?******************************************
? Problem Set 3: Multinomial Logit Model
? Tutorial in Microeconometrics
? Summer term 2008
? Katrin Sommerfeld
?******************************************

options crt;
freq N;
read (file='L:\Microeconometrics\job.raw') job age sex low med high exper ;

? 1. Descriptive Statistics:
msd(terse) @all;
?hist job;
?stop;

? Number of observations in every single job category 
select job=1;
set blue=@nob;			? Blue collar
select 1;

select job=2;
set self=@nob;			? Self-employed
select 1;

select job=3;
set white=@nob;			? White collar
select 1;

select job=4;
set civil=@nob;			? Civil service
select 1;

print blue self white civil;
?stop;

? 2. Multinomial Logit Model:
logit (suffix=(_blue,_self,_white,_civil)) job c age sex low high exper ;
?print @coef;
?stop;


? 3. Relative Risk Ratios = Odds Ratios
? Here: Reference group = "Baseline alternative": Blue collar


? considered alternative: white collar
genr rrhigh = exp(@coef(7) + @coef(8)*age + @coef(9)*sex + @coef(10)*low + @coef(11)*1 + @coef(12)*exper );
genr rrmed  = exp(@coef(7) + @coef(8)*age + @coef(9)*sex + @coef(10)*low + @coef(11)*0 + @coef(12)*exper );
genr rrr =rrhigh/rrmed;
msd(terse) rrr;
?stop;

? Same result, but quicker:
set rrrage = exp(@coef(8));
print rrrage;

set rrrsex = exp(@coef(9));
print rrrsex;

set rrrlow = exp(@coef(10));
print rrrlow;

set rrrhigh = exp(@coef(11));
print rrrhigh;

set rrrexper = exp(@coef(12));
print rrrexper;
?stop;



? 4. Marginal effects
? Here: for sex
? "e" refers to: e to the power of x'bj, i.e. alternative-specific for alternative j
genr eself = exp(@coef(1)  + @coef(2)*age  + @coef(3)*sex  + @coef(4)*low  + @coef(5)*high  + @coef(6)*exper )  ;
genr ewhite= exp(@coef(7)  + @coef(8)*age  + @coef(9)*sex  + @coef(10)*low + @coef(11)*high + @coef(12)*exper )  ;
genr ecivil= exp(@coef(13) + @coef(14)*age + @coef(15)*sex + @coef(16)*low + @coef(17)*high + @coef(18)*exper )  ;

? "sum" refers to the sum over all alternatives; 1 for reference category
genr esum  = 1 + eself + ewhite + ecivil ;

? "p" refers to the probability of choosing alternative j, i.e. the  ratio of the two above
genr pself  = eself/esum;
genr pwhite = ewhite/esum;
genr pcivil = ecivil/esum;

? this sum refers to the sum of the products of alternative-specific probability with beta(j)
genr sumsex = pself*@coef(3) + pwhite*@coef(9) + pcivil*@coef(15) ;

? "ME" refers to the marginal effect
genr MEself  = pself*(@coef(3)  -sumsex);
genr MEwhite = pwhite*(@coef(9) -sumsex);
genr MEcivil = pcivil*(@coef(15)-sumsex);

? Now for the reference category:
genr pblue = (1-pself-pwhite-pcivil);
genr MEblue= pblue*(0-sumsex);

msd(terse) MEself MEwhite MEcivil MEblue;


end;