Comparing mprobit and probit specifications

[Arnaud Millien]

Dear Statalisters,

I'm estimating a mprobit model and want to make sure that I'm doing it properly, by comparing this model to the initial probit specification from which I started my meta-analysis.

Here is the probit specification :
probit Iconcl ib2.E13g
where :
a/ Iconcl is a dummy such as :

.
  Effect is |
     proven |
   (null if |
  not sig.) |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |      1,429       82.36       82.36
          1 |        306       17.64      100.00
------------+-----------------------------------
      Total |      1,735      100.00

where the dataset is compounded by studies on decentralized electricity. Effect is proven if authors have found a significant estimate in their study.

b/
E13g describes the evaluation method used by authors to deliver a result and it's categorical, as follow :

      E13g - Groups of Methods |      Freq.     Percent        Cum.
-------------------------------+-----------------------------------
                Identification |        722       41.61       41.61
Econometrics without inference |         70        4.03       45.65
                  No inference |        943       54.35      100.00
-------------------------------+-----------------------------------
                         Total |      1,735      100.00

Running probit Iconcl ib2.E13g yields the following warning :

note: 3.E13g != 0 predicts failure perfectly
3.E13g dropped and 943 obs not used

because simple methods (without inference : E13g = 3) implies unproven effect (Iconcl = 0 ; see following table).

 Effect is |
    proven |
  (null if |     E13g - Groups of Methods
 not sig.) | Identific  Econometr  No infere |     Total
-----------+---------------------------------+----------
         0 |       446         40        943 |     1,429
         1 |       276         30          0 |       306
-----------+---------------------------------+----------
     Total |       722         70        943 |     1,735

Now, I'm writing the following mprobit (options are used to help Stata going out of an initially not concave sub-space) :

mat b =(0)
mprobit Ifav ib2.E13g, from(b, skip) difficult tol(0.1) nrtol(0.1) ltol(0.1) iter(50)

where Ifav is such as :

      Economic direction of |
                     effect |      Freq.     Percent        Cum.
----------------------------+-----------------------------------
  Proven effect - favorable |        225       12.97       12.97
Proven effect - unfavorable |         81        4.67       17.64
          not proven effect |      1,429       82.36      100.00
----------------------------+-----------------------------------
                      Total |      1,735      100.00

Ifav and E13g do cross as follow :

             
Economic direction of |     E13g - Groups of Methods
               effect | Identific  Econometr  No infere |     Total
----------------------+---------------------------------+----------
Proven effect - favor |       207         18          0 |       225
Proven effect - unfav |        69         12          0 |        81
    not proven effect |       446         40        943 |     1,429
----------------------+---------------------------------+----------
                Total |       722         70        943 |     1,735

In this model Sata, uses all observations, including the 943 that were previously excluded with probit. I want to make sure to understand why those 943 observations are not excluded in mprobit and that there is no error in Stata coding of mprobit.

My intuition is the following.
In the probit, P(Iconcl=0) = 1 <=> P(Iconcl=1) = 0
But in mprobit, there is no strict equivalence :
P(Ifav=3) = P(Ifav = 1) + P(Ifav = 2).
Hence P(Ifav=3) = 1 = > P(Ifav=2) + P(Ifav=1) = 0 but P(Ifav=3) = 1 is not a necessary condition to have P(Ifav=1) = 0 or P(Ifav=2) = 0 alone.
And the reciprocity is not true, neither : P(Ifav = 2) = 0 does not imply alone that P(Ifav=3) = 1

Is my intuition sufficient to sustain a demonstration and does it sustain the explanation about the way probit is running in Stata ?

Many thanks for the time dedicated to read and answer to my question.
Best,
Arnaud.