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

[Pfaff, Bernhard]

> 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?
> 

Dear James, Wettenhall,

as far as the CES production function is concerned, you might want to
utilise the Kmenta approximation. The following link elucidates this
approach and other feasible estimation techniques.

http://www.cu.lu/crea/projets/mod-L/prod.pdf


HTH,
Bernhard

> 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

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