# [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
linearizing)
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

```