Thank you Jack and Allin,

Jack's right asking "Why should it be anything else?" but I do not have the answer actually. I read in the litterature that  the 0.5 probability threshold looks somewhat arbitrary and I was guessing may be gretl is performing based any other criteria, such as the ROC Curve, in order to maximize the % of correctly predicted cases. Stata has some in-build commands for this purpose and the ROC curves are generally used to compare the performance of different binary dependent variable models.  
As an illustration I expanded Jack's script and found that maximizing the % of correctly predicted occurs at a threshold of 0.56. 
Best,
Artur

<hansl>
open mroz87 --quiet
logit LFP const WA WE KL6

# actual values
genr actual_0 = sum(LFP=0)
genr actual_1 = sum(LFP=1)

# compute: sensitivity, specificity, 1-specificity, % of correctly predicted, threshold

matrix result=zeros(98,5)
cnames = " sensitivity specificity 1-specificity correctly_predicted threshold"
colnames(result, cnames)
  
scalar count = 1

loop for (threshold=0.01; threshold<=.99; threshold+=.01) --quiet
    series predict = $yhat>threshold
    correct_0 = sum(predict=0 && LFP=0)
    correct_1 = sum(predict=1 && LFP=1)
    result[count,1]= correct_1/actual_1 # true positive; sensitivity
    result[count,2]= correct_0/actual_0 # true negative; specificity
    result[count,3]= 1-result[count,2]   # 1 - specificity
    result[count,4]= (correct_0 + correct_1)/$nobs # % of correctly predicted  
    result[count,5]= threshold
    count+=1 
endloop

gnuplot 1 3 --matrix=result --with-lines --suppress-fitted --output=display {set title 'ROC Curve'; set xrange [-0.01:1.01]; set yrange [-0.01:1.01]; set grid; show grid}
gnuplot 4 5 --matrix=result --with-lines --suppress-fitted --output=display {set title 'Correctly predicted %'; set grid; show grid}
</hansl>

2014-09-19 19:30 GMT+02:00 Riccardo (Jack) Lucchetti <r.lucchetti@univpm.it>:
On Fri, 19 Sep 2014, Artur Bala wrote:

Dear all,
Does anyone know how the threshold value for the predicted probalities in a
logit/probit estimation is being calculated in gretl?

I assume that by "threshold" you mean "the value of P(x'b) at which we shwitch from predicting a 0 to predicting a 1". I haven't looked at the source code, but I'm pretty sure it's 0.5. Why should it be anything else?

Try this:
<hansl>
open mroz87 --quiet
logit LFP const WA WE KL6
series pred = $yhat>0.5
xtab LFP pred
</hansl>

-------------------------------------------------------
  Riccardo (Jack) Lucchetti
  Dipartimento di Scienze Economiche e Sociali (DiSES)

  Università Politecnica delle Marche
  (formerly known as Università di Ancona)

  r.lucchetti@univpm.it
  http://www2.econ.univpm.it/servizi/hpp/lucchetti
-------------------------------------------------------
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