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

[WilDscOp]

Dear all,

For estimating Cobb-Douglad production Function [ Y = ALPHA * (L^(BETA1)) * 
(K^(BETA2))  ], i want to use nls function (without linearizing it). But 
how can i get initial values?

------------------------------------
 > options(prompt=" R> " )
  R> Y <- c(59.6, 63.9, 73.5, 75.6, 77.3, 82.8, 83.6, 84.9, 90.3, 80.5, 
73.5, 60.3, 58.2, 64.4, 75.4, 85, 92.7, 85.4, 92.3, 101.2, 113.3, 107.8, 
105.2, 107.1, 108.8, 131.4, 130.9, 134.7, 129.1, 147.8, 152.1, 154.3, 
159.9) # production
  R> L <- c(39.4, 41.4, 43.9, 43.3, 44.5, 45.8, 45.9, 46.4, 47.6, 45.5, 
42.6, 39.3, 39.6, 42.7, 44.2, 47.1, 48.2, 46.4, 47.8, 49.6, 54.1, 59.1, 
64.9, 66, 64.4, 58.9, 59.3, 60.2, 58.7, 60, 63.8, 64.9, 66) # employment
  R> K <- c(236.2, 240.2, 248.9, 254.5, 264.1, 273.9, 282.6, 290.2, 299.4, 
303.3, 303.4, 297.1, 290.1, 285.4, 287.8, 292.1, 300.3, 301.4, 305.6, 
313.3, 327.4, 339, 347.1, 353.5, 354.1, 359.4, 359.3, 365.2, 363.2, 373.7, 
386, 396.5, 408) # capital
  R> klein <- cbind(Y,L,K)
  R> klein.data<-data.frame(klein)
  R> coef(lm(log(Y)~log(L)+log(K)))
# i used these linearized model's estimated parameters as initial values
(Intercept)      log(L)      log(K)
  -3.6529493   1.0376775   0.7187662
  R> nls(Y~ALPHA * (L^(BETA1)) * (K^(BETA2)), data=klein.data, start = 
c(ALPHA=-3.6529493,BETA1=1.0376775,BETA2=0.7187662), trace = T)
6852786785 :  -3.6529493  1.0376775  0.7187662
1515217 :  -0.02903916  1.04258165  0.71279051
467521.8 :  -0.02987718  1.67381193 -0.05609925
346945.7 :   -0.5570735  10.2050667 -10.2087997
Error in numericDeriv(form[[3]], names(ind), env) :
         Missing value or an Infinity produced when evaluating the model
------------------------------------

1. What went wrong? I think the initial values are not good enough: How can 
i make a grid search?

2. How can i estimate C.E.S Production Function [  Y = GAMA * 
((DELTA*K^(-BETA)) + ((1-DELTA)*L^(-BETA)))^(-PHI/BETA)  ] using the same 
data? How to get the initial value?

N.B.: The data file is available at http://www.angelfire.com/ab5/get5/klein.txt

Any response / help / comment / suggestion / idea / web-link / replies will 
be greatly appreciated.

Thanks in advance for your time.

_______________________

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