# Why is sensitivity analysis for phi\_pi different across models

**URL:** <https://forum.dynare.org/t/why-is-sensitivity-analysis-for-phi-pi-different-across-models/24993>\
**Category:** Identification/Sensitivity\
**Created:** [19 January 2024 14:52 UTC](https://forum.dynare.org/t/why-is-sensitivity-analysis-for-phi-pi-different-across-models/24993 "2024-01-19T14:52:22Z")\
**Posts on this page:** 2\
**Page:** 1

<div class="post-metadata">

**Author:** ![kofiemma](https://forum.dynare.org/letter_avatar_proxy/v4/letter/k/439d5e/32.png) [@kofiemma](https://forum.dynare.org/u/kofiemma)\
**Post date:** [19 January 2024 14:52 UTC](https://forum.dynare.org/t/why-is-sensitivity-analysis-for-phi-pi-different-across-models/24993/1 "2024-01-19T14:52:23Z")

</div>

I expected sensitivity analysis for **phy\_pi** in the Taylor rule to be similar across models, but it seems that is not the case.

1. I added the following to **Gali\_2015\_chapter\_4.mod**

```auto
varobs pi y_gap y_nat y yhat r_nat r_real i n m_real m_growth_ann nu a r_real_ann i_ann r_nat_ann pi_ann z;
estimated_params;
phi_pi, 1.5, 0, 2;
phi_y, 0.125, 0, 2;
end;
dynare_sensitivity;

```

Which gave me **indeterminacy** and **unique Single Saddle-Path** graphs

![ch4](https://forum.dynare.org/uploads/default/original/3X/1/8/18fcc445cf3599761ba215dac00adb54cdf8910e.png)  
 ![ch42](https://forum.dynare.org/uploads/default/original/3X/9/f/9ff2b4dfb95cd850d2bb885c9525a2a612f32ad2.png)

1. Then I added the following to **Gali\_2015\_chapter\_6.mod**

```auto
varobs pi_p y_gap y_nat y yhat r_nat r_real i n m_real m_growth_ann m_nominal nu a r_real_ann i_ann r_nat_ann pi_p_ann z p w c w_real w_gap pi_w w_nat mu_p pi_w_ann;
estimated_params;
phi_pi, 1.5, 0, 2;
phi_y, 0.125, 0, 2;
end;
dynare_sensitivity;

```

Which gave me **explosive solution** and **unique Single Saddle-Path** graphs

![ch6](https://forum.dynare.org/uploads/default/original/3X/7/6/760a5c2b3ebc9268db95e18ff2de46e30600e2ba.png)  
 ![ch62](https://forum.dynare.org/uploads/default/original/3X/d/8/d8f4fcf9a1cbff70e454e442d2c7b2d6f11b9912.png)

**QUESTIONS**  
a. Why does **phy\_y** appear in **(2)** and not **(1)**?  
b. And why does **indeterminacy** in the little box below the graph change to **explosive solution**? I know indeterminacy means explosive solution, but just curious about the different names used.  
c. I am also confused about the interpretation in (2). In (1), the graph shows \*\*phy\_pi \*\* should be more than 1 (approximately) to ensure a unique solution, and the blue line is at the right of the red line. Why is it that in (2), the blue line is at the left of the red line instead? How to interpret it? It seems \*\*phy\_pi \*\* should be less than 1 (approximately) to ensure a unique solution, which can not be.

1. Lastly, I added the following to **Gali\_2015\_chapter\_8.mod**

```auto
varobs y_gap pi_h i y_nat r_nat s_nat y s_gap s pi n r_real w nx c yhat p_h p er d_er y_star a nu z r_real_ann i_ann r_nat_ann pi_ann pi_h_ann;
estimated_params;
phi_pi, 1.5, 0, 2;
phi_y, 0.125, 0, 2;
end;
dynare_sensitivity;

```

Which gave me no graphs but

```auto
 0.0% of the prior support gives unique saddle-path solution.
100.0% of the prior support gives explosive dynamics.
All parameter values in the specified ranges are not acceptable!
Sensitivity computations stopped: no parameter set provided a unique solution
Total computing time : 0h00m35s

```

**QUESTIONS**  
If 100.0% of the prior support (I guess from 0 to 2) gives explosive dynamics, why do I not have ‘ **The rank condition isn’t verified** ’ error when I set `phi_pi = 1.5` and `phi_y = 0.125` in the model?

Sorry for such a long post.

---

<div class="post-metadata">

**Author:** ![jpfeifer](https://forum.dynare.org/user_avatar/forum.dynare.org/jpfeifer/32/5044_2.png) [@jpfeifer](https://forum.dynare.org/u/jpfeifer)\
**Post date:** [22 January 2024 11:06 UTC](https://forum.dynare.org/t/why-is-sensitivity-analysis-for-phi-pi-different-across-models/24993/2 "2024-01-22T11:06:55Z")

</div>

1. 

> [@kofiemma](#):
>
> Why does **phy\_y** appear in **(2)** and not **(1)**?

Because for the simple model, only inflation feedback is relevant. However, once you add wage rigidity, that changes and output feedback becomes relevant as well.

2. 

> [@kofiemma](#):
>
> why does **indeterminacy** in the little box below the graph change to **explosive solution**

Those are two different concepts. **Instability/explosiveness** means that no bounded solution exists as variables explode. **Indeterminacy** means there are many solutions and nothing tells you which one you should pick. Those are two instances for which the Blanchard-Kahn conditions can be violated.

3. 

> [@kofiemma](#):
>
> It seems \*\*phy\_pi \*\* should be less than 1 (approximately) to ensure a unique solution, which can not be.

The model has a unit root and you did not set `diffuse_filter`. That screws up the graphs and also is the problem for `Gali_2015_chapter_8.mod`