* refer to table 4.2, page 158 of Greene's Econometric Analysis, edition 4
* the corresponding table of edition 5 is table 17.1 on page 491
* first import data

use http://fmwww.bc.edu/ec-p/data/Greene2000/TBL4-1, clear

* note that the variable e is actually the independent variable x
* assume the conditional distribution is gamma
* the coefficient of e is restricted to be one.
* this is a two-paremeter restricted MLE model


capture program drop mle_gamma
program define mle_gamma
version 8.0
args lnf theta1 theta2
quietly replace `lnf'=-`theta2'*ln(`theta1')-lngamma(`theta2')+(`theta2'-1)*ln($ML_y1)-$ML_y1/`theta1'
end

constraint define 1 e=1
ml model lf mle_gamma (y=e) (), constraints(1)
ml maximize


/*

i	y	e
1	20.5	12
2	31.5	16
3	47.7	18
4	26.2	16
5	44	12
6	8.28	12
7	30.8	16
8	17.2	12
9	19.9	10
10	9.96	12
11	55.8	16
12	25.2	20
13	29	12
14	85.5	16
15	15.1	10
16	28.5	18
17	21.4	16
18	17.7	20
19	6.42	12
20	84.9	16


. capture program drop mle_gamma

. program define mle_gamma
  1. version 8.0
  2. args lnf theta1 theta2
  3. quietly replace `lnf'=-`theta2'*ln(`theta1')-lngamma(`theta2')+(`theta2'-1)*ln($ML_y1)-$ML_y1/`theta1'
  4. end

. 
. constraint define 1 e=1

. ml model lf mle_gamma (y=e) (), constraints(1)

. ml maximize

initial:       log likelihood =     -<inf>  (could not be evaluated)
feasible:      log likelihood = -1287.8497
rescale:       log likelihood = -109.84554
rescale eq:    log likelihood = -87.102313
Iteration 0:   log likelihood = -118.44291  (not concave)
Iteration 1:   log likelihood = -86.296196  
Iteration 2:   log likelihood = -83.735966  
Iteration 3:   log likelihood = -83.088558  
Iteration 4:   log likelihood = -82.924748  
Iteration 5:   log likelihood = -82.916083  
Iteration 6:   log likelihood = -82.916049  
Iteration 7:   log likelihood = -82.916049  

                                                  Number of obs   =         20
                                                  Wald chi2(0)    =          .
Log likelihood = -82.916049                       Prob > chi2     =          .

 ( 1)  [eq1]e = 1
------------------------------------------------------------------------------
           y |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
eq1          |
           e |          1          .        .       .            .           .
       _cons |  -4.718502   2.345027    -2.01   0.044     -9.31467   -.1223335
-------------+----------------------------------------------------------------
eq2          |
       _cons |   3.150896   .7942619     3.97   0.000     1.594171    4.707621
------------------------------------------------------------------------------

. 
end of do-file

*/