Non-Gaussian SVAR: Reduced Form

Reduced Form

This page explores the relationship between reduced-form shocks and structural shocks in our Non-Gaussian SVAR model.

The Relationship Between Reduced and Structural Form Shocks

In our simplified SVAR model, the reduced-form shocks $u_t$ can be viewed as a rotation of the structural shocks $\epsilon_t$ by angle $\phi_0$:

$ \begin{bmatrix} u_{1,t} \\ u_{2,t} \end{bmatrix} = B_0(\phi_0) \begin{bmatrix} \epsilon_{1,t} \\ \epsilon_{2,t} \end{bmatrix} $

Interactive Simulation

In the simulation below, the structural shocks are independently drawn from a uniform distribution. Move the $\phi_0$ slider above to see how $B(\phi_0)$ leads to different rotations $u_t$ of $\epsilon_t$. Click the New Data button to draw a new set of structural shocks $\epsilon_t$.

Implications for Identification

Understanding this relationship is crucial for our identification strategy:

  1. We observe $u_t$ but not $\epsilon_t$ or $\phi_0$.
  2. Our goal is to estimate $\phi_0$ and recover $\epsilon_t$ from $u_t$.
  3. The non-Gaussian properties of $\epsilon_t$ will be key to our identification strategy.

Next Steps

In the next section, we'll delve deeper into the identification problem and why traditional methods fall short for non-Gaussian shocks. Proceed to The Identification Problem to continue.