GLS for non-linear equation

[Changho Moon]

ln (P_it) = a*ln(R_it + b*V_it) + u_it

I want to estimate a, b for wide panel data (i = 1~16, t = 2007~1016) by using GLS

The problem is that b is in the logarithm

please help me out

[Scott Merryman]

You could use -nl-

. clear

. set obs 1000
number of observations (_N) was 0, now 1,000

. gen R = runiform()

. gen V = runiform()

. gen u = rnormal()

. gen P = ((5*V + R)^2.5)*exp(u)

. gen lnP = ln(P)

. nl (lnP = {a=1}*ln(R + {b=1}*V)), nolog
(obs = 1,000)


      Source |      SS            df       MS
-------------+----------------------------------    Number of obs =      1,000
       Model |  8427.5155          2  4213.75775    R-squared     =     0.8949
    Residual |  990.18942        998  .992173766    Adj R-squared =     0.8946
-------------+----------------------------------    Root MSE      =   .9960792
       Total |  9417.7049       1000  9.41770493    Res. dev.     =   2828.018

------------------------------------------------------------------------------
         lnP |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          /a |   2.504446   .0568576    44.05   0.000     2.392872    2.616021
          /b |   5.058831   .1660434    30.47   0.000     4.732996    5.384665
------------------------------------------------------------------------------