Questions about Bayes factor and GSA

Identification/Sensitivity
1

Dear all,

I would like to raise a couple of questions about GSA and the Bayes factor. I use dynare 4.4.3

  1. When I run dynare_senssitivity I get the results of the Smirnov-Kolmogorov test. I would like to know where are stored the result of this statistics. Moreover, is it possible to print also the statistics value for the parameters that do not significately affect the model’s behavior? I used the command “ksstat=0.001” as option into dynare_sensitivity, but it does print only the parameter with smirnov stat>0.1. I tried also ksstat=0.5, but it also print parameters with smirnov stat >0.1 but lower than 0.5.

  2. Second question is about the log data density computed by dynare (after the estimation): I want to compare 2 models via Bayes factor. Let assume model1 has log data density=1300, whereas model2 has log data density=1307
    according to the jeffreys scale of evidence en.wikipedia.org/wiki/Bayes_factor#Interpretation may I conclude that there is “substantial evidence” favoring model1 (as the difference is 7)?
    Moreover, let assume there is further model, let’s say model3 with log data density=1322. As the difference is 22, does this difference involve “strong evidence” in favor of model3?

thanks in advance for the help.

2
  1. Could you please provide me with the file.
  2. Regarding the interpretation of differences, you are right. However, you need to be careful with the direction. In your example, you provide log data densities. Thus, the higher the better. You would favor model 2, because it has density 1307, which is bigger than the 1300 of model 1.
3

Dear Prof. Pfeifer,

thanks for your kind reply.

I attach you the .mod file.

With regard to the way to interpretate the log density I have a further question: for a given model I take the log data density gave me by dynare and simply compare it with that arising in the other model I want to compare, am I right? Moreover, according to the Jeffreys scale of evidence reported in this table en.wikipedia.org/wiki/Bayes_factor#Interpretation, when interpreting the difference among two models, in order to decide if the evidence favoring a model over the other is strong, very strong, decisive etc, have I to consider the K column or the dHart column?

thanks a lot!
nk_basic.mod (1.9 KB)

4
  1. You seem to be looking for
pvalue_ks=1

(see the manual)
2. The results are not saved, only printed into a table.
3. Dynare by default uses the natural logarithm. The scales you are referring to use a different base. You need to transform the numbers by Dynare into the associated ones provided in the tables.
You also might want to have a look at Kass and Raftery (1995): Bayes Factors

5

Thanks a lot for giving me the code to print all the values

best,
marco