[R] Maximum Likelihood Estimation

[Prof. John C Nash]

What do you mean by the "estimates were very bad"? In nearly 40 years of
working with optimization, I've seen badly set-up  functions cause
troubles, I've seen multiple minima situations, I've seen comparisons of
results from one data set to the estimates for another, and I've seen
optimization produce the proper results when published ones were just
plain wrong.

So there are many possibilities.

And for Cobb-Douglas functions, I've seen least squares estimates based
on the log of the production function give estimates with different
signs from those using a nonlinear least squares objective on the
original exponential form.

You are not the first to step in the cow pie of Cobb Douglas.

We need some numbers please. If you send a file or files (I don't think
you can attach files to Rhelp, but can do so off-list) with a runnable
script and the data, I'll be willing to try it out.

JN





> Message: 84
> Date: Tue, 3 Nov 2009 19:49:17 +0000
> From: Andre Barbosa Oliveira <andreabosn at hotmail.com>
> Subject: [R] Maximum Likelihood Estimation
> To: <r-help at r-project.org>
> Message-ID: <BLU109-W2D5A97DBFD61D3976E589C2B20 at phx.gbl>
> Content-Type: text/plain
> 
> 
> Hi,
> 
> I would like estimate a model for function of production's Coob-Douglas using maximum likelihood. The model is log(Y)= beta[1]+beta[2]*log(L)+beta[3]*log(K). I tried estimate this model using the tools nlm ( ) and optim ( ) using the log-likelihood function below:
>
> > mloglik <- function (beta, Y, L, K) {
> + n <- length(Y)
> + sum ( (log(Y)- beta[1]-beta[2]*log(L)-beta[3]*log(K))2)/2*beta[4]2 + n/2*log(2*pi)+ n*log(beta[4])
> + }
> Then I did estimates the parameters using nlm ( ) and optim ( ), but the estimates were very bad. I used these codes:
>
>> > mlem <- nlm (mloglik, c(1,1,1,1), Y=Y, L=L, K=K)
> 
>> > mlem2 <- optim(c(1,1,1,1), mloglik, Y=Y, L=L, K=K, method="BFGS")
> 
> How I improve the estimates???? What's the best and more simple form for estimate a modelo using the  maximum likelihood's method???
> 
> Best regards,
> 
> Andre' Barbosa Oliveira
> 
> Student of Master in Economics at University Federal of Rio Grande do Sul - Brazil 
>  		 	   		  
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