## Estimation of Restricted Cobb-Douglas Production Function

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Imran Ali
Posts: 3
Joined: Wed Feb 03, 2010 9:00 pm

### Estimation of Restricted Cobb-Douglas Production Function

How I can estimate the restricted Cobb-Douglas Production Function with three factor inputs of the form:

Y = A*(K^alpha)(L^beta)(N^gamma); alpha + beta + gamma = 1
where
Y = Output
K = Capital
L = Labor, and
N = Land

startz
Non-normality and collinearity are NOT problems!
Posts: 3606
Joined: Wed Sep 17, 2008 2:25 pm

### Re: Estimation of Restricted Cobb-Douglas Production Function

You can take logs and do a linear regression or you can do a nonlinear regression.

Perhaps you should tell what us you've done so far and where you got stuck.

Imran Ali
Posts: 3
Joined: Wed Feb 03, 2010 9:00 pm

### Re: Estimation of Restricted Cobb-Douglas Production Function

Given function:

Y = A*(K^alpha)*(N^beta)*(L^gemma)
where,
K = Capital
N = Labour
L = Land
and, given restriction:

alpha + beta + gemma = 1

I want to run a regression of the form.

log(Y) = A + (1 - beta - gemma)*log(K) + (1-alpha - gemma)*log(N) + (1-alpha - beta)*log(L)

I failed to run this regression in Eviews.

Please help me either with the estimation of the function in Eviews and with the functional form.

Thanks.

startz
Non-normality and collinearity are NOT problems!
Posts: 3606
Joined: Wed Sep 17, 2008 2:25 pm

### Re: Estimation of Restricted Cobb-Douglas Production Function

Given function:

Y = A*(K^alpha)*(N^beta)*(L^gemma)
where,
K = Capital
N = Labour
L = Land
and, given restriction:

alpha + beta + gemma = 1

I want to run a regression of the form.

log(Y) = A + (1 - beta - gemma)*log(K) + (1-alpha - gemma)*log(N) + (1-alpha - beta)*log(L)

I failed to run this regression in Eviews.

Please help me either with the estimation of the function in Eviews and with the functional form.

Thanks.

In EViews, coefficients are named c(1), c(2), etc., rather than "beta,"

so you want to do something like
log(y) = c(1) +c(2)*log(k) + c(3)*log(N) + (1-c(2)-c(3))*log(L)

Imran Ali
Posts: 3
Joined: Wed Feb 03, 2010 9:00 pm

### Re: Estimation of Restricted Cobb-Douglas Production Function

Once again thanks for your help. But my this does not solve my problem. See if i run this regression i did not get the sum of all three coefficients equal to one. So please tell me if there's any problem with the functional form. How do I specify the Cobb-Douglass Production function with three inputs and neutral technology in the Eviews. Regards

startz
Non-normality and collinearity are NOT problems!
Posts: 3606
Joined: Wed Sep 17, 2008 2:25 pm

### Re: Estimation of Restricted Cobb-Douglas Production Function

Maybe you should post exactly what you are doing, so people can take a look.

Did you use forum search?
Posts: 1518
Joined: Thu Nov 20, 2008 12:04 pm

### Re: Estimation of Restricted Cobb-Douglas Production Function

The discussion under the Putting limits on estimated coefficient values thread might help. Please always do a simple search before posting your questions, since they may have already been answered somewhere in the forum.

alinapop
Posts: 2
Joined: Thu Jun 30, 2016 7:51 am

### Re: Estimation of Restricted Cobb-Douglas Production Functio

HI,
i want to estimate a translog cost function and I need to put some restrictions, I used the following model
log(y) = c(1) +c(2)*log(k) + c(3)*log(N) + (1-c(2)-c(3))*log(L)
I get the cofficient for c(1), c(2), c(3)
For (1-c(2)-c(3))*log(L) am I suppose to just do 1 minus the results for the two coefficient?

startz
Non-normality and collinearity are NOT problems!
Posts: 3606
Joined: Wed Sep 17, 2008 2:25 pm

### Re: Estimation of Restricted Cobb-Douglas Production Functio

Those don't look like the right restrictions for a Cobb-Douglas.

alinapop
Posts: 2
Joined: Thu Jun 30, 2016 7:51 am

### Re: Estimation of Restricted Cobb-Douglas Production Functio

this si the translog cost function
ln(C(q;wL,wK,wM)) = c + cq * ln(q) + cL * ln(wL) + cK * ln(wK) + cM * log(wM)
+ .5 * [dqq * ln(q)^2 + dLL * ln(wL)^2 + dKK * ln(wK)^2 + dMM * ln(wM)^2]
+ .5 * [(dLK + dKL) * ln(wL)*ln(wK) + (dLM + dML) * ln(wL)*ln(wM) + (dKM + dMK) * ln(wK)*log(wM)]
+ dLq * ln(wL)*ln(q) + dKq * ln(wK)*ln(q) + dMq * ln(wM)*ln(q)
and the restrictions are:
1 = cL + cK + cM
0 = dLL + dLK + dLM
0 = dKL + dKK + dKM
0 = dML + dMK + dMM
0 = dLq + dKq + dMq
0 = dLq, 0 = dKq, 0 = dMq, 1 = cq

startz
Non-normality and collinearity are NOT problems!
Posts: 3606
Joined: Wed Sep 17, 2008 2:25 pm

### Re: Estimation of Restricted Cobb-Douglas Production Functio

Then yes, "c(4)" = 1 -c(2) -c(3)

pka
Posts: 22
Joined: Wed Apr 25, 2018 1:54 pm

### Re: Estimation of Restricted Cobb-Douglas Production Functio

Hello,

I am running a regression with a linear restriction on a coefficient as in

Y = alpha*X1 + beta*X2 + (1-alpha-beta)*X3 + error

Eviews only returns the estimates for alpha and beta as well as their standard errors.

To get the estimate of the coefficient for X3, I do manually 1-alpha-beta.

However, how do I compute the standard error of this paramater?

Thanks

startz
Non-normality and collinearity are NOT problems!
Posts: 3606
Joined: Wed Sep 17, 2008 2:25 pm

### Re: Estimation of Restricted Cobb-Douglas Production Function

View/Wald statistic

Code: Select all

`0=1-alpha-beta`

pka
Posts: 22
Joined: Wed Apr 25, 2018 1:54 pm

### Re: Estimation of Restricted Cobb-Douglas Production Function

startz wrote:View/Wald statistic

Code: Select all

`0=1-alpha-beta`

Hello Startz,

Many thanks indeed for your valuable help.

Much appreciated.

Kind regards.