[R] Simalteneous Equation Doubt in R

[Berend Hasselman]

On 22-03-2012, at 11:48, Priya.Saha at zycus.com wrote:

> Hi Berend
> Thanks for your help. The model which l have mentioned shows that Pt is dependent on Ft, EXt, FAIt, My objecttive is not only to find the impact of these varibles on Pt but also to see the extent of effect of variables influencing  Ft, EXt, FAIt which are mentioned in respective equation 2,3,4 on Pt. 
> So, l m still not clear how creation of matrix A will help with my objective .

But this formula gives you everything you need:

y = solve(diag(4)-A) %*% z

solve(diag(4)-A) is an inverse.
z is a vector consisting of the exogenous parts of the equations and these can be written as

B %*% <vector-of-exogenous-variables>

So you'll get

y = inverse of (I-A) %*% B %*% <exogenous-variables>

Berend


> Regards,
> Priya Saha
> .
>  
> 
> 
>  
> 
> 
> 
> From:        Berend Hasselman <bhh at xs4all.nl>
> To:        Priya.Saha at zycus.com
> Cc:        R help <r-help at r-project.org>
> Date:        22-03-2012 15:50
> Subject:        Re: [R] Simalteneous Equation Doubt in R
> 
> 
> 
> 
> 
> On 22-03-2012, at 09:15, Priya.Saha at zycus.com wrote:
> 
> > Hi List
> > 
> > l am interested in developing price model. I have found a research paper 
> > related to price model of corn in US market where it has taken demand & 
> > supply forces into consideration. Following are the equation:
> > Supply equation:
> > St= a0+a1Pt-1+a2Rt-1+a3St-1+a5D1+a6D2+a7D3+U1                -(1)
> > Where   D1,D2,D3=Quarterly Dummy Variables(Since quarterly data are 
> > considered)
> > Here, Supply equation has 1 endogenous (St) & 6 exogenous variables  (P
> > t-1,Rt-1,St-1,D1,D2,D3) 
> > Demand Side: 
> > Demand of corn is divided into 3 equations:
> > Feed equation:
> > Ft=b0+b1Pt+b2P(sm)t+b3Bt+b4COFt+b5Ht+a6D1+a7D2+a8D3+U2           -(2)
> > here there are 2 endogenous variable(Ft, Pt) & 7 exogenous variables 
> > (P(sm)t,Bt,COFt,D1,D2,D3) 
> > Export equation:
> > EXt= c0+c1Pt+c2EXt-1+c3Wt+c4DXt+c5GDPt+c6D1+c7D2+c8D3+U3         -(3)
> > here there are 2 endogenous variable(EXt, Pt) & 7 exogenous variables (EX
> > t-1,Wt,DXt,D1,D2,D3) 
> > Food, Alcohol, Industry (FAI) Demand Equation:
> > FAIt= d0+d1Pt+d2Etht+d3Popt+d4Tt+d5D1+d6D2+d7D3+U4      -(4)
> > here there are 2 endogenous variable(FAIt, Pt) & 6 exogenous variable(Eth
> > t,Popt,Tt,D1,D2,D3) 
> > Price Equation: price of corn is determined by supply and demand 
> > simultaneously, following is the reduced form equation: 
> > Pt=µ0+µ1St+µ2Ft+µ3EXt+µ4FAIt+µ5Pt-1+µ6D1+µ7D2+µ8D3+U5               -(5)
> > here there are 5 endogenous variable(St, Ft,EXt, FAIt, Pt) & 4 exogenous 
> > variable(Pt-1,D1,D2,D3)
> > Now my question is :
> > By applying 3SLS in the price equation, it will show the impact of 
> > variables on Pt which are mentioned in equation (5).But if l want to find 
> > impact of ETHt from equation (4) on Pt , l'll have to substitute equation 
> > (1),(2),(3),(4) in price equation(5), which manually becomes very tedious, 
> > is there any way this could be done directly in R?
> 
> Your system can be written compactly as
> 
> St  =                    + zS
> Ft  = b1Pt               + zF
> EXt = c1Pt               + zEX
> FAIt= d1Pt               + zFAI
> Pt  = µ2Ft+µ3EXt+µ4FAIt  + zP
> 
> St is exogenous so can be ignored.
> The system is linear and can be written as where the zXXX are the exogenous terms of the equation for XXX.
> 
> ( Ft   )      ( 0   0  0 b1 )  ( Ft   )         ( zF   ) 
> ( EXt  ) = ( 0   0  0 c1 )  ( EXt  )      +  ( zEX  ) 
> ( FAIt )      ( 0   0  0 d1 )  ( FAIt )         ( zFAI ) 
> ( Pt   )      ( µ2 µ3 µ4  0 )  ( Pt   )         ( zP   ) 
> 
> (Note: read the stacked ( and ) as a single large ( or ))
> or
> 
> y = A %*% y + z
> 
> which can be written as
> 
> y = solve(diag(4)-A) %*% z
> 
> You only need to construct the matrix A.
> 
> Berend
> 
> 
> 
>