# Sensitivity analysis problem

Dear Dynare users,

I’m having a problem in interpreting global sensitivity analysis outputs and Smirnov tests results
I searched for Ratto’s paper (2008) treating the issue, but unfortunately I couldn’t have access to it.
How can I interpret these results ?
Is the p-value is interpreted as being inferior to the significance threshold, and therefore we reject null hypotesis, which is that those parameters’ cdf is similar to acceptable behavior parameters’ cdf ?
how about those driving indeterminacy and instability ?
Thank you

Smirnov statistics in driving acceptable behaviour
delta_2 d-stat = 0.522 p-value = 0.000
rho_inf d-stat = 0.416 p-value = 0.000

Smirnov statistics in driving indeterminacy
alppha d-stat = 0.171 p-value = 0.000
delta_2 d-stat = 0.307 p-value = 0.000
mu d-stat = 0.132 p-value = 0.000
rho_inf d-stat = 0.302 p-value = 0.000

Smirnov statistics in driving instability
alppha d-stat = 0.323 p-value = 0.000
delta_2 d-stat = 0.315 p-value = 0.000
mu d-stat = 0.264 p-value = 0.000
rho_R d-stat = 0.131 p-value = 0.000
rho_inf d-stat = 0.142 p-value = 0.000

Starting bivariate analysis:

Correlation analysis for prior_stable
[alppha,rho_R]: corrcoef = 0.111
[delta_2,rho_inf]: corrcoef = 0.205

Correlation analysis for prior_unacceptable
[alppha,rho_R]: corrcoef = -0.160
[delta_2,rho_inf]: corrcoef = -0.585
[rho_is,rho_rstar]: corrcoef = -0.127

Correlation analysis for prior_indeterm
[alppha,delta_2]: corrcoef = -0.231
[alppha,rho_inf]: corrcoef = 0.196
[delta_2,rho_R]: corrcoef = 0.142
[delta_2,rho_inf]: corrcoef = -0.573
[mu,rho_inf]: corrcoef = -0.161
[rho_R,rho_inf]: corrcoef = -0.347

Correlation analysis for prior_unstable
[alppha,delta_2]: corrcoef = 0.279
[alppha,mu]: corrcoef = -0.357
[alppha,rho_R]: corrcoef = -0.247
[alppha,rho_inf]: corrcoef = -0.406
[delta_2,mu]: corrcoef = -0.426
[delta_2,rho_R]: corrcoef = -0.257
[delta_2,rho_inf]: corrcoef = -0.614
[mu,rho_inf]: corrcoef = 0.422
[rho_R,rho_inf]: corrcoef = 0.507

Yes, the Smirnov test provides the significance level at which the null hypothesis that both parameter CDFs are equal can be rejected. The dstat is the supremum norm over the difference between the CDFs. That is, the higher the difference, the lower the p-value and the more strongly we can reject the null that the parameter under consideration does not drive the respective behavior (e.g. indeterminacy)

Thank you dear Professor for taking time to reply,

So I should interpret those results as the following :

• delta_2 and rho_inf DOES NOT drive acceptable behaviour

-alppha, delta_2, mu, and rho_inf DOES NOT drive indeterminacy

-alppha, delta_2, mu, rho_R, and rho_inf DOES NOT drive instability

and how about the bivariate analysis, how can I interpret those correlation coefficients ?

Thank you again Professor.

No, for delta_2 and rho_inf the null hypothesis that they are not responsible for driving acceptable behaviour can be rejected. Thus, the DO drive acceptable behaviour.

The correlations are simple bivariate correlations between the parameters that resulted in e.g. non-acceptable behaviour.

[quote]Correlation analysis for prior_unacceptable
[delta_2,rho_inf]: corrcoef = -0.585[/quote]

for example means that within the unacceptabel draws from the prior, delta_2 was high when rho_inf was low and vice versa.

I really can’t thank you enough Professor, I will learn more about the issue for the sake of scientific integrity.