You could consider for specific out-of-sample values of your Xs.

e.g., first then

HI Jeffrey Cisyk thank you very much for your advise.

was new for me,

just for better understanding: is multipliers (15) & (-0.5) just examples which we expect to find them in reg estimation?

Xs are Independent variables?

in between 5 independent variables on the right side of ARDL, should I regress one independent variable with another one? or all of them with their trends?

best

Hi Lilian Mboya thank you very much I will refer to that link hope to be useful,

my best

I think your equation is misspecified. I assume that G is government spending and that oil revenues are a considerable part of budget revenues, the Deficit=G-OilRevenues-other revenues or D/GDP=G/GDP-OilR/GDP-OtherR/GDP+.... That means you estimate, in essence, the log of an (incomplete) additive definitional equation or implicitly OtherR. Because of the division by GDP, a more or less strong correlation (colinearity) between the exogenous variables is produced, which will likely lead to biased estimates for the coefficients. My proposal is to estimate OtherR and then to use the definitional equation for D. For forecasts, you need, of course, forecasts of G and OilR and of the determinants of OtherR. For these forecasts, one can, in principle, use AR (to calculate them on the base of past values), but it may be better (especially what concerns G) to look at budget plans of the government.

@Anton Rainer thanks a lot.

Your interpretation is right.

I didn't put any sign before exogenouses in advance.

When one puts variables in an Ardl like below mentioned:

Ardl Ln Deficit Ln G Ln Oil ..., aic ec

Estimated coefficient shows exactly the sign you expect. i.e. G _ Oil (Oil is dominant factor in revenues time series)

I rearranged model by considering other variables plus G:

Oil Revenue Fluctuations to show instability

Expenditure Fluctuations to show instability

Other socio-economic and political economic determinant.

Regarding using AR for forecasting it is interesting and thank you I'll use it

Hoping forcasted variables don't fall into an divergent path cause I need them to show cointegration for ardl.

My best

I am not sure, if you have understood my comment correctly. D=G-R with R=OilR+OtherR are linear definitions (also if you divide them by GDP), and it is senseless to estimate definitional equations and especially to apply ARDL (because past values do not play any role here), and it is, in general, forbidden to estimate a linear equation in log-form, because that means a change of an originally correctly-specified model. My proposal was to take D/GDP=G/GDP-OilR/GDP-OtherR/GDP as given and to try to estimate equations of the variables on the right side of the equation - maybe using ARDL (if you think, that they are strongly dependent on past values). One problem is, that supposedly tax revenue has the highest share in OtherR and there is a strong dependency between GDP and taxes. Therefore, it is better to take OtherR instead of OtherR/GDP as dependent variable. The lags in this equation are, of course, i.a. from the rules for assessment and (pre)payments for the most important taxes. You can also estimate equations for these important taxes, but that could become too complicated, because it could mean more disaggregation (differentiation of GDP-components, which are nearer to the tax base of the estimated taxes) of the whole model.

Thank you again @Anton Rainer

Yes you are right

I wrote my comment very short

this is assumed to use Ln(G/GDP) and etc. I didn't put G and Oil and... strictly in an ARDL model

I'm using ARDL as you said budget deficit is a structural problem and depends to its past values even if government doesn't have a fiscal rule and at the same time ARDL models help to escape from endogeenety, reverse causality and o.v.

Based on your advise I will run ARDL with LnD/GDP on time with Ln G/GDP and its flactuations with revenues flactuations and other structural variables

One time with Ln Oil/GDP and flactuations.

Both above are separate estimations then I can understand budget deficit is a revenue FOLLOWER or expenditure FOLLOWER.

I also used Ln(Tax/GDP) together with Oil revenues, since in resource based countries Tax is directly related to Resource Revenues.

So it was not useful for estimation.

By this plan I don't estimate an equation and can capture effect of other determinants.

If still I didn't understood your idea would be appreciated to have your complementary notes.

Best

I think the easiest way to solve the problem is to to start from the definition of the deficit D=G-OilR-OtherR (all variables as percentage of GDP) and try to find an autoregressive equation for GDP - like GDP=a*GDP(-1)+b*GDP(-2) etc. (can also be in logs, differences or %-changes). The next step could be to have the variables on the right side of the definition as dependent variables explained by GDP and one or two (lagged) variables in the equation. One could e.g. assume that high deficits in preceding years could force the government to reduce expenditures (where possible). Unfortunately, this estimation (of GDP dependency) will likely not function for OilR, because these are mainly dependent on factors outside your country (e.g. from the presidential elections in the USA). But, in general, one must expect falling revenues from oil, because of the climate change, many countries try to reduce oil and gas consumption. Apart from that, if you find good and reasonable relations of the above variables with GDP and with (lagged) other variables in the definion, it is easy to forecast the variables and their GDP-percentages. Unfortunately, your inflation is so high and the main driver of nominal GDP, which may make it difficult to find reasonable relations and to interpret the results.

Best wishes