Which Econometric Model Should I Use?

[aaronhonour]

I want to build a model and I currently have the equation:

Y = x1 + x2 + x3 + u1

I then have explanatory variables for each of the variables on the right
So:
x1= p1+p2+p3+u2
x2= s1+s2+s3+s2
x3= a1+a2+a3+u2

Which model will allow me to ensure that all of these variables are considered when I am creating the model? I thought about using a simultaneous equation model but my initial independent variable Y does not occur in the later equations so I do not think I can or I do not know how to use this model

Any tips or advice is greatly appreciated!

[vascop]

By considering the form of your equations I would guess that s2 at the end of the equation for x2 should be u2 - is that right?
Even then I don't think you have stated your problem very clearly and so I have no idea what you are asking for.

[vascop]

... and don't you mean "dependent variable Y"?

[fiction-factory]

Maybe i am not understanding what you want but isn't it simply:
Y= p1+p2+p3+u2 + s1+s2+s3+u2* + a1+a2+a3+u2 **

*Assuming you meant u2 not s2 again
** or did you mean u3?

[aaronhonour]

Hello, yes thankyou i did make a few errors in the initial post

I did mean the dependent variable Y
The s2 should have been u2 to represent the error term
and the error term of x3 should be u3

really sorry about those mistakes...

So should I use a linear model? are there any alternatives?

My equations in a less abstract way would be as follows

∆Y =α+b1Y+b2CIVIL+b3 POLIT+b4 CORUP+ϵ1
CIVIL= δ1 SPEECH+δ2BELIEF+δ3 PRESS+δ4PERAT+ϵ2
POLIT=γ1 VOTE+γ2PUBO+γ2 ACCOUNT+ϵ3

Where ∆Y_it = Change in GDP per Capita, Y= GDP per Capita CIV=Civil Liberties, POL= Political Rights, COR= Corruption, SPH = Freedom of speech, BEL = Freedom of belief, PRS = Freedom of Media, PAT = Personal Autonomy, VTE = Freedom to vote, PBO = Ability to obtain public office, ACC = Accountability of those in power to electorate.

I am not sure if this even makes any difference. Mainly I am unsure what my options would be?

Thanks again for any help

[New Judge]

I spent around ten years of my working life running doing multiple regression analysis models with just three or sometimes four independent variables. I saw the results of the early forecasts I produced.

You asked for advice: mine is don't bother! Multiple regression analysis simply replaces the problem of forecasting one variable with the far greater problem of forecasting many more. My advice seems particulary appropriate when looking at some of what you call "less abstract" independent variables :-)

[New Judge]

And I forgot to add that many of the independent variables you mention seem as if they could be very interdependent. The chances of producing a reliable model, particularly on the simple basis you propose, with so many variables and with so much interdependency are as good a zero.