[R] Non-Linear Regression (Cobb-Douglas and C.E.S)

Mohammad Ehsanul Karim wildscop at yahoo.com
Sun Apr 18 09:40:21 CEST 2004

Dear Sundar Dorai-Raj,

Thank you very much for mentioning to exponentiate ALPHA.

However, so far i understand that the parameters in the non-linear equation
Y = ALPHA * (L^(BETA1)) * (K^(BETA2))
and the coefficients of log(L) and log(K) of the following equation (after 
log(Y) = log(ALPHA) +(BETA1)*log(L) + (BETA2)*log(K)
should be the same when estimated from either equation. Is it true? If it 
is, then why the estimates of the two procedure (see below) are different? 
Can you please explain it?
 > coef(lm(log(Y)~log(L)+log(K), data=klein.data))

(Intercept)      log(L)      log(K)
  -3.6529493   1.0376775   0.7187662
 > nls(Y~ALPHA * (L^(BETA1)) * (K^(BETA2)), data=klein.data, start = 
c(ALPHA=exp(-3.6529493),BETA1=1.0376775,BETA2 = 0.7187662), trace = TRUE)

Nonlinear regression model
   model:  Y ~ ALPHA * (L^(BETA1)) * (K^(BETA2))
    data:  klein.data
       ALPHA       BETA1       BETA2
0.003120991 0.414100040 1.513546235
  residual sum-of-squares:  3128.245

Thanks in advance for your time and effort - and sorry for my late reply.

Mohammad Ehsanul Karim <appstat at HotPOP.com>
Institute of Statistical Research and Training
University of Dhaka, Dhaka- 1000, Bangladesh

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