total investments / GDP) , 3) log ( fiscal variable as a ratio ) .

I conducted the CIPS test, which suggests:
1)the growth rate of GDP is I(0),
2) total investments is trend stationary,
3) the fiscal variable is I(1).

I considered using the ardl command to select the optimal order of lags using the BIC criterion. Specifically, I implemented the following loop:

forval i = 1/105 {
quietly ardl y x1 x2 if (id==`i'), maxlag(3 3 3)
matrix `results'[`i',1] = `i'
matrix `results'[`i',2] = e(lags)[1,1]
matrix `results'[`i',3] = e(lags)[1,2]
matrix `results'[`i',4] = e(lags)[1,3]
}

The test results suggest:
1) For most GDP growth series: 1 or 2 lags.
2) For the other two variables: I have a bunch of 0 lags

When I take the average of the suggested lag orders:
1) GDP growth:1,3,
2) Total investments / GDP:0.4
3) Fiscal variable: 0.56.

Would it be appropriate to use an ARDL (2, 1, 1) specification based on these averages? Alternatively, is there a more robust or preferable approach for determining the lag structure in this context?
Thank you in advance for your time