# [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?
-----------------------------
> 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
-----------------------------