Question on Seemingly Unrelated Regression

[jack]

Dear tom,

I want to estimate a Linear Expenditure System based on the Stone-Geary utility function:


where: demand for commodity i; marginal expenditure share with ; and minimum quantity demanded from commodity i.

Maximizing this function subject to the expenditure restriction where is price of commodity i and m is total expenditure, leads to the linear expenditure system:
.

Time series form of the above equation is:
.

At first, I estimate by using the Engel function as: .
And after estimation of , I plug it into the above equation and finally I estimate the above equation by SUR.

But I don’t know how to estimate it in RATS by SUR. I don't know how to write a program for it in RATS.
I would be grateful if you could possibly guide me through it.

[TomDoan]

Sorry. If you have the alpha's, what are the parameters to be estimated?

[jack]

Thank you for your kind reply.

I want to derive demand functions and therefore cost functions for n commodities. The utility function is the Stone-Geary utility function. Maximizing utility function with respect to budget constrain leads to the linear expenditure system:


As you see, each equation has two parameters: and . In the first step, I use an Engel function (a panel model) for estimating : .

Then I use obtained from the first step in the linear expenditure system and obtain parameter via SUR method.

But I don’t know how to write a SUR program in RATS.

[TomDoan]

Use NLSYSTEM, not SUR.

[jack]

Dear Tom,

As you know, it is really beyond my ability to write a program for it. I used to sue a kind of prototype one and adjust it according to my problem as I did with respect to MVGARCH and VAR models in the past.

It would be really kind of you to guide and help me in writing a model for it.

[TomDoan]

consumer.rpf is the closest thing we have to that. It doesn't look like it's all that difficult---you almost literally just write down the FRML's that match your equations. You just need to add a mu>=0 to your PARMSET to force the mu's to be non-negative.

[jack]

I installed winRATS standard 9.2. But I can't find consumer.wks. How I can find it?

[TomDoan]

With the program files (including consumer.rpf) in your Examples and Procedures folder.

[jack]

Dear Tom,

with two commodities, the linear expenditure system will be as follow:


I have data on p*x, p and m.

Is it possible to estimate alpha and mu with a program like consumer.rft? Because the first term in right hand sides of each equation is multiplication of alpha with mu.

[TomDoan]

Sure. That's the whole point of doing it with NLSYSTEM rather than SUR. Your model is linear in the observables, but not linear in the parameters. Also, it's not "seemingly unrelated" anyway---the mu's show up in both equations so they're very much related.

[jack]

I wrote a code (based on consumer.rpf) and run it but I received this error from RATS:

## REG12. SIGMA Is Singular/Not PSD At Row 8. Too Many Equations for Data Set Size?


This is the code:

Code: Select all

open data C:\les1.xlsx
data(format=xlsx,org=cols) / c1	c2	c3	c4	c5	c6	c7	c8	p1	p2	p3	p4	p5	p6	p7	p8	m
nonlin(parmset=base) mu1 mu2 mu3 mu4 mu5 mu6 mu7 mu8 $
   a1 a2 a3 a4 a5 a6 a7 a8
nonlin(parmset=nonnegative) mu1>=0.0 mu2>=0.0 mu3>=0.0 mu4>=0.0 $
    mu5>=0.0 mu6>=0.0 mu7>=0.0 mu8>=0.0
nonlin(parmset=summation) a1+a2+a3+a4+a5+a6+a7+a8==1
*
frml fx1 c1 = (1-a1)*mu1*p1+a1*m-a1*mu2*p2+$
   -a1*mu3*p3-a1*mu4*p4-a1*mu5*p5-a1*mu6*p6-a1*mu7*p7-a1*mu8*p8
frml fx2 c2 = (1-a2)*mu2*p2+a2*m-a2*mu1*p1+$
   -a2*mu3*p3-a2*mu4*p4-a2*mu5*p5-a2*mu6*p6-a2*mu7*p7-a2*mu8*p8
frml fx3 c3 = (1-a3)*mu3*p3+a3*m-a3*mu1*p1+$
   -a3*mu2*p2-a3*mu4*p4-a3*mu5*p5-a3*mu6*p6-a3*mu7*p7-a3*mu8*p8
frml fx4 c4 = (1-a4)*mu4*p4+a4*m-a4*mu1*p1+$
   -a4*mu2*p2-a4*mu3*p3-a4*mu5*p5-a4*mu6*p6-a4*mu7*p7-a4*mu8*p8
frml fx5 c5 = (1-a5)*mu5*p5+a5*m-a5*mu1*p1+$
   -a5*mu2*p2-a5*mu3*p3-a5*mu4*p4-a5*mu6*p6-a5*mu7*p7-a5*mu8*p8
frml fx6 c6 = (1-a6)*mu6*p6+a6*m-a6*mu1*p1+$
   -a6*mu2*p2-a6*mu3*p3-a6*mu4*p4-a6*mu5*p5-a6*mu7*p7-a6*mu8*p8
frml fx7 c7 = (1-a7)*mu7*p7+a7*m-a7*mu1*p1+$
   -a7*mu2*p2-a7*mu3*p3-a7*mu4*p4-a7*mu5*p5-a7*mu6*p6-a7*mu8*p8
frml fx8 c8 = (1-a8)*mu8*p8+a8*m-a8*mu1*p1+$
   -a8*mu2*p2-a8*mu3*p3-a8*mu4*p4-a8*mu5*p5-a8*mu6*p6-a8*mu7*p7
*
compute mu1=mu2=mu3=mu4=mu5=mu6=mu7=mu8=0.0
compute a1=a2=a3=a4=a5=a6=a7=a8=0.0
*
nlsystem(parmset=base+nonnegative+summation,iters=500) / fx1 fx2 fx3 fx4 fx5 fx6 fx7 fx8
*

[TomDoan]

Can you estimate all 8? Most demands systems have an adding up constraint so you can also estimate N-1.

[jack]

I deleted equation 8 but I again got the error:
## REG12. SIGMA Is Singular/Not PSD At Row 7. Too Many Equations for Data Set Size?

Code: Select all

open data C:\Users\LapTop118\Desktop\les1.xlsx
data(format=xlsx,org=cols) / c1	c2	c3	c4	c5	c6	c7	c8	p1	p2	p3	p4	p5	p6	p7	p8	m
nonlin(parmset=base) mu1 mu2 mu3 mu4 mu5 mu6 mu7 mu8 $
   a1 a2 a3 a4 a5 a6 a7 a8
nonlin(parmset=nonnegative) mu1>=0.0 mu2>=0.0 mu3>=0.0 mu4>=0.0 $
    mu5>=0.0 mu6>=0.0 mu7>=0.0 mu8>=0.0
nonlin(parmset=summation) a1+a2+a3+a4+a5+a6+a7+a8==1
*
frml fx1 c1 = (1-a1)*mu1*p1+a1*m-a1*mu2*p2+$
   -a1*mu3*p3-a1*mu4*p4-a1*mu5*p5-a1*mu6*p6-a1*mu7*p7-a1*mu8*p8
frml fx2 c2 = (1-a2)*mu2*p2+a2*m-a2*mu1*p1+$
   -a2*mu3*p3-a2*mu4*p4-a2*mu5*p5-a2*mu6*p6-a2*mu7*p7-a2*mu8*p8
frml fx3 c3 = (1-a3)*mu3*p3+a3*m-a3*mu1*p1+$
   -a3*mu2*p2-a3*mu4*p4-a3*mu5*p5-a3*mu6*p6-a3*mu7*p7-a3*mu8*p8
frml fx4 c4 = (1-a4)*mu4*p4+a4*m-a4*mu1*p1+$
   -a4*mu2*p2-a4*mu3*p3-a4*mu5*p5-a4*mu6*p6-a4*mu7*p7-a4*mu8*p8
frml fx5 c5 = (1-a5)*mu5*p5+a5*m-a5*mu1*p1+$
   -a5*mu2*p2-a5*mu3*p3-a5*mu4*p4-a5*mu6*p6-a5*mu7*p7-a5*mu8*p8
frml fx6 c6 = (1-a6)*mu6*p6+a6*m-a6*mu1*p1+$
   -a6*mu2*p2-a6*mu3*p3-a6*mu4*p4-a6*mu5*p5-a6*mu7*p7-a6*mu8*p8
frml fx7 c7 = (1-a7)*mu7*p7+a7*m-a7*mu1*p1+$
   -a7*mu2*p2-a7*mu3*p3-a7*mu4*p4-a7*mu5*p5-a7*mu6*p6-a7*mu8*p8


*
compute mu1=mu2=mu3=mu4=mu5=mu6=mu7=mu8=0.0
compute a1=a2=a3=a4=a5=a6=a7=a8=0.0
*
nlsystem(parmset=base+nonnegative+summation,iters=10000) / fx1 fx2 fx3 fx4 fx5 fx6 fx7
*

[TomDoan]

There's nothing fundamentally wrong with the model---if I put in random data, it works. So there must be something wrong with your data set. How much data do you have?

[jack]

10 years for each variables (17 variables).