Moment Selection Criteria & Relevance Moment Selection Criteria

Suppose that you want to estimate the parameters of a model and you have more than one set of moment conditions available.
For example, consider the case that you have n, normally distributed observation and you want to estimate the mean.
In addition, let's suppose that you want to use two moment conditions, so that you can have an overidentified model. Recall that a normally distributed variable is symmetric, meaning that mean = median, and curtosis = skewness = 0. Which of the following sets of moments will perform the best?

Set 1: Sample mean, and variance
Set 2: Sample median, and variance
Set 3: Sample mean, and skewness
Set 4: Sample median, and skewness
Set 5: Sample mean, and kurtosis
Set 6: Sample median, and kurtosis

In this case, you can estimate the mean using each possible set of moment conditions and then calculate a moment selection criterion to select the set that performs the best. The program currently supports two type of selection criteria (select the one you want help on): MSC and the RMSC.
Due to the similarity of the two procedures, they are explained simultaneously below.

MSC - RMSC

To use the MSC, click on the Testing drop down menu and select the MSC entry; to use the RMSC, select the RMSC entry.
What you should see in each case will be siimilar to the following

Moment Selection Criterion
Relevance Moment Selection Criterion

The listbox that appears on the top of both windows will not, in general, be empty (actually, it must be non-empty in order to perform the tests).
This listbox will automatically read and list the name of all variables that exist in your workspace.
For example, suppose that you used the GMM-GUI to perform the estimation that we talked about in the example above, and you saved the output using the names set1, set2,..., set6. In this case, opening the MSC or RMSC windows will result to:

Moment Selection Criterion
Relevance Moment Selection Criterion

As you can see, the listbox displays the name of the variables that you have saved in your workspace. With this example in mind, let's continue defining the way these windows work.

Fields' explanation

Select the output structure of the models you want to compare

From the listbox, you have to select the variables that hold the models you want to compare. Two things are of great importance here:
First, the variables you select must be the output of the GMM-GUI estimation procedure; selecting any other variable will result to an error.
Second, you can select any variable by clicking its name; if you want to select multiple entries, hold down the Ctrl key while you click the variables you want.
Bonus term [Only on MSC window]

Select the type of bonus term you want to use (BIC, or Hannan & Quinn).
Constant b (Hannan & Quinn) [Only on MSC window]

This field is initially grayed out, i.e. not accessible. If the type of bonus term is the Hannan & Quinn, this field will become active.
You must input a positive integer that is greater than 2.
Save output as

The output will be saved under the name you enter in this field.
The output will be a Kx1 vector, where K is the number of models that you are selecting. The ith entry will be the value of the selection criterion for your ith model. For example, if you are comparing models set1, set2, and set6, the output will be a 3x1 vector, where the first entry is the value of the selection criterion for model "set1", the second is the value for model "set2", etc.

IMPORTANT: The order that the variables appear in the listbox is the same with the order that they appear in the output. For example, if the order of the listbox variables is
set3
set1
set2
set5
...
and you compare models set2 and set3, the first row of the output will be the value of the selection criterion for set3, and the second for set2.