* exercise 5.3 of Greene's textbook, edition 4, page 208-209
* input the data

use 53_poisson.dta, clear

capture program drop mle_poisson

program define mle_poisson
version 8.0
args lnf theta1 
quietly replace `lnf'=-exp(`theta1')+$ML_y1*(`theta1')-lngamma($ML_y1+1)  
end

ml model lf mle_poisson (y=x) 
ml maximize


capture program drop mle_poisson1

program define mle_poisson1
version 8.0
args lnf theta1 
quietly replace `lnf'=-exp(`theta1')+$ML_y1*(`theta1')   
end

ml model lf mle_poisson1 (y=x) 
ml maximize

/*

y	x
6	1.5
7	1.8
4	1.8
10	2
10	1.3
6	1.6
4	1.2
7	1.9
2	1.8
3	1
6	1.4
5	.5
3	.8
3	1.1
4	.7


. do "C:\Documents and Settings\jlee\My Documents\EC671\53_poisson.do" 

. 
. * exercise 5.3 of Greene's textbook, edition 4, page 208-209
. * input the data
. 
. use 53_poisson.dta, clear

. 
. capture program drop mle_poisson

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

. 
. ml model lf mle_poisson (y=x) 

. ml maximize

initial:       log likelihood = -102.38698
alternative:   log likelihood = -72.117799
rescale:       log likelihood = -38.222822
Iteration 0:   log likelihood = -38.222822  
Iteration 1:   log likelihood = -32.137797  
Iteration 2:   log likelihood = -32.066088  
Iteration 3:   log likelihood = -32.066011  
Iteration 4:   log likelihood = -32.066011  

                                                  Number of obs   =         15
                                                  Wald chi2(1)    =       2.72
Log likelihood = -32.066011                       Prob > chi2     =     0.0993

------------------------------------------------------------------------------
           y |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           x |   .4248897   .2578109     1.65   0.099    -.0804104    .9301898
       _cons |   1.078078   .3886433     2.77   0.006     .3163506    1.839805
------------------------------------------------------------------------------


. capture program drop mle_poisson1

. 
. program define mle_poisson1
  1. version 8.0
  2. args lnf theta1 
  3. quietly replace `lnf'=-exp(`theta1')+$ML_y1*(`theta1')   
  4. end

. 
. ml model lf mle_poisson1 (y=x) 

. ml maximize

initial:       log likelihood =        -15
alternative:   log likelihood =  15.269181
rescale:       log likelihood =  49.164159
Iteration 0:   log likelihood =  49.164159  
Iteration 1:   log likelihood =  55.254407  
Iteration 2:   log likelihood =  55.320936  
Iteration 3:   log likelihood =   55.32097  
Iteration 4:   log likelihood =   55.32097  

                                                  Number of obs   =         15
                                                  Wald chi2(1)    =       2.72
Log likelihood =   55.32097                       Prob > chi2     =     0.0993

------------------------------------------------------------------------------
           y |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           x |   .4248897   .2578109     1.65   0.099    -.0804104    .9301898
       _cons |   1.078078   .3886433     2.77   0.006     .3163506    1.839805
------------------------------------------------------------------------------

. 
end of do-file

*/