Dear forum guests!

I need to introduce a range constraint for the sum on parameters in MLE model. This is necessary for economics reasons. At the moment, I have two ways to do that, inside of do-file. One is to add constraint directly to the sum of parameters, second one is to add constraint to every parameter separately. In last case, the sum is automatically constrained. I give you some example.

Suppose the parameters are b1, b2 and b3. Now, let's suppose that the sum is positive and less or equal to 1.5. Also, the sum is marked with the variable "scale". So, scale = 1.5*invlogit(b1+b2+b3), which means that 0≤scale≤1.5. In this case, no additional parameters.

The second option means I have to add some additional parameters, something like b01=invlogit(b1), b02=0.2*invlogit(b2) and b03=0.3*invlogit(b3). So, in that case scale=b01+b02+b03.
The choice of these multipliers is based on alternative estimates of parameters with another model. There is also some space left there.

Now becomes the tricky part. These two ways act very differently. The first option gives very realistic (economically) results. The sum of parameters is around 1.1. The second option gives not very realistic results, these parameters are not statistically significant, also likelihood has difficulties in converging.

But, I have been told, that this second option is correct and the first one is not? The reason, why this first option is not correct, is exactly because of the lack of these constraints directly for parameters. So, these constraints must be present in likelihood expression also, It is not enough that only the sum has constraints. In this case this is already some other model.
Is it really so?
Why should I use three constraints, when only one seems already enough? I would prefer to let the parameters vary freely and only restrict the range of their sum. Moreover, there is possibility to use "constraint" command separately, before the command "ml model". Only problem is that inequality constraint is not possible. But, in this case this is also only for the sum and is perfectly correct.
I am very grateful if anyone can explain and advise on this topic.