⬅️ Back to list of blog posts

In this post, I explore the variations in Structural VARs (SVARs) and their recent applications. This is mostly an amalgam of notes based on my readings of multiple lecture notes, papers, and documentations.

Motivation: Endogeneity Problem in Macroeconomics

Discussion of issues and challenges in identification is as important as in empirical macroeconomics as it is applied microeconomics. Here are two motivating examples:

1. Effect of Monetary Policy

   1. The central bank anticipates a rise in inflation.
   2. The central bank increases the monetary policy rate, but inflation rises as expected.

   Conclusion: interest rate hike $\Rightarrow$ rise in inflation

2. Effect of Fiscal Spending

   1. The government anticipates a decrease in private demand.
   2. The government increases public spending, but the output decreases nonetheless.

   Conclusion: public spending $\Rightarrow$ decline in output

In both examples, the primary issue is that policy choices (rates, fiscal spending) are endogenous to expectations of economic variables (inflation, output). To circumvent this issue, we want to identify purely exogenous shocks.

A Mathematical Formulation

The goal of an SVAR is to go from a reduced form VAR:

$$ X_t = F X_{t-1}+e_t $$

in which $e_t$ are not structural shocks, to a structural VAR:

$$ AX_t = G X_{t-1} + u_t $$

where $F = A^{-1}G, e_t = A^{-1}u_t$. So as long as we obtain $A$, we should be done.

How many restrictions are necessary?